On The TesseralHarmonics Resonance Problem in ArtificialSatellite Theory
Abstract
The longitudedependent part of the geopotential usually gives rise only to shortperiod effects in the motion of an artificial satellite. However, when the motion of the satellite is commensurable with that of the earth, the path of the satellite repeats itself relative to the earth and perturbations build up at each passage of the satellite in the same spot, so that there can be important longperiod effects. In order to take these effects into account in deriving a theoretical solution to the equations of motion of an artificial satellite, it is necessary to select terms in the longitudedependent part of the geopotential that will contribute significantly to the perturbations. We have tried to make a selection that is valid in a general case, regardless of the initial eccentricity of the orbit and of the order of the resonance. The solution to the equations of motion of an artificial satellite, in a geopotential thus determined, is then derived by using Hori's method by Lie series, which, by its properties regarding canonical invariance, has proved advantageous in the classical theory.
 Publication:

SAO Special Report
 Pub Date:
 March 1975
 Bibcode:
 1975SAOSR.365.....R