Analysis of Gravitational and Geometric Aspects of Geodetic Utilization of Satellites

Expressions are derived for the first-order effects of any period of any term, , of the gravitational potential on the orbital elements, plus the second-order effects arising from the interaction of with , the oblateness. The order of magnitude of some daily and semi-daily variations is estimated to be ± 100 m from statistical data on the gravitational harmonics. A general geometric and statistical treatment of all types of observations is developed, with the purposes of obtaining rigorous evaluations of orbital and observational schemes, and optimum solutions for geodetic positions, gravitational harmonic coefficients, and orbital elements.