Untruncated perturbation analysis for a satellite orbiting in a nonrotating gravitational field
Abstract
It was assumed previously that the gravitational field was axisymmetric and due to a mass distribution entirely within the orbital region. By use of a particular system of spherical polar coordinates, an orbital theory was developed that led to compact firstorder perturbation formulas associated with the general zonal harmonic, J sub l. No eccentricity truncation was involved in these formulas, though there was an implicit restriction to elliptic orbits. The theory has now been given a logical completeness by three distinct extensions: by allowing for tesseral harmonics, the assumption of axial symmetry can be dropped; by permitting the harmonic index, l, to be negative, mass outside the orbital region can be allowed for; and the formulas can be so expressed that hyperbolic orbits are covered. The extensions are straightforward so long as the field is still assumed to be timeinvariant, i.e., to be nonrotating, and this assumption is made. The second extension has been the one to involve the most new work, since the planetary equations have to be formulated with the eccentric anomaly as integration variable when l is less than 0.
 Publication:

Astrodynamics 1989
 Pub Date:
 1990
 Bibcode:
 1990asdy.conf...25G
 Keywords:

 Gravitational Fields;
 Mass Distribution;
 Orbital Mechanics;
 Satellite Perturbation;
 Tesseral Harmonics;
 Planetary Orbits;
 Polar Coordinates;
 Spherical Coordinates;
 Astrodynamics