Analysis of \(J_2\)-perturbed motion using mean non-osculating orbital elements
type: Item
instance of: scholarly article
title: Analysis of \(J_2\)-perturbed motion using mean non-osculating orbital elements
zbMATH Open document ID: 1147.70309
author: Pini Gurfil
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 2005-02-28T00:00:00Z
review text: The perturbed motion of a satellite in the gravitational field of the oblate planet is well formulated problem of celestial mechanics since Lagrange (his name is given to the proper differential equations), has the long history and a huge amount of publications. It is well known that if one takes into consideration only the second harmonic of the gravitational potential of the oblate planet \(J_2\) the so called positional orbit elements, i.e. the semi-major axis, the eccentricity and the inclination of the osculating orbit, are constant in the averaged problem. Here, a so-called gauge-generalization of the Lagrange equations (the terminology was adopted from the electrodynamics by \textit{M. Efroimsky} and \textit{P. Goldreich} [J. Math. Phys. 44, No. 12, 5958--5977 (2003; Zbl 1063.70008)] is used to show that if one adopts the secular variations of the eccentricity and inclination then some angular orbit elements (say, the node and the argument of periapsis) can be constant. In any case a combination of three orbit elements (position and angular as well) can be chosen as constants.
reviewed by: Sergei Georgievich Zhuravlev
Mathematics Subject Classification ID: 70F10
Mathematics Subject Classification ID: 70F15
Mathematics Subject Classification ID: 70K65
zbMATH DE Number: 2139810
zbMATH Keywords: orbital mechanics
zbMATH Keywords: Keplerian motion
zbMATH Keywords: Lagrange's equations
zbMATH Keywords: oblateness
zbMATH Keywords: osculating elements
zbMATH Keywords: averaged system
zbMATH Keywords: secular and long periodic perturbations
MaRDI profile type: Publication
full work available at URL: s10569-004-0890-x
OpenAlex ID: W2119742772
cites work: Gauge symmetry of the N-body problem in the Hamilton–Jacobi approach
cites work: Gauge freedom in theN-body problem of celestial mechanics
cites work: The method of variation of constants and multiple time scales in orbital mechanics
cites work: \(J_2\) invariant relative orbits for spacecraft formations
DOI: 10.1007/S10569-004-0890-X
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description: scientific article; zbMATH DE number 2139810