Gravitational harmonics from shallow resonant orbits

Abstract

Until very recently, there has been no identification of the significant gravitational constraints on the many common artificial earth satellite orbits in shallow resonance. Without them it is difficult to compare results derived for different sets of harmonics from different orbits. With them it is possible to extend these results to any degree without reintegration of the orbits. All such constraints are shown to be harmonic in the argument of perigee with constants determinable from tracking data: $$(C*,S*) = (C_0 ,S_0 ) + \sum\limits_{i = 1}^\infty {(C_{Ci} ,S_{Ci} )\cos i\omega + (C_{Si} ,S_{Si} )\sin i\omega .} $$ The constants are simple linear combinations of geopotential harmonics. Five such constants (lumped harmonics) have been derived for the GEOS-2 orbit (order 13, to 30th degree) whose principal resonant period is 6 days. These five lumped harmonics are shown to account for almost all (>98%) of the resonant information in the tracking. They agree well with recent gravitational models which include substantial amounts of GEOS-2 data.