Analytic solution of perturbed motion in nearcircular orbit due to J2, J3 earth zonal harmonics in rotating and inertial Cartesian reference frames
Abstract
The analytic first order solution of the J2 and J3 earthzonal harmonics' J2 and J3 perturbation effect on the motion of a spacecraft in a nearcircular orbit with small eccentricity and arbitrary inclination, energy, node, and perigee location is presented. The secondorder EulerHill differential equations are solved in closed form after expanding the forcing terms to first order in the small parameter defining the orbit eccentricity. The circular reference orbit defines the rotating Cartesian reference frame with respect to which the relative motion is described. For the case of the J2 harmonic, a position error of 200 m per revolution is sustained when the initial orbit is circular. These equations can be used to carry out terminal rendezvous on nearcircular orbit around the oblate earth.
 Publication:

27th AIAA Aerospace Sciences Meeting
 Pub Date:
 January 1989
 Bibcode:
 1989aiaa.meetW....K
 Keywords:

 Circular Orbits;
 Earth Rotation;
 Hill Method;
 Spacecraft Motion;
 Zonal Harmonics;
 Acceleration (Physics);
 Cartesian Coordinates;
 Orbit Perturbation;
 Position Errors;
 Astrodynamics