Abstract
The mean values % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamaalaaabaGaaGymaaqaaiaaikdacqaHapaCaaWaa8qCaeaacaGG% OaacbaGaa8NKbiabgkHiTiaadYgacaGGPaGaa8hiaiGacogacaGGVb% Gaai4Caiaa-bcacaWGRbGaa8NKbiaa-bcacaWGKbGaamiBaaWcbaGa% aGimaaqaaiaaikdacqaHapaCa0Gaey4kIipakiaa-bcacaqGHbGaae% OBaiaabsgacaWFGaWaaSaaaeaacaaIXaaabaGaaGOmaiabec8aWbaa% daWdXbqaaiaacIcacaWFsgGaeyOeI0IaamiBaiaacMcacaWFGaGaci% 4CaiaacMgacaGGUbGaa8hiaiaadUgacaWFsgGaa8hiaiaadsgacaWG% SbaaleaacaaIWaaabaGaaGOmaiabec8aWbqdcqGHRiI8aaaa!6BC2!\[\frac{1}{{2\pi }}\int\limits_0^{2\pi } {(f - l) \cos kf dl} {\rm{and}} \frac{1}{{2\pi }}\int\limits_0^{2\pi } {(f - l) \sin kf dl}\] (where f and l are respectively the true anomaly and the mean anomaly in the elliptic motion and k is an integer) are given in closed form.
Similar content being viewed by others
References
Asknes, K.: 1971, ‘A note on ‘The main problem of satellite theory for small eccentricities’, by A. Deprit and A. Rom, 1970’, Celest. Mech. 4, 119
Brouwer, D.: 1959, ‘Solution of the problem of artificial satellite theory without drag’, Astron. J. 64, 378
Brouwer, D. and Clemence, G.M.: 1961, ‘Methods of celestial mechanics’, Academic Press
Claes, H.: 1980, ‘Analytical theory of Earth's artificial satellites’, Celest. Mech. 21, 193
Claes, H., Henrard, J., Zune, J.M., Moons, M. and Lemaitre, A.: 1988, ‘Guide d'utilisation du manipulateur de séries [MS]’, Internal publication. Department of Mathematics, FUNDP, Namur
Deprit, A.: 1969, ‘Canonical transformations depending on a small parameter’, Celest. Mech. 1, 12
Deprit, A. and Rom, A.: 1970, ‘The main problem of artificial satellite theory for small and moderate eccentricities’, Celest. Mech. 2, 166
Kelly, T.J.: 1989, ‘A note on first-order normalizations of perturbed keplerian systems’, Celest. Mech. 46, 19
Kozai, Y.: 1962, ‘Mean values of cosine functions in elliptic motion’, Astron. J. 67, 311
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Metris, G. Mean values of particular functions in the elliptic motion. Celestial Mech Dyn Astr 52, 79–84 (1991). https://doi.org/10.1007/BF00048588
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00048588