General Relativity and Celestial Mechanics

Einstein discovered the celestial mechanical consequences of GRT in 1914, just before his completion of GRT. General relativity produces a change in the gravitational field in the vicinity of a massive body. The distortion is equivalent to introducing an additional term in the harmonic oscillator equation 

Two types of GRT corrections are required for orbits. One is due to the precession of the orbit, the other is the radiation of gravitational waves. While not important in the vast majority of dynamical systems, it plays a role in binary star systems in which the components are massive, compact, and revolving with very short periods. The rate of gravitational wave radiation varies as where 2 is the orbital frequency, so that for binaries like PSR 1913-1-21 (the best studied of the binary pulsars) it produces a secular change in the semimajor axis that can be measured from several years of observation. These effects can be incorporated into the standard perturbation evolution equations through modifications to the distubing function. 

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