Showing papers on "Trojan published in 1970"

The Trojan Manifold — Survey and Conjectures

Abstract: Recent results concerning the families of periodic orbits emanating from the triangular equilibrium L 4 are interpreted in an attempt to establish the evolution of these manifolds as the mass ratio varies from Routh’s critical value down to its value in the system sun-jupiter.

The Planar Motion of a Trojan Asteroid

Abstract: The planar motion of an asteroid in an orbit close to that of Jupiter is considered within the framework of the restricted circular three-body problem. The solution is derived asymptotically to second order using the two-variable expansion procedure for the case of small Jupiter-sun mass ratio. It is shown that the solution derived under the assumption of small Jupiter-sun mass ratio becomes singular for orbits that approach Jupiter. The nature of the singularity is exhibited as a guide for future work valid for this case. The results are given in explicit form for the coordinates as functions of time including both short and long periodic terms. Finally, the present solution is specialized to the family of long periodic Trojan orbits about the sun-Jupiter libration points.

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.

The “Trojan Relay” as a Method of Ensuring Uninterrupted Radio Communication Throughout the Solar System

Abstract: Publisher Summary This chapter explains the Trojan relay as a method of ensuring uninterrupted radio communication throughout the solar system. The Trojan relay principle embodies in its concept a number of distinct and separate features. Primarily, it is a twin-satellite system in which both satellites are uniquely stationed in space in regard to the planet they serve. The round-the-clock ability to contact a spacecraft or a ground station on another world is the ability that is clearly the most significant attribute of the Trojan relay principle. The twin-satellite system has another benefit in that it may be used to circumvent the effects of solar occulation of a distant signal. Throughout the year, as the earth moves round the sun, an area of the sky behind the sun is progressively blotted from view. Though in itself not a large area, it lies square to the ecliptic plane, itself the preferred plane for space flight trajectories. It also moves relatively slowly. Hence, during a blind period, which could well last several days, weak signals emanating from a source behind the sun could be severely attentuated, if not blocked altogether, by an active corona equivalent perhaps to as much as three solar diameters. Inevitably, this could lead to a hiatus in communication with possible dire effects if it happened to coincide with an emergency. In such a situation, the Trojan relays deployed either side of the earth, would both be well clear of solar interference that may temporarily obscure direct communication from the earth. The chapter reviews Trojan relay design concept and potential disadvantages of the Trojan relay system.