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Gravitational waves have been detected emanating from the decaying orbits of massive bodies, such as binary neutron star or black hole systems.

To my understanding, two such bodies in what would otherwise be a stable orbit, will instead slowly radiate away their orbital momentum as gravitational waves and spiral inwards towards a merger.

My question: if the circular motion of masses in spacetime can be lost as spiral gravitational waves, why can't the linear motion of masses in spacetime be lost as bow/wake shaped gravitational waves, as seen in familiar water bow/wake waves?

I imagine the answer lies in the linear acceleration of masses compared to the linear inertial motion of them?

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It is not about circular or linear motion specifically. It is just that the requirements for creating GWs is very hard to satisfy.

GWs are radiated by objects whose motion involves acceleration and its change, provided that the motion is not spherically symmetric or rotationally symmetric.

A simple example of this principle is a spinning dumbbell. If the dumbbell spins around its axis of symmetry, it will not radiate gravitational waves; if it tumbles end over end, as in the case of two planets orbiting each other, it will radiate gravitational waves.

https://en.wikipedia.org/wiki/Gravitational_wave

In reality, the second time derivative of the quadrupole moment needs of an isolated systems stress-energy tensor must be non-zero.

Gravitational waves (GW) are emitted by all systems which have an 'accelerating quadrupole moment' --- which means that the systems have to be undergoing some sort of acceleration (i.e. a constant velocity is not enough), and they have to be asymmetric.

Do only black holes emit gravitational waves?

So the motion of the masses needs to satisfy all these requirements, to emit gravitational waves. A system of masses can satisfy this, and only if they are asymmetric, and the acceleration itself changes too.

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