# Why the Earth does no work on the satellites that revolve around it? [closed]

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?

## closed as unclear what you're asking by John Rennie, ACuriousMind♦, garyp, heather, Emilio PisantyAug 2 '16 at 17:54

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• From the satellite's point of view gravity does perform work on satellites that are not in circular orbits. While the satellite is getting closer, it speeds up, when it moves further away, it slows down. There is a constant transfer of energy between kinetic and potential energy, even though the sum of the two is the same, i.e. in the closed system view the total energy is constant, just as it should be. – CuriousOne Aug 2 '16 at 5:23
• Work or energy may be a concept we have discovered but we believe that what we are describing really represents the way the world works. If that wasn't the case then there would really be no point to doing physics. – tfb Aug 2 '16 at 5:24
• I don't understand what you are asking. Work isn't a human defined concept it is a human discovered concept. It would still exist if humans had never evolved. – John Rennie Aug 2 '16 at 9:09
• Be aware that the physics means of work ("a transfer of energy by mechanical means" or similar) differs slightly from the casual usage of the term even we the casual usage involves apply a force. See Why does holding something up cost energy while no work is being done?. – dmckee Aug 2 '16 at 17:14

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.

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.

• your answer is my question :p – Aaryan Dewan Aug 2 '16 at 5:05
• What do you mean? – Dawood ibn Kareem Aug 2 '16 at 5:06
• i mean, it would be helpful if you could improve your answer! – Aaryan Dewan Aug 2 '16 at 5:07
• In what way? Which part don't you understand? In what way do you feel I haven't answered your original question? – Dawood ibn Kareem Aug 2 '16 at 5:07
• Please read my question again. The answer that you have given, is already mentioned in my question! I am looking for a deeper meaning. – Aaryan Dewan Aug 2 '16 at 5:35

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.