Evaluation of Flat-Earth Approximation Results for Geopotential Missions

Abstract

Simplie ed calculations can approximate the formal uncertainties in estimates of the spherical harmonic coefe cients representing the Earth’ s gravitational potential. The calculations model the Earth locally as a plane, producing errors negligible for wavelengths shorter than the radius of the Earth. Information derived from observations of low-altitude polar orbiting satellites is considered. With some constraints, the e nal model uncertainties derivefromapriorigravitationale eldinformation,specie corbitalelements,andparametersdescribinginstrumentation characteristics. We demonstrate how to ree ne the technique to accept inputs from the currently operational Navstar global positioning system (GPS) constellation and how to use information from partial tensor gravitational gradiometers. Thisapproach is benee cial when evaluating prospective satellitegeodesy missions becausethe covariance analyses for various mission scenarios can be made efe ciently and expeditiously. We demonstrate the utility of the e at-Earth approach by comparing results with those of more elaborate and time consuming calculations performed for the European Space Agency ARISTOTELES (Applications and Research Involving Space Techniques Observing The Earth’ s Field From Low Earth Orbiting Satellite ) proposed geopotential mapping mission, the NASA Gravity Probe B Relativity mission, and the NASA/Center National d’ Etudes Spatiales Topographic Ocean Experiment Satellite (TOPEX)/Poseidon mission. We also show that the e at-Earth approximations are consistent with reductions of the GPS tracking data obtained by TOPEX/Poseidon. Nomenclature e = natural logarithm base F.!/ = factor of reduction in geopotential variance at spatial frequency! H.$/ = information vector associated with instrument observations