GEOS-II and 13th order terms of the geopotential

The resonance of GEOS-II (1968-002A) with 13th-order terms of the geopotential is analyzed. The odd-degree geopotential coefficients (13, 13), (15, 13), and (17, 13) given by Yionoulis most accurately model the resonance effects on GEOS-II of any of the published sets of 13th-order coefficients. However, this set is not adequate for precision orbit determination; additional even-degree coefficients are required.Values ofC _14,13(=0.57×10^–21) andS _14,13(=6.5×10^–21) to be used with the odd-degree set of Yionoulis were obtained from an analysis of the observed along-track position variation of GEOS-II. These coefficients, when used with those of Yionoulis, yield greatly improved fits to the data and orbital prediction capability. However, further refinement is possible because the small effects of the remaining even-degree resonant terms were not modeled.The composite coefficientsC _13,13(=1.7×10^–20) andS _13,13(=+2.7×10^–20) were obtained under the assumption that the (13, 13) spherical harmonic of the geopotential is responsible for all of the observed along-track variation of GEOS-II due to resonance. The good agreement of these deliberately composite values with some published values ofC _13,13 andS _13,13 suggests that some of the published values may also be composite to some extent.These coefficients are hereinafter referred to as the APL coefficients.