Abstract
The secular variations of the orbital elements of principal planets are calculated by means of classical Lagrange's method. The terms of the second order with respect to mass, introduced by Hill (1897) and Brouwer and van Woerkom (1950), have been taken into account as well. The best contemporary values of planetary masses and mean elements (Bretagnon, 1982) served as the starting data set for this calculation. Considerable differences with respect to previous solutions of the same type (Brouwer and van Woerkom, 1950: Sharaf and Boudnikova, 1967) were found in the coefficientsA 55,A 56, andA 66 of the system of equations of variation of elements and in the roots (frequencies)r 5 andr 6. Results are compared with some higher order/higher degree solutions and their accuracy discussed. It is confirmed that the solutions like that of Brouwer and van Woerkom, although not being completely inferior to all higher order/higher degree ones, can be considered as the first approximation only. Hence, they should be replaced by more accurate ones (Duriez, 1979: Bretagnon, 1984: Laskar, 1984) in the future applications.
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Anolik, M. V., Krasinsky, G. A., and Pius, L. Yu.: 1969,Trans. Inst. Theor. Astron. (Leningrad) 14, 3–47.
Arnold, J. R.: 1969,Astron. J. 74,1235–1242.
Berger, A.: 1984, in A. Berger, J. Imbrie, J. Hays, G. Kukla, and B. Saltzman (Eds.),Milankovitch and Climate, Part I, D. Reidel Publ. Co., Dordrecht, Holland, pp. 3–39.
Bretagnon, P.: 1974,Astron. Astrophys. 30, 141–154.
Bretagnon, P.: 1982,Astron. Astrophys. 114, 278–288.
Bretagnon, P.: 1984, in A. Berger, J. Imbrie, J. Hays, G. Kukla, and B. Saltzman (Eds.),Milankovitch and Climate, Part I, D. Reidel Publ. Co., Dordrecht, Holland, pp. 41–53.
Brouwer, D.: 1951,Astron. J. 56, 9–32.
Brouwer, D. and Clemence, G. M.: 1961,Methods of Celestial Mechanics, Academic Press, New York and London.
Brouwer, D. and van Woerkom, A. J. J.: 1950,Astron. Papers Amer. Eph. 13, Pt. 2, 81–107.
Brumberg, V. A., Evdokimova, L. S., and Skripnichenko, V. I.: 1975,Celes. Mech. 11, 131–138.
Carusi, A. and Massaro, E.: 1978,Astron. Astrophys. Suppl. 34, 81–90.
Dermott, S. F., Nicholson, P. D., Burns, J. A., and Houck, J. R.: 1984,Nature 312, 505–509.
Duriez, L.: 1979, ‘Approche d'une theorie generale planetaire en variables elliptiques heliocentriques.’, Thesis, Lille.
Harzer, P.: ‘Die Sacularen Veranderungen der Bahnen der Grossen Planeten’, Preisschrift, Leipzig.
Hill, G. W.: 1889,Astron. J. 9, 89–91.
Hill, G. W.: 1897.Astron. J. 17, 81–87.
Hill, G. W.: 1913,Astron. J. 28, 59–71.
Knežević, Z.: 1982,Bull. Astron. Inst. Czech,33, 267–281.
Kozai, Y.: 1979,Ann. Tokyo Astron. Obs. 17, 194–220.
Krasinsky, G. A. and Pius, L. Yu.: 1971,Nablyudenya Iskusstvenykh Nebesnykh Tel. 62, 93–112.
Laskar, J.: 1984, ‘Theorie generale planetaire: Elements orbitaux des planetes sur 1 million d'annes,’, Thesis, Paris.
Laskar, J.: 1985,Astron. Astrophys. 144, 133–146.
LeVerrier, U.-J.: 1876,Ann. Obs. Paris11,20–56.
Newcomb, S.: 1895, ‘The Elements of the Four Inner Planets and the Fundamental Constants of Astronomy’, Government Printing Office, Washington.
Sharaf, S. G. and Boudnikova, N. A.: 1967,Trans. Inst. Theor. Astron. (Leningrad)11, 231–261.
Shoemaker, E. M., Bus, S. J., Dunbar, R. S., Helin, E. F., Dawe, J., Barrow, J., Hartley, M., Morgan, D., Russel, K., and Savage, A.: 1984,Bull. Amer. Astron. Soc. 16 (Part I), 691.
Simon, J. L.: 1983,Astron. Astrophys. 120, 197–202.
Simon, J. L. and Bretagnon, P.: 1984,Astron. Astrophys. 138, 169–178.
Stockwell, J. N.: 1872,Smiths. Contr. No. 232.
Williams, J. G.: 1979, in T. Gehrels (Ed.),Asteroids, Univ. Arizona Press, Tuscon, pp. 1040–1063.
Zappala, V., Farinella, P., Knežević, Z., and Paolicchi, P.: 1984,Icarus 59, 261–285.
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Knežević, Z. Secular variations of major planets' orbital elements. Celestial Mechanics 38, 123–138 (1986). https://doi.org/10.1007/BF01230425
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DOI: https://doi.org/10.1007/BF01230425