Chapter 4: Problem 16

At what point in a planet's elliptical orbit does it move fastest? At what point does it move slowest? At what point does it sweep out an area at the fastest rate?

Short Answer

Expert verified

The planet moves fastest at the point of perihelion (closest to the star) and slowest at the point of aphelion (farthest from the star). There is no specific point where the planet sweeps out the maximum area as per Kepler's second law as the area swept is always constant for a given time interval.

Step by step solution

Understanding Kepler's second law- the 'Area law'

Kepler's second law states that a line joining a planet and its star sweeps out equal areas during equal intervals of time. This implies that a planet moves faster when it is closer to its star and slower when it is farther away.

Identifying the speediest point in the orbit

According to Kepler's second law, the planet moves fastest when it is closest to its star, a point known as perihelion.

Identifying the slowest point in the orbit

Similarly, the planet moves slowest when it is farthest from its star, a point known as aphelion.

Identifying when the planet sweeps out the maximum area

Since the 'Area Law' states that the planet sweeps out equal areas in equal time intervals, this suggests that the area being swept does not change throughout the orbit. Therefore, there is no specific point where the planet sweeps out the maximum area. The area being swept is always constant for a given time interval.

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At what point in a planet's elliptical orbit does it move fastest? At what point does it move slowest? At what point does it sweep out an area at the fastest rate?

Short Answer

Step by step solution

Understanding Kepler's second law- the 'Area law'

Identifying the speediest point in the orbit

Identifying the slowest point in the orbit

Identifying when the planet sweeps out the maximum area

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