A geodetic gravitation gradiometer coexperiment to Gravity Probe B

Geodesy is the science of measuring the gravitational field of and positions on the Earth. Estimation of the gravitational field via gravitation gradiometry, the measurement of variations in the direction and magnitude of gravitation with respect to position, is this dissertation's focus.; Gravity Probe B (GP-B) is a Stanford satellite experiment in gravitational physics. GP-B will measure the precession the rotating Earth causes on the space-time around it by observing the precessions of four gyroscopes in a circular, polar, drag-free orbit at 650 km altitude. The gyroscopes are nearly perfect niobium-coated spheres of quartz, operating at 1.8 K to permit observations with extremely low thermal noise. The permissible gyroscope drift rate is less than 10{dollar}sp{lcub}-11{rcub}{dollar} degrees/hour, so the torques on the gyros must be tiny. A drag-free control system, by canceling accelerations caused by nongravitational forces, minimizes the support forces and hence torques.; We explore the feasibility of using the residual suspension forces centering the GP-B gyros as gradiometer signals for geodesy. The objective of this work is a statistical prediction of the formal uncertainty in an estimate of the Earth's gravitation field using data from GP-B. We perform an instrument analysis and apply two mathematical techniques to predict uncertainty. One is an analytical approach using a flat-Earth approximation to predict geopotential information quality as a function of spatial wavelength. The second estimates the covariance matrix arising in a least-squares estimate of a spherical harmonic representation of the geopotential using GP-B gradiometer data.; The results show that the GP-B data set can be used to create a consistent estimate of the geopotential up to spherical harmonic degree and order 60. The formal uncertainties of all coefficients between degrees 5 and 50 are better by factors of up to 30 than uncertainties in current satellite-only estimates and up to 7 than uncertainties in estimates such as GEM-T3 (Lerch 1992) which include surface data. The primary conclusion resulting from this study is that the gravitation gradiometer geodesy coexperiment to GP-B is both feasible and attractive.