Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
v
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Kepler’s Laws Lab 3
Name
Materials
Computer with Internet Access
In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his three laws of planetary motion. These laws were empirically determined without any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.
Kepler’s First Law – The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse.
Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle.
Kepler’s Second Law – An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time.
While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize. The main significance of this law is that planets will orbit faster when they are closer to the Sun and slower when farther away. Planetary orbit speeds are not constant, but instead change with time.
Kepler’s Third Law – The square of a planet’s orbital period is proportional to the cube of its semi-major axis.
Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.
Where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant, G. Rather, k depends on the particular body that is being orbited (e.g., the Sun).
We will do an experiment using software which can be found at the PhET simulations page:
https://archive.cnx.org/specials/ee816dff-0b5f-4e6f-8250-f9fb9e39d716/my-solar-system/#sim-mysolar-system
Click on the simulation to run it (you do not need to download it). You should then see this:
!
the simulation as before. Record the distance and orbital period in the table on the next page. Move the planet outward, in increments of 10, and observe (and record) the orbit period.
Note: For the orbit period, you can use the “Time” value in the bottom right of the simulation. You can start the simulation and then stop it when the planet is near the same starting position. The amount of time elapsed in the “Time” value is the period of the orbit. (These values are not realworld times but are instead calculated by the simulation. Don’t use a stopwatch! Use the simulation’s time!)
Continue to move the purple planet outwards in increments of 10. Do not move the planet past 200. (As the distance increases, you may want to move the slider so that it is midway between the center and “fast”.)
| Distance | Orbital Period |
| 80 | |
| 90 | |
| 100 | |
| 110 | |
| 120 | |
| 130 | |
| 140 | |
| 150 | |
| 160 | |
| 170 | |
| 180 |
Make a graph of distance (from the star) vs. period of orbit using the data you record in the table. (Use the graph paper on the last page or create a graph using Excel. Label the axes and use a scale that makes sense. Draw a smooth curve through your data points.)
A few notes on making a graph:
The y-axis on the graph is the vertical axis (up and down)
The x-axis on the graph is the horizontal axis (side to side) Graphs are always titled as “Something vs. Something else”.
The “something” is plotted along the y-axis.
The “something else” is plotted along the x-axis.
First comes y, and then comes x. Think of it that way.
Dole, in 1964, estimated that the average amount of energy received by a planet could not vary by more than 10% without affecting its habitability. This means the planet would need to receive a consistent amount of energy from the star(s) it orbits. It could not swing in close to a star and then far away from both of them. This would heat the planet too much and then it would freeze. The planet needs consistency in the light it receives in order to sustain life.
Note that light follows an inverse square law just as gravity does. The amount of light received from a star falls off as 1 / distance2. If you get a little closer (or further) from your stars, the amount of light will increase (or decrease) dramatically.
try again. There are a couple of options to potentially make your planet habitable. It is your goal to try and find one of these situations.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
Once you believe you have found a simulation that could support life on your planet, take a screenshot and include it below. Carefully describe the new initial conditions you created. Describe your observations and conclusions that support or refute the ability of your planet to support life. Keep in mind, this is not just about the planet not crashing into the stars or getting flung into outer space. It’s about maintaining a consistent level of light and heat from the stars.
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