Note on the central differential equation in the relativity theory of gravitation
1920; Royal Society; Volume: 97; Issue: 682 Linguagem: Inglês
10.1098/rspa.1920.0019
ISSN2053-9150
Autores Tópico(s)Cosmology and Gravitation Theories
ResumoThe critical equation in Prof. Einstein’s relativity theory of gravitation is given in the form ( du / dϕ ) 2 + u 2 = c 2 — 1/ h 2 + 2 mu / h 2 + 2 mu 3 , where m is the mass of the sun, u is the reciprocal of the distance of the moving body from the sun, h 2 = ma (1— e 2 ), c 2 — 1 = — m / a , a is the “major semi-axis of the orbit,” the units being astronomical, and e is the “excentricity” of the orbit. The foregoing equation can be integrated exactly, the functions involved being elliptic and not circular; and the approximations for the solar system are easily obtained, because the modulus of the elliptic functions is small.
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