Abstract
For treating the perturbed two-body problem in rectangular coordinates a new method is developed. The method is based on the reduction of the variational equations of the two-body problem with arbitrary elements to the Jordan system. The equations of perturbed motion rewritten in the quasi-Jordan form are subjected to a transformation excluding fast variables and leading to a system governing the long term evolution of motion. The method may be easily extended to the problem of the heliocentric motion of the major planets. For performing this method on computer it is suitable to use facilities of Poissonian and Keplerian processors.
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References
Brumberg, V. A.: 1970, ‘Application of Hill's Lunar Method in General Planetary Theory’, in G. E. O. Giacaglia (ed.),Periodic Orbits, Stability and Resonances, Reidel, Dordrecht, p. 409
Brumberg, V. A. and Chapront, J.: 1973, ‘Construction of a General Planetary Theory of the First Order’,Celest. Mech. 8, 335.
Duriez, L.: 1977, ‘Théorie Générale Planétaire en Variables Elliptiques’,Astron. Astrophys. 54, 93.
Musen, P.: 1965, ‘On the General Perturbations of the Position Vectors of a Planetary System’,J. Observ. 48, 11.
Musen, P. and Carpenter, L.: 1963, ‘On the General Planetary Perturbations in Rectangular Coordinates’,J. Geophys. Res. 68, 2727.
Stumpff, K.: 1974,Himmelsmechanik, Bd. 3, DVW, Berlin.
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Brumberg, V.A. Perturbation theory in rectangular coordinates. Celestial Mechanics 18, 319–336 (1978). https://doi.org/10.1007/BF01230346
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DOI: https://doi.org/10.1007/BF01230346