Gravitational Stress: Source of Energy for Orbiting Bodies

[T S Bailey]

Orbiting bodies are often stressed and twisted by the tidal forces of the larger body. My question is, if these stresses cause the planet to heat up then what system provides the energy to do this? Does the larger body lose energy? Can the gravitational field act as a medium for energy exchange?

 

[PeterDonis]

if these stresses cause the planet to heat up then what system provides the energy to do this?

The general answer is, it depends.

Let's take the innermost large moon of Jupiter, Io, as an example. Io is heated by the tidal effect of Jupiter. What else happens to the Jupiter-Io system in the process? At least two possible things can happen: Jupiter's rotation rate can slow down; or Io's orbital motion can change. Both of these involve energy being taken from some other part of the system and put into heating Io: in the first case, Jupiter's rotational kinetic energy is the source; in the second, Io's orbital kinetic energy is the source. In general, both are possible, but it is not necessarily true that both will take place in a particular case.

Does the larger body lose energy?

It can, but it does not necessarily have to, as the above example shows.

In fact, it is even possible for the larger body to gain energy in the process of tidal interaction. If the larger body is not rotating at all, then the effect of tidal interaction will be to start the larger body rotating; so in addition to any heating of the smaller body, energy also has to be supplied to increase the rotational kinetic energy of the larger body. In this case, the smaller body's orbital kinetic energy will have to decrease.

Can the gravitational field act as a medium for energy exchange?

This is the easiest of your questions to answer; the answer is yes, as the above examples clearly show.

 

[Dale]

Can the gravitational field act as a medium for energy exchange

PeterDonis' answer above is correct and pretty complete. I will just point out that gravity as a means of energy exchange is not just theoretical, but it is the basis for hydroelectric power.