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This is a bit a bit of a weird question. Simply put, if a body orbits something such as a black hole there is no internal issue (that I know of) that would cause it to eventually stop (by internal I mean that an external force can't be applied as an example). I'm assuming the reason this 'perpetual motion machine' fails is one of the following:

  • The laws of thermodynamics do factor in external issues (because those laws are what prevents perpetual motion)

  • This would only work if every object could maintain their gravity (proton decay, hawking radiation etc would pretty much decay the system) and the laws of physics say that they cannot.

To reiterate because see this a lot: I'm not asking if this is a perpetual motion machine, I'm asking why it isn't.

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    $\begingroup$ I do not think an orbit would be considered a perpetual motion machine because it neither creates energy nor spontaneously converts thermal energy into mechanical work. in any case, orbits may appear perpetual, but are actually subject to many processes that slowly dissipate their kinetic energy, such as solar wind, interstellar medium resistance, gravitational radiation and thermal radiation, so they will not keep moving forever. $\endgroup$ – Wolphram jonny Oct 13 '20 at 16:58
  • $\begingroup$ @Wolphramjonny Tbh this seems to be in line with the second bullet point. If you phrase it a bit more explicitly this could constitute an answer. I will edit the question to be a bit more clearer $\endgroup$ – yolo Oct 13 '20 at 17:04
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    $\begingroup$ Yes, I didnt make my point clear. I think that most people do not consider machines of the 3rd kind a perpetual motion machine $\endgroup$ – Wolphram jonny Oct 13 '20 at 17:13
  • $\begingroup$ @Wolphramjonny. Just wondering, why not if they are as impossible as other perpetual motion machines? $\endgroup$ – yolo Oct 13 '20 at 17:16
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    $\begingroup$ because they do not provide an unlimited amount of work $\endgroup$ – Wolphram jonny Oct 13 '20 at 17:25
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If a body orbits something else, then there is gravitational waves (GW) emission and the orbit shrinks (eventually the two bodies will merge).

Neglecting GW emission (assuming Newtonian dynamics is the correct description), the motion goes on forever, but this is not problematic since any kind of friction is neglected. So the system is no more or less problematic than an oscillating mass on a spring, as long as there is no friction and the spring does not heat up.

Hence, such a system is a "perpetual motion machine of the third kind", defined as one that completely eliminates friction and other dissipative forces, to maintain motion forever due to its mass inertia. Clearly, it is impossible to build such a machine (in your two-body example, it is only possible on paper because you are neglecting GW emission or friction with the low-density space medium).

Most importantly, a machine is useful if you can extract work from it. Extracting work from an orbit it's possible, but again.. the orbit will "shrink" (for example, extracting work from an orbit is used to accelerate spacecrafts: to increase speed, the spacecraft flies with the movement of the planet, acquiring some of the planet's orbital energy in the process).

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    $\begingroup$ Slightly off-topic but pretty relevant. Do the laws of thermodynamics play an active part in refuting perpetual motion or do they merely just guarantee that some other law of nature will. In this example, would GW emissions occur due to the LoTD or are they their own thing? $\endgroup$ – yolo Oct 13 '20 at 17:12
  • $\begingroup$ Thermodynamics tells you that it is more probable for energy to be transferred from large scales to smaller ones than vice versa. Macroscopically you loose some energy, because there is a "sink" for the energy: the microscopic degrees of freedom. GW emission will occur independently on thermodynamics (but then, the "energy cascade" may continue and the GW wave may "die" as well.. but we do not know how because we do not have a microscopic theory of gravity). Thermodynamics tells you which is the "direction of the cascade", the physics of the system tells you "how the cascade takes place". $\endgroup$ – Quillo Oct 13 '20 at 17:22
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    $\begingroup$ what about spinning bodies? $\endgroup$ – yolo Oct 13 '20 at 18:18
  • $\begingroup$ That's a more subtle question which deserves a new post I think. Can a hot ball that rotating in perfect vacuum spin down due to the cooling mechanism? something like that.. arxiv.org/abs/1009.4107 $\endgroup$ – Quillo Oct 14 '20 at 9:16

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