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Work is done whenever the given two conditions are satisfied:
(i) A force acts on the body.
(ii) There is a displacement of the body by the application of force in or opposite to the direction of force.
If the direction of force is perpendicular to displacement, then the work done is zero.
If the satellite is in a perfectly circular orbit, then the force of gravity is always
perpendicular to the satellite's velocity, and gravity never does any work.
If the orbit isn't circular, then there is a radial component of velocity at most points in
the orbit, and some gravitational acceleration, work, etc., but those are exactly matched
by negative values at other points in the orbit, and the total over a complete orbit
is zero again.
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CoachDuring the time that the rocket motors or attitude thrusters are firing, an astronaut in space is acted on by the force of the acceleration of his spacecraft against his body. At all times, the astronaut is acted upon by a gravitational force in the direction of every piece of mass in the universe. The nearer, more massive bodies cause greater forces of attraction, while the farther, less massive bodies cause lesser forces. Even when he is not in space, the astronaut, as well as you and I, experience those same forces at all times. You and I may also be acted upon by the force of the atmosphere, such as when the wind blows, but the astronaut in space isn't.
Anything in motion continues moving in a straight line at a constant speed,
unless an external force acts on it. That's what would happen to satellites if
there were no force to bend their straight-line path into a curve around the
Earth. The force is the gravitational attraction between the Earth and the
satellite, and it's a 'centripetal' one because it always attracts the satellite
toward the 'center' of the Earth.
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