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Chapter 8: Problem 10

Does the gravitational force of the Sun do work on a planet in a circular orbit? In an elliptical orbit? Explain.

Short Answer

Expert verified
The gravitational force of the Sun does not do work on a planet in a circular orbit as the force of gravity is directed towards the center of the path causing only a directional change. In contrast, it does perform work in an elliptical orbit where the planet鈥檚 speed varies, showing an exchange of kinetic and potential energy.

Step by step solution

01

Consider a circular orbit

In a circular orbit, the gravitational force directed toward the Sun causes the direction of the planet's velocity to deviate toward the Sun, but it doesn't change the planet's speed. The force and displacement vectors are perpendicular (i.e., the angle is 90掳), therefore the work done will be W = Fd cos 90 = 0. Here the force of gravity doesn't do any work as it's not changing the kinetic energy of the planet.
02

Consider an elliptical orbit

In an elliptical orbit, the gravitational force has a component in the direction (or opposite to the direction) of motion. Thus, it does perform work in speeding up or slowing down the planet. When the planet is moving away from the Sun, the gravitational force does negative work by slowing it down, and when it is moving towards the Sun, the opposite happens. Hence, in an elliptical orbit, the gravitational force does do work.

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