Relativistic Orbits: Can Mass Increase Keep Planets Together?

[Meatbot]

Can you have an orbit held together simply by relativistic mass increase? Let's say you have two equal sized planets orbiting each other at .999c. Wouldn't it be the case that if mass didn't increase they'd fly apart? What are your thoughts on this general topic?

 

[pervect]

If you consider instead whether massless fields can be held together by gravity, you arrive at the geon.

You can consider the geon, above, to be the limiting case of your planets, where the rest mass of the "planets" shrinks to zero.

The answer as to whether geons exist appears to be yes, though there is consdierable doubt about their stability (i.e. known examples would fly apart after a short amount of time).

See also This old thread.

Note, however, that it is a mistake to assume that one can plug "relativistic mass" into Newtonian formulas for gravity and get sensible results. For instance, if you have two light beams (or two planets with an ultra-relativistic velocity) moving in the same direction, they will not attract. In the case of light, the attractive force will be exactly zero, in the case of planets it will be small. Anti-parallel light beams will attract, however.

 

[Mentz114]

I don't think the question is well put. We don't know if your scenario could ever arise from natural causes. However, if two bodies were orbiting each other at such extreme speeds it is likely ( according to GR) they would radiate a lot of energy as gravitational waves and so the orbits would be unstable.

When you use the term 'relativistic mass', be sure to specify a frame of reference.