Schwarzschild geodesics

General relativity
${\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}$
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In general relativity, Schwarzschild geodesics describe the motion of test particles in the gravitational field of a central fixed mass ${\textstyle M,}$ that is, motion in the Schwarzschild metric. Schwarzschild geodesics have been pivotal in the validation of Einstein's theory of general relativity. For example, they provide accurate predictions of the anomalous precession of the planets in the Solar System and of the deflection of light by gravity.

Schwarzschild geodesics pertain only to the motion of particles of masses so small they contribute little to the gravitational field. However, they are highly accurate in many astrophysical scenarios provided that ${\textstyle m}$ is many-fold smaller than the central mass ${\textstyle M}$, e.g., for planets orbiting their star. Schwarzschild geodesics are also a good approximation to the relative motion of two bodies of arbitrary mass, provided that the Schwarzschild mass ${\textstyle M}$ is set equal to the sum of the two individual masses ${\textstyle m_{1}}$ and ${\textstyle m_{2}}$. This is important in predicting the motion of binary stars in general relativity.