A restricted four body solution for resonating satellite with an oblate earth

Statistics – Computation

Scientific paper

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Earth Orbits, Four Body Problem, Resonance, Satellite Perturbation, Ephemerides, Graphs (Charts), Mathematical Models, Oblate Spheroids

Scientific paper

A method of averaging is used to study two general problems for the drag free motion of an artificial earth satellite. First, the four body oblate earth problem which describes the satellite motion perturbed by the point mass effects of the moon and sun as well as the oblate earth is analyzed. In this problem the first-order harmonic J2 and the second-order harmonics J3 and J4 are included. Several transformations are introduced and the transformed dynamical system is analytically integrated. Secondly, two specific classes of orbits for the resonant four-body oblate-earth problem due to the sectoral and tesseral potential of the earth are examined. The transformed dynamical system for this problem is also analytically integrated except for a numerical evaluation of the main resonance effect. Both problems consider satellites with orbital periods up to 24 hours. The resultant model is a mostly analytic computationally efficient ephemeris generator which includes the most significant perturbations for satellites with orbital periods up to 24 hours.

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