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Published in:
2021 | OriginalPaper | Chapter
2. Analytic Solutions for the Perturbed Motion of a Spacecraft in Near-Circular Orbit, Under the Influence of the J2 and J3 Earth Zonal Harmonics, in Rotating and Inertial Cartesian Reference Frames
Author : Jean Albert Kéchichian
Published in: Orbital Relative Motion and Terminal Rendezvous
Publisher: Springer International Publishing
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Abstract
The analytic first-order solution of the Earth zonal harmomics J2 and J3 perturbation effect on the motion of a spacecraft in a near-circular orbit with small eccentricity and arbitrary inclination, energy, node and perigee location is analyzed. The second-order Euler-Hill differential equations are solved after expanding the forcing terms to first-order in the small parameter defining the orbit eccentricity. The construction of the circular reference orbit which defines the rotating Cartesian reference frame with respect to which the relative motion is described, is also shown. For the case of the J2 harmonic, a position error of 200 m per revolution is sustained when the initial orbit is circular. The equations developed in this chapter can be used to carry out terminal rendezvous in near-circular obit around the oblate Earth.