Trojan-type orbits in the system of two gravitational centers with variable masses and separation

Details Trojan-type orbits in the system of two gravitational centers with variable masses and separation Trojan-type orbits in the system of two gravitational centers with variable masses and separation

Jun 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982m%26p....26..371d&link_type=abstract

Moon and the Planets, vol. 26, June 1982, p. 371-382.

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4

Lagrangian Equilibrium Points, Three Body Problem, Trojan Orbits, Asteroid Belts, Libration, Planetary Evolution

Scientific paper

Trojan-type orbits in the system of two gravitational centers with variable separation are studied within the framework of the restricted problem of three bodies. The backward numerical integration of the equations of motion of the bodies, starting in the triangular libration points L4 and L5 (reverse problem), finds the breakdown of librations as the separation decreases because of (1) the mass gain of the smaller component, and (2) an approach of the body of negligible mass to the latter up to the distance below its sphere of action with a relative velocity that is approximately equal to the escape velocity on this sphere. The breakdown of librations about L5 occurs under a mass gain of the smaller component which is considerably larger than in the case of L4. Implications are drawn for the asymmetry of the number of librators about L4 and L5 in the solar system (Greeks and Trojans). Other parameters of the libration motion near 1/1 commensurability are obtained, namely, the asymmetry of the libration amplitudes about the triangular points, as well as the value of periods and amplitudes within the limits of those for real Trojan asteroids. Trojans could be formed inside the Proto-jupiter, escaping during its intensive mass loss.

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