The deviation of light by a star and the precession of the perihelion of a planetary orbit are usually derived by independent methods. In the present paper the equations of motion for weak gravitation are integrated approximately and both effects are derived simultaneously.
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L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Nauka, Moscow, 1988).
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Sean M. Carroll, “Lecture notes on general relativity,” 〈http://pancake.uchicago.edu/∼carroll/notes/〉.
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4.
See solutions to Problem 15.7a (perihelion precession with small eccentricity) and Problem 15.9 (deviation of a particle by a star) in S. Lightman, W. H. Press, R. H. Price, and S. A. Teukolski, Problem Book in Relativity and Gravitation (Princeton U. P., Princeton, 1975).
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In Newtonian physics the Runge–Lenz vector is conserved.
11.
We will consider a particle moving far away from the star with arbitrary velocity Light bending is a special case, when
12.
This method of performing the integral in Eq. (14) was suggested by A. D. Dolgov.
13.
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