Geodesic effect near an elliptical orbit. (English) Zbl 1243.83020

Summary: Using a differential geometric treatment, we analytically derive the expression for De Sitter (geodesic) precession in the elliptical motion of the Earth through the gravitational field of the Sun with Schwarzschild’s metric. The expression obtained in this paper in a simple way, using a classical approach, agrees with that given in B. M. Barker and R. F. O’Connell (1970, 1975) in a different setting, using the tools of Newtonian mechanics and the Euler-Lagrange equations.


83C10 Equations of motion in general relativity and gravitational theory
70H03 Lagrange’s equations
70F15 Celestial mechanics
85A05 Galactic and stellar dynamics
83C57 Black holes


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