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Q. 7.CA1

Work and orbital motion

A communications satellite moves in a circular orbit at constant speed in response to gravity, as shown in Figure 7.11. Which of the following statements is correct?

A. The earth does positive work on the satellite.
B. The earth does negative work on the satellite.
C. The earth does no work on the satellite.
D. Once a coordinate system is specified, the work changes sign every half orbit, so that the average work is zero.

Verified Solution

In circular gravitational orbits, the force on the orbiting object is always perpendicular to the object’s velocity, as indicated in the figure. The displacement of the object is always along the direction of the velocity, so the force is always perpendicular to the displacement. Therefore, $F_{\parallel} = 0$, and the work is zero for any displacement along the orbit. This result still might seem confusing, since your intuition may correctly guess that orbiting objects have energy. But remember that work is the transfer of energy that changes an object’s speed. Since the speed of an object is constant in uniform circular motion, W = 0, and all answers other than choice C can be rejected. As we’ll see later, energy is required to set an object in orbital motion, and the orbital system holds onto this energy, but no additional energy needs to be supplied to maintain the object in its orbit. Our solar system has been executing orbital motion for about 5 billion years and does not require an energy source to maintain its orbits.