Abstract
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 pointsL 4 andL 5 (reverse problem) finds the breakdown of librations as the separation decreases because of the mass gain of the smaller component and an approach of the body of negligible, mass to the latter up to the distance below its sphere of action with a relative velocity approximately equal to the escape one on this sphere. The breakdown of librations aboutL 5 occurs under the mass gain of the smaller component considerably larger than in the case ofL 4 and implications are made for the asymmetry of the number of librators aboutL 4 andL 5 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 values of periods and amplitudes within the limits of those for real Trojan asteroids. Trojans could be supposedly, formed inside the Proto-jupiter and escape during its intensive mass loss.
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Djakov, B.B., Reznikov, B.I. Trojan-type orbits in the system of two gravitational centers with variable masses and separation. The Moon and the Planets 26, 371–382 (1982). https://doi.org/10.1007/BF00941639
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DOI: https://doi.org/10.1007/BF00941639