For two orbiting bodies of very different masses like the
Sun and Mercury or the stars of a galaxy, the expression becomes
For two radiating and orbiting bodies like a binary star of
equal masses, there is an additional vector gravity term that is the ratio of
radiation and relative velocity.
Mercury has the largest eccentricity of any planet in its orbit with the Sun and the perihelion advance of Mercury has long validated Einstein’s relativity. Mercury’s perihelion advance is a result of gravity quadrupole radiation as Table 1 shows that decays its orbit and increases its velocity.
The emission of 5.2e-15 kg/s gravity quadrupole results in the Mercury orbit decay that is the perihelion advance. Since the same quadrupole emission occurs for discrete aether, the Mercury perihelion advance also validates discrete aether.
The Milky Way galaxy has a dipole luminosity of 4.3e19 kg/s, which is 1e10 x the Sun luminosity and due to its 2.5e11 stars. The gravity quadrupole Milky Way luminosity is much smaller at 1.3e15 kg/s than the dipole luminosity, but the much larger dipole luminosity also results in a quadrupole luminosity of 1.4e14 kg/s. This 13% increase in gravity wave emission decays all star orbits and therefore increases their orbital velocities just like the perihelion advance of Mercury.
The merger of two 6.0e31kg blackholes over 0.25 s results in quadrupole emissions of 3.0e29 kg/s at 1% of the total mass loss of the event. The onset of the inspiral occurs at r = 7.6e12 m, which is the point when the quadrupole radiation is just 1% of the total. There is also dipole emission from gravitation, but that emission is spread all over the universe.