Mathematics
Scientific paper
Feb 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977azh....54..224k&link_type=abstract
Astronomicheskii Zhurnal, vol. 54, no. 1, 1977, p. 224-227. In Russian.
Mathematics
Astronomical Models, Celestial Mechanics, Gravitational Fields, Many Body Problem, Natural Satellites, Saturn (Planet), Legendre Functions, Saturn Rings, Series (Mathematics)
Scientific paper
The paper analyzes a version of the two-dimensional problem of four fixed centers in which two centers lie on the x-axis and two on the y-axis. It is shown that this problem is equivalent to two real problems in celestial mechanics that concern the motion of a passively gravitating point in the gravitational field of Saturn plus its rings and the motion of the same point in the gravitational field of a body consisting of a system of an arbitrary number of bodies or a system of rings (disks) of different masses. For the case of Saturn, the point is assumed to move in the equatorial plane of the planet outside the rings. It is concluded that the first equivalent problem is suitable for developing an exact analytical theory for the motion of Saturn's near-equatorial satellites, while the second can be applied in cases where the point moves in the gravitational field of a very complex structure such as a galaxy or an asteroid.
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