Resonance studies of artificial earth satellites

Abstract

Orbit determination from artificial satellite observations is a key process in obtaining information about the Earth and its environment. A study of the perturbations experienced by these satellites enables knowledge to be gained of the upper atmosphere, the gravity field, ocean tides, solid-Earth tides and solar radiation. The gravity field is expressed as a double infinite series of associated Legendre functions (tesseral harmonics). In contemporary global gravity field models the overall geoid is well determined. An independent check on these gravity field harmonics of a particular order may be made by analysis of satellites that pass through resonance of that order. For such satellites the perturbations of the orbital elements close to resonance are analysed to derive lumped harmonic coefficients. The orbital parameters of 1984-106A have been determined at 43 epochs, during which time the satellite was close to 14th order resonance. Analysis of the inclination and eccentricity yielded 6 lumped harmonic coefficients of order 14 whilst analysis of the mean motion yielded additional pairs of lumped harmonics of orders 14, 28 and 42, with the 14th order harmonics superseding those obtained from analysis of the inclination. This thesis concentrates in detail on the theoretical changes of a near-circular satellite orbit perturbed by the Earth's gravity field under the influence of minimal air-drag whilst in resonance with the Earth. The satellite 1984-106A experienced the interesting property of being temporarily trapped with respect to a secondary resonance parameter due to the low air-drag in 1987. This prompted the theoretical investigation of such a phenomenon. Expressions obtained for the resonance parameter led to the determination of 8 lumped harmonic coefficients, coincidental to those already obtained. All the derived lumped harmonic values arc used to test the accuracy of contemporary gravity field models and the underlying theory in this thesis.