GRT: Can Identical Objects Orbit Center of Gravity?

[exmarine]

Would it be possible for 2 identical objects to orbit their center of gravity in an otherwise empty universe?

I am guessing that the answer is no, but how would GRT address / answer that question?

Would the objects’ spins affect the answer?

 

[PAllen]

Would it be possible for 2 identical objects to orbit their center of gravity in an otherwise empty universe?

I am guessing that the answer is no, but how would GRT address / answer that question?

Would the objects’ spins affect the answer?

Depends on your time scale and precision. There is no such stable co-orbit in GR due to gravitational radiation. However, for ordinary bodies and time scales, you can show exactly how tiny the effects would be. I think the most rigorous approach to such a problem in GR would be the effective one body methods of : http://arxiv.org/abs/1212.3169

Yes, the spins would definitely have an impact.

 

[exmarine]

Thanks for that paper. But it and your answer seem to pertain to the current universe - with many distant masses. What would be the answer "in an otherwise empty universe"?

 

[Bill_K]

Thanks for that paper. But it and your answer seem to pertain to the current universe - with many distant masses. What would be the answer "in an otherwise empty universe"?

Exactly the same. In GR, distant masses have no effect on the motion of local masses.

 

[Meir Achuz]

I think he's referring to Mach's principle. I don't know what Mach would say.

 

[PAllen]

Thanks for that paper. But it and your answer seem to pertain to the current universe - with many distant masses. What would be the answer "in an otherwise empty universe"?

The effective one body methods apply precisely only in the case of two bodies alone in the universe.

 

[Naty1]

In GR, distant masses have no effect on the motion of local masses.

yes, especially when not in the past lightcone of the local masses...no causal connection .