Analytical Method for the Effects of the Asteroid Belt on Planetary Orbits
Abstract
Analytic expressions are derived for the perturbation of planetary orbits due to a thick constant density asteroid belt. The derivations include extensions and adaptations of Plakhov's analytic expressions for the perturbations in five of the orbital elements for closed orbits around Saturn's rings. The equations of Plakhov are modified to include the effect of ring thickness and additional equations are derived for the perturbations in the sixth orbital element, the mean anomaly. The gravitational potential and orbital perturbations are derived for the asteroid belt with and without thickness, and for a hoop approximation to the belt. The procedures are also applicable to Saturn's rings and the newly discovered rings of Uranus. The effects of the asteroid belt thickness on the gravitational potential coefficients and the orbital motions are demonstrated. Comparisons between the Mars orbital perturbations obtained using the analytic expressions and those obtained using numerical integration are discussed. The effects of the asteroid belt on the Earth based ranging to Mars are also demonstrated.
 Publication:

Celestial Mechanics
 Pub Date:
 May 1979
 DOI:
 10.1007/BF01231011
 Bibcode:
 1979CeMec..19..317M
 Keywords:

 Asteroid Belts;
 Gravitational Effects;
 Orbit Perturbation;
 Orbital Mechanics;
 Planets;
 Solar Orbits;
 Gas Giant Planets;
 Gravitational Fields;
 Orbital Elements;
 Saturn Rings;
 Terrestrial Planets;
 Uranus Rings;
 ASTEROID BELT;
 ASTEROIDS;
 PLANETS;
 ORBITS;
 PERTURBATIONS;
 MARS;
 RINGS;
 SATELLITES;
 SATURN;
 MASS;
 GRAVITY;
 DATA;
 URANUS;
 ANOMALIES;
 Astronomy; Asteroids