The gauge-generalized Gyldén Meshcherskii Problem

Details The gauge-generalized Gyldén Meshcherskii Problem The gauge-generalized Gyldén Meshcherskii Problem

Oct 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008adspr..42.1313g&link_type=abstract

Advances in Space Research, Volume 42, Issue 8, p. 1313-1317.

Mathematics

Logic

1

Scientific paper

The Gyldén Meshcherskii Problem (GMP) extends the classical two-body problem of Newton and Kepler by considering time-varying gravitating masses, an important extension of the two-body problem for modeling cometary motion and cosmological phenomena. In this paper, we consider the GMP in a specialized setup, the setup of gauge theory. We show that the variational equations, modeling the effect of the mass time variation on the orbital elements, can be derived by fixing a gauge of a particular form that is different from the Lagrange gauge. Thus, the orbital elements modeling the effect of a time-varying secondary mass are non-osculating. This implies that the trajectory of a celestial body whose mass is continuously changing cannot be approximated by a series of Keplerian orbits. Finally, we provide the first-order averaged equations written in terms of non-osculating elements.

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