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I read that the satellites donnot have to use their fuel to remain in orbit as they need no do any work against gravity, which is doing 0 work on the satellite. Well, according to he equation $W=F.d $, we get an answer i.e if the angle is 90, $W=0$.

This does not make sense to me. It is a human defined concept and nature does not work according to whatever we say. WHAT does really happen, so that the satellites won’t use their fuel to circle around the earth?

Qmechanic
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Aaryan Dewan
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3 Answers3

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Work expression which you have mentioned has been verified in experiments, so it is true of nature. One way to think why satellite does not burn fuel is that it is in free fall, but it has a tangential velocity such that instead of falling vertically downward (which would be a disaster) it circles the earth.

Deep
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If there were no gravity, each satellite would carry on in a straight line, and eventually get further and further from the earth. But the earth's gravity pulls them in.

However, if the satellite is travelling at just the right speed, the earth's gravity can pull the satellite around in such a way that the speed remains the same, but the direction changes; and the satellite will then have a circular path.

Because the speed of the satellite doesn't change, its kinetic energy doesn't change ($E=\frac{1}{2}mv^2$); so no work has been done on it. If work had been done on it, its kinetic energy would have increased.

Dawood ibn Kareem
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When driving a car, you can push the gas pedal to speed up, but you burn gas. Work is done. But if you steer the wheel, the car changes directions without speeding up or slowing down (maybe there is some drag, but that's not the point). Since the car's speed doesn't change, no work is done. The Earth's gravity pulls sideways compared to the direction the satellites move, so the satellites are just turning in circles like a car steering, not speeding up or slowing down.

Consider a circular orbit for simplicity. If the satellites stay at the same height, their potential energy doesn't change. If the satellites stay at the same speed, their kinetic energy doesn't change. If no energy changes, clearly no work has been done.

EL_DON
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