Abstract
The Hamiltonian of the second order with respect to the disturbing mass, as defined in the higher order-higher degree theory of asteroid secular perturbations by Yuasa (1973), is expressed in the heliocentric, ecliptic coordinate system. Errors found in the original paper with terms coming from the principal part of the disturbing function are removed, and corrected values of the coefficients are computed. The importance of second-order perturbations and the improvement in the accuracy of proper element determination, achieved by using the newly-obtained coefficients, are demonstrated. Finally, a table of the secular frequencies as functions of the semimajor axis is given, and compared with the analogous one by Kozai (1979).
Similar content being viewed by others
References
Brouwer, D. and van Woerkom, A. J. J.: 1950, Astron. Papers American Eph. Naut. Almanac 13, 85.
Carpino, M., Gonczi, R., Farinella, P., Froeschlé, Ch., Froeschlé, Cl., Paolicchi, P. and Zappalá, V.: 1986, Icarus 68, 55.
Farinella, P., Froeschlé, Cl. and Knežević, Z.: 1988, in Long-Term Dynamical Behaviour of Natural and Artificial N body Systems, A. E. Roy, Ed., Kluwer Acad. Publ., 237.
Hori, G.: 1966, Publ. Astron. Soc. Japan 18, 287.
Kneěvić, Z.: 1988, Bull. Obs. Astron. Belgrade 139, 1.
Kozai, Y.: 1979, in Asteroids, T. Gehrels, Ed., Univ. Arizona Press, Tucson, 334.
LeVerrier, U. J.: 1855, Ann. Obs. Paris 1, 272.
Yuasa, M.: 1973, Publ. Astron. Soc. Japan 25, 399.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Knežević, Z. Asteroid long-periodic perturbations: The second order Hamiltonian. Celestial Mech Dyn Astr 46, 147–158 (1989). https://doi.org/10.1007/BF00053044
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00053044