×

zbMATH — the first resource for mathematics

An analytical solution of the Lagrange equations valid also for very low eccentricities: influence of a central potential. (English) Zbl 1145.70014
Summary: This paper presents an analytic solution of the equations of motion of an artificial satellite, obtained using non singular elements for eccentricity. The satellite is under the influence of the gravity field of a central body, expanded in spherical harmonics up to an arbitrary degree and order. We discuss in details the solution we give for the components of the eccentricity vector. For each element, we have divided the Lagrange equations into two parts: the first part is integrated exactly, and the second part is integrated with a perturbation method. The complete solution is the sum of the so-called “main” solution and of the so-called “complementary” solution. To test the accuracy of our method, we compare it to numerical integration and to the method developed in W. M. Kaula [Theory of satellite geodesy, New York: Blaisdell Publ. Co. (1966), reprint Dover (2000; Zbl 0973.86001)], expressed in classical orbital elements. For eccentricities which are not very small, the two analytical methods are almost equivalent. For low eccentricities, our method is much more accurate.

MSC:
70M20 Orbital mechanics
70F05 Two-body problems
70F15 Celestial mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[2] Deleflie F., Métris G., Exertier P. (2006). Long-period variations of the eccentricity vector valid also for near-circular orbits around a non-spherical body, Celest. Mech. Dynam. Astron., this issue. · Zbl 1145.70013
[3] Demailly J.-P. (1996). Analyse numérique et équations différentielles, EDP Sciences.
[10] Tisserand F. 1890, Traité de Mécanique Céleste, Gauthiers Villards, reprinted. 1960–1962.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.