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On the Calculation of Secular Perturbations in the Case of Close Commensurability

Published online by Cambridge University Press:  14 August 2015

N. I. Lobkova  and
M. S. Petrovskaya
N. I. Lobkova
Affiliation:
Institute of Theoretical Astronomy, Leningrad, U.S.S.R.
M. S. Petrovskaya
Affiliation:
Institute of Theoretical Astronomy, Leningrad, U.S.S.R.

Abstract

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In a previous paper the authors derived expansions of the derivatives of the disturbing function for the general case including the orbits close to intersection. The present paper deals especially with the case of close commensurability of the mean motions. A new variable v is introduced characterizing the deviation of the mean anomalies from the exact commensurability, and is considered further as an unknown quantity. In the equations of motion the short-period terms are eliminated. The form of expansions of the right-hand sides is chosen basing on the same principles as in the general case. The factors are separated, corresponding to the poles in the case of circular intersecting orbits. For rapidity of calculation the summation in powers of the major semi-axes ratio is made the inner one.

Type
Research Article
Information
Symposium - International Astronomical Union , Volume 62: The Stability of the Solar System , 1974 , pp. 157 - 163
Copyright
Copyright © Reidel 1974 

References

Brumberg, V. A., Evdokimova, L. S., and Kochina, N. G.: 1971, Celes. Mech. 3, 197.CrossRefGoogle Scholar
Giacaglia, G. E. O.: 1968, Smithsonian Astrophys. Obs. , Special Report No. 278.Google Scholar
Giacaglia, G. E. O. and Nacozy, P. E.: 1969, in Giacaglia, G. E. O. (ed.), Periodic Orbits, Stability and Resonances , D. Reidel, Dordrecht, The Netherlands, p. 96.Google Scholar
Hori, G. and Giacaglia, G. E. O.: 1968, Research in Celestial Mechanics and Differential Equations (University of Paulo) 1, 4.Google Scholar
Kozai, Y.: 1962, Astron. J. 67, 591.CrossRefGoogle Scholar
Kozai, Y.: 1968, in Giacaglia, G. E. O. (ed.), Periodic Orbits, Stability and Resonances , D. Reidel, Dordrecht, The Netherlands, p. 451.Google Scholar
Petrovskaya, M. S.: 1972, Celes. Mech. 6, 328.CrossRefGoogle Scholar
Sack, R. A.: 1964, J. Math. Phys. 5, 245.CrossRefGoogle Scholar