Would there be any way to avoid gravitational wave emissions?

[Suekdccia]

TL;DR

Would there be any way to avoid gravitational waves emission in some orbital configurations?

In principle every object orbiting another (e.g. a planet revolving around a star) would emit gravitational waves, relaxing the orbit over time.However, this would not happen if the orbits had a time-invariant and symmetric quadrupole moment. As it is indicated in this question (), it appears that if the masses were perfectly symmetrically ordered around a star (e.g. 4 planets separated by 90º from each other orbiting the same star), then the system would not emit gravitational waves. Are there any other examples of orbits that would not emit gravitational waves?

 

[PeterDonis]

Are there any other examples of orbits that would not emit gravitational waves?

Gravitational wave emission is driven by the third time derivative of the quadrupole moment. So any system for which that is zero will not emit gravitational waves.

 

[Vanadium 50]

driven by the third time derivative of the quadrupole moment

I believe that is the leading order, but I also believe that higher order multipoles exist, as they do in electromagnetism. So this would reduce but not eliminate the gravitational wave emission.

 

[ohwilleke]

Gravitational wave emission is driven by the third time derivative of the quadrupole moment. So any system for which that is zero will not emit gravitational waves.

The natural follow up to that answer would be to describe some examples of systems for which this would be zero, rather than leaving the solution of the differential equation to the reader.

 

[renormalize]

The natural follow up to that answer would be to describe some examples of systems for which this would be zero, rather than leaving the solution of the differential equation to the reader.

How about a spherically-symmetric ball of fluid that expands, contracts, or oscillates only in the radial direction, but with arbitrary time-dependence? No gravitational radiation is emitted by Birkhoff's Theorem.