Minor Planets on Commensurable Orbits with Approaches to Jupiter

Abstract

1. It is well known, that the Trojan planets avoid close approaches to Jupiter by a mechanism of libration, although parts of their orbits are very close to the orbit of Jupiter. The difference of the longitudes of a Trojan and Jupiter librates in such a way, that it does not come close to 0^°. Belyaev and Tchebotarev [1] have recently investigated the orbital motion of 14 Trojans and of 40 other interesting minor planets by numerical integrations extended over an interval of 400 years. They find the minimum distance of a Trojan to Jupiter as 2.6 AU, while in the contrary (944) Hidalgo can approach Jupiter to a distance of 0.4 (AU). Among 20 planets of the Hilda group and (279) Thule, the closest encounter with Jupiter occurs in case of (334) Chicago (1.1 AU). The planet Chicago has a small orbital eccentricity, while other planets in the Hilda group have much larger eccentricities. Since these planets have also a large mean distance from the sun, some of them come close to the orbit of Jupiter, if they pass the aphelion of their orbit. In spite of this, there are no very close encounters with Jupiter in such a case. The planets in the Hilda group are characterized by a mean motion which is nearly commensurable to that of Jupiter according to the commensurability ratio $\frac{3}{2}$. The near commensurability allows a mechanism of libration, which acts in the more eccentric cases among the orbits. As a consequence of this mechanism, a conjunction of the minor planet with Jupiter takes only place, if the minor planet is not too far from the perihelion of its orbit. In this way the minor planet avoids very close encounters with Jupiter.