A special case in the problem of n fixed centers

Details A special case in the problem of n fixed centers A special case in the problem of n fixed centers

Oct 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976sval....2..199a&link_type=abstract

(Pis'ma v Astronomicheskii Zhurnal, vol. 2, Oct. 1976, p. 509-511.) Soviet Astronomy Letters, vol. 2, Sept.-Oct. 1976, p. 199, 2

Astronomy and Astrophysics

Astronomy

Celestial Mechanics, Many Body Problem, Orbital Mechanics, Satellite Orbits, Astrodynamics, Computer Techniques, Equations Of Motion, Gravitational Fields, Orbit Calculation, Quadratures

Scientific paper

The motion of a passively gravitating material point (a satellite) in the Newtonian gravitational field of n fixed centers is considered in the case where the centers are distributed on the coordinate axis such that the satellite can move only in the xy plane. Polar coordinates are employed, and the equations of satellite motion are reduced to quadratures for values of n up to 3. A solution to the problem of four fixed centers is discussed, and solutions are obtained for two variants in which the number of fixed centers is even and odd, respectively. These are reduced to quadratures analogous to those for the problem of four fixed centers.

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