Einstein–Infeld–Hoffmann equations

The Einstein -Infeld - Hoffmann equation is an equation of motion, which was jointly developed by Albert Einstein, Leopold Infeld and Hoffmann Banesh. There is a differential equation that describes the kinetics of a system of point-like masses under mutual gravitational attraction approximation taking into account general relativistic effects. It uses a post -Newtonian expansion of the first order and is therefore valid in areas in which the velocities of the masses are correspondingly weak small compared to the speed of light and the gravitational fields acting on them.

For a system of N masses are indicated by the indices a = 1, ..., N, the barycentric Beschleunigungsvekter of the body A is given by:

The following applies:

The first term on the right-hand side corresponds to the Newtonian gravitational acceleration on A. In the limit c → ∞, one obtains the Newtonian equation of motion.

The acceleration of a body depends on the specific accelerations of all the other body. Since the acceleration vector appears on both sides of the equation, the equation system must be solved iteratively. In practice, however, it is sufficient to Newton 's equation of motion in order to achieve sufficient accuracy.