Schwarzschild geodesics

In general relativity, the geodesics of the Schwarzschild metric describe the motion of particles of infinitesimal mass in the gravitational field of a central fixed mass M. The Schwarzschild geodesics have been pivotal in the validation of the Einstein's theory of general relativity. For example, they provide quite accurate predictions of the anomalous precession of the planets in the Solar System, and of the deflection of light by gravity.The Schwarzschild geodesics pertain only to the motion of particles of infinitesimal mass m, i.e., particles that do not themselves contribute to the gravitational field. However, they are highly accurate provided that m is many-fold smaller than the central mass M, e.g., for planets orbiting their sun. The Schwarzschild geodesics are also a good approximation to the relative motion of two bodies of arbitrary mass, provided that the Schwarzschild mass M is set equal to the sum of the two individual masses m1 and m2. This is important in predicting the motion of binary stars in general relativity.