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Einstein's perihelion formula and its generalization

### Abstract

Einstein's perihelion advance formula can be given a geometric interpretation in terms of the curvature of the ellipse. The formula can be obtained by splitting the constant term of an auxiliary polar equation for an elliptical orbit into two parts that, when combined, lead to the expression of this relativistic effect. Using this idea, we develop a general method for dealing with orbital precession in the presence of central perturbing forces, and apply the method to the determination of the total (relativistic plus Newtonian) secular perihelion advance of the planet Mercury.

© 2015 American Association of Physics Teachers

Received 07 July 2014
Accepted 19 November 2014

Article outline:

I. INTRODUCTION
II. RELATIVISTIC EQUATION
III. ELLIPTICAL ORBIT
IV. ANGULAR PERIOD OPERATOR
V. THE ROTATING ELLIPSE
VI. A SMALL CHANGE OF CURVATURE
VII. RELATIVISTIC PRECESSION
VIII. CENTRAL PERTURBING FORCES
IX. NEWTONIAN PRECESSION
A. The model
B. Effective orbital radii
C. Perihelion shifts
D. A proper perspective
X. CONCLUSION