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I've been told that acceleration orthogonal to an objects movement direction doesn't require energy. Thus when a satellite goes around the earth, the change in direction caused by gravity doesn't use any energy.

But, say we remove the earth and we still want the satellite to go in its usual circular pattern, then we need to mount a vector thruster (rocket) on the satellite and keep it thrusting continuously to maintain the circular pattern. This rocket thrust will require energy, even if it thrusts perfectly orthogonal to the direction of movement of the satellite.

Thus we have two scenarios with the exact same movement pattern, but in one scenario it takes no energy to uphold the pattern, and in the second scenario it takes continuous energy consumption to uphold the pattern.

How come gravity is said to use no energy in its maintenance of the circular movement pattern?

EDIT: Both scenarios has to uphold Newtons first law (conservation of inertia). The earth scenario does it by moving the earth ever so slightly in opposite way to the satellite. The rocket scenario does it by shooting gas into space at high velocity. However, in both cases something happens in order to conserve inertia (in opposition to nothing). Thus, arguing that the rocket spends energy to conserve the inertia of the turning satellite does nothing to answer why the earth doesn't have to spend energy as well, to conserve inertia of the turning satellite. Even arguing that the rocket is inefficient (waste heat) wouldn't answer that question.

EDIT 2: The rope scenario seems to be isomorphic to the earth scenario: the only difference is that the weak gravitational force has been replaced with the stronger nuclear forces that holds the rope together.

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    $\begingroup$ Pay attention to the fact, that if you use the rocket instead of the earth you will feel the acceleration. That is why Einstein say that gravity is not a force. $\endgroup$ – HolgerFiedler Aug 7 '15 at 11:34
  • $\begingroup$ Well, that would be because gravity applies it's acceleration evenly to every atom in my body. The rocket will apply it to my seat in my space capsule and I then feel the pull through my connection with the seat (seatbelts and such). But they are both still just acceleration. There's no qualitative difference. $\endgroup$ – loldrup Aug 7 '15 at 11:54
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Because in the second scenario you described, the exhaust gases from the rocket fly off at high speed into space. This is where the extra energy goes.

A better alternative to get circular motion of the satellite with the earth removed, would be a second satellite, connected to the first satellite with a long cable. If, for example, both satelittes have the same mass, you can rotate them around the center of the cable. Once everything is set up, it needs no extra energy.

If you ride on the satellite, you will definitely notice that the earth was replaced with another satellite and a cable: You felt weightless before, but now you are pushed against the outside wall of the satellite.

The difference between using a second satellite and using a rocket is not noticeable inside the satellite (assuming the rocket is ultra-silent). On the outside, however, you have the hot rocket exhausts flying off at high velocity into outer space. The rocket has to continuously accelerate rocket fuel outwards to keep the satellite on a circular orbit. While the energy of the satellite does not change, the kinetic energy of the rocket fuel does. The kinetic energy of the rocket actually goes down as the rocket mass is getting smaller and smaller.

To push something around on a circular path you need little to no energy, but no law of physics prevents you from wasting as much energy as you want.

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  • $\begingroup$ Please see my edit of the original question :) $\endgroup$ – loldrup Aug 7 '15 at 11:29

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