Journal Article•
Numerical exploration of the restricted problem. VI. Hill's case: Non-periodic orbits.
About: This article is published in Astronomy and Astrophysics.The article was published on 1970-11-01 and is currently open access. It has received 123 citations till now.
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TL;DR: In this article, the authors examined the mechanisms of capture of the irregular satellites and found that none of the suggested mechanisms, including gas-drag, pull-down, and three-body capture, convincingly fit the group characteristics of irregular satellites.
Abstract: All four giant planets in the Solar system possess irregular satellites, characterized by large, highly eccentric and/or inclined orbits that are distinct from the nearly circular, uninclined orbits of the regular satellites. This difference can be traced directly to different modes of formation. Whereas the regular satellites grew by accretion within circumplanetary disks the irregular satellites were captured from initially heliocentric orbits at an early epoch. Recently, powerful survey observations have greatly increased the number of known irregular satellites, permitting a fresh look at the group properties of these objects and motivating a re-examination of the mechanisms of capture. None of the suggested mechanisms, including gas-drag, pull-down, and three-body capture, convincingly fit the group characteristics of the irregular satellites. The sources of the satellites also remain unidentified.
164 citations
TL;DR: In this article, the authors focus on the solar system cases in which chaotic solutions of Newton's equations are important, such as chaotic rotation and orbital evolution, and suggest that chaotic orbital evolution is of fundamental importance to an accounting for the Kirkwood gaps in asteroid distribution and for the phase space boundary of the chaotic zone at the 3/1 mean motion commensurability with Jupiter.
158 citations
TL;DR: In this paper, the authors define the limiting case of the planar three-body problem when two of the masses are very small and describe analytic developments for encounter-type solutions, in which the two small bodies approach each other from an initially large distance, interact for a while, and separate.
Abstract: Hill's problem is defined as the limiting case of the planar three-body problem when two of the masses are very small. This paper describes analytic developments for encounter-type solutions, in which the two small bodies approach each other from an initially large distance, interact for a while, and separate. It is first pointed out that, contrary to prevalent belief, Hill's problem is not a particular case of the restricted problem, but rather a different problem with the same degree of generality. Then we develop series expansions which allow an accurate representation of the asymptotic motion of the two small bodies in the approach and departure phases. For small impact distances, we show that the whole orbit has an adiabatic invariant, which is explicitly computed in the form of a series. For large impact distances, the motion can be approximately described by a perturbation theory, originally due to Goldreich and Tremaine and rederived here in the context of Hill's problem.
156 citations
TL;DR: In this paper, the authors considered a three-body problem consisting of the Sun, an asteroid, and an infinitesimal particle initially placed about the asteroid and found that the starting distance from the asteroid is varied, a fairly abrupt transition between trapped and untrapped objects occurs, and defined the distance where the transition occurs to be the critical distance.
155 citations
TL;DR: In this article, the authors studied the dynamics of the three-body problem when two objects are in the 1:1 mean motion commensurability and can experience close encounters, and three orbit families are relevant to the dynamics: horseshoe orbits, passing orbits, and retrograde satellite orbits.
149 citations