Computer Science – Numerical Analysis
Scientific paper
Apr 1975
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975azh....52..420b&link_type=abstract
Astronomicheskii Zhurnal, vol. 52, Mar.-Apr. 1975, p. 420-430. In Russian.
Computer Science
Numerical Analysis
4
Equations Of Motion, Orbit Calculation, Orbital Resonances (Celestial Mechanics), Planetary Mass, Solar Orbits, Algorithms, Astronomical Coordinates, Eccentric Orbits, Exponential Functions, Numerical Analysis
Scientific paper
Particular quasi-periodic solutions of the equations of motion of the major planets in rectangular heliocentric coordinates have been constructed by means of successive iterations with respect to the planetary masses. These solutions are presented as exponential series in multiples of the mean longitudes of the planets, the sum of all exponential indices in every term being equal to zero. The corresponding inequalities in the planetary motion are of the zero order in eccentricities and inclinations of the planetary orbits. The resonance terms due to the close commensurabilities among three or more mean motions of the planets are given. These resonance terms are of the zero order in eccentricities and inclinations. With respect to the planetary masses they are analytically at least of the second order, but numerically they are comparable with the terms of the first order.
Brumberg Victor A.
Evdokimova L. S.
Skripnichenko V. I.
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