TITLE:
Schwarzschild Geodesics in Terms of Elliptic Functions and the Related Red Shift
AUTHORS:
Gunter Scharf
KEYWORDS:
Schwarzschild Geodesics, Red Shift
JOURNAL NAME:
Journal of Modern Physics,
Vol.2 No.4,
April
22,
2011
ABSTRACT: Using Weierstrassian elliptic functions the exact geodesics in the Schwarzschild metric are expressed in a simple and most transparent form. The results are useful for analytical and numerical applications. For example we calculate the perihelion precession and the light deflection in the post-Einsteinian approximation. The bounded orbits are computed in the post-Newtonian order. As a topical application we calculate the gravitational red shift for a star moving in the Schwarzschild field.