The Effect of the Mutual Gravitational Interactions on the Perihelia Displacement of the Orbits of the Solar System’s Planets
2018, Vol. 14, no. 3, pp. 291-300
Author(s): Vilke V. G., Shatina A. V., Osipova L. S.
This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License
Author(s): Vilke V. G., Shatina A. V., Osipova L. S.
The classical $N$-body problem in the case when one of the bodies (the Sun) has a much larger
mass than the rest of the mutually gravitating bodies is considered. The system of equations
in canonical Delaunay variables describing the motion of the system relative to the barycentric
coordinate system is derived via the methods of analitical dynamics. The procedure of averaging
over the fast angular variables (mean anomalies) leads to the equation describing the evolution
of a single Solar system planet’s perihelion as the sum of two terms. The first term corresponds
to the gravitational disturbances caused by the rest of the planets, as in the case of a motionless
Sun. The second appears because the problem is considered in the barycentric coordinate system
and the orbits’ inclinations are taken into account. This term vanishes if all planets are assumed
to be moving in one static plane. This term contributes substantially to the Mercury’s and
Venus’s perihelion evolutions. For the rest of the planet this term is small compared to the
first one. For example, for Mercury the values of the two terms in question were calculated
to be 528.67 and 39.64 angular seconds per century, respectively.
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