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arxiv: 1101.1207 · v2 · pith:J3FWONS7new · submitted 2011-01-06 · 🌌 astro-ph.GA

Schwarzschild geodesics in terms of elliptic functions and the related red shift

classification 🌌 astro-ph.GA
keywords schwarzschildcalculateellipticfunctionsgeodesicsshiftanalyticalapplication
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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.

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