Equations of motion for two-body problem according to an observer inside the gravitational field

Abstract

In this paper we consider equations of motion for 2-body problem according to an observer close to one of the gravitational bodies. The influence of the Thomas precession of the observer's frame has an important role. The equations of motion are based on a nonlinear connection modified by the action of an orthogonal tensor which synchronizes the 4-velocities of the considered two bodies. Finally we present periastron shift according to an observer inside the gravitational field, using the orthonormal coordinates. This is different approach than that used in General Relativity where the periastron shift is only given as observed far from the massive bodies.

References in corpus (4)

• Research of Gravitation in Flat Minkowski Space
• Deformation of the Planetary Orbits Caused by the Time Dependent Gravitational Potential in the Universe
• Hubble red shift and the anomalous acceleration of Pioneer 10 and 11
• Geodetic precession and frame dragging observed far from massive objects and close to a gyroscope