Kepler’s Second Law



Kepler’s Second Law

Part 1: Equal Areas in Equal Time Intervals/Speed of Planets

Kepler’s second law of planetary motion states that a line joining a planet and the Sun sweeps out equal amounts of area in equal intervals of time.

Imagine the situation shown to the right in which a planet is moving in a perfectly circular orbit around its companion star. Note that the time between each position is exactly one month.

1. Does this planet obey Kepler’s second law? How do you know?

2. If you were carefully watching this planet during the entire orbit, would the speed of the planet be increasing, decreasing, or staying the same? How do you know?

The drawing below shows another planet’s orbit. In this case, the twelve positions shown (A-L) are each exactly one month apart. As before, the planet shown obeys Kepler’s second law.

3. Does the area that the planet “sweeps” from Point A to B appear to be larger, smaller or equal to the area that the planet “sweeps” between points H and I?

4. How long does it take the planet to move from point H and I?

5. Does the planet appear to be traveling the same distance each month?

6. At which position would the planet be traveling the fastest? The slowest? Explain you reasoning.

7. Complete the sentence by circling your answers: The CLOSER a planet is to the star it orbits, the _____ (Faster Slower) the planet must be traveling. For example, the planet is moving _____ ( Quickly Slowly ) at position A.

8. Complete the sentence by circling your answers: The FARTHER a planet is to the star it orbits, the _____ (Faster Slower) the planet must be traveling. For example, the planet is moving _____ ( Quickly Slowly ) at position G.

Part 2: Kepler’s Second Law and Eccentricity

Consider the table below listing the orbit eccentricities for objects in the solar system. Recall that an orbit with an eccentricity of zero is perfectly circular whereas the highly elliptical orbit shown in Part 1 would have a high eccentricity of approximately 0.90.

|Object |Eccentricity of Orbit |

|Mercury |0.206 |

|Venus |0.007 |

|Earth |0.016 |

|Mars |0.093 |

|Jupiter |0.048 |

|Saturn |0.054 |

|Uranus |0.047 |

|Neptune |0.008 |

|Pluto |0.248 |

9. Which of the three orbits shown below (A, B, or C) would you say most closely matches the shape of the Earth’s orbit around the Sun? Explain your reasoning.

10. Which of the objects listed in the table would experience the largest change in orbital speed and which would experience the smallest change in orbital speed?

11. Describe the extent to which you think Earth’s orbital speed changes throughout the year? Explain your reasoning.

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