Journal ArticleDOI
On the stability of close binaries in hierarchical three-body systems
Reads0
Chats0
TLDR
In this article, the Hill-type stability of general hierarchical three-body systems is examined analytically in the case where the total mass of the binary is small in comparison to the mass of an external body (e.g., Planet-Satellite-Sun, Planet-Planet-Star).Abstract:
The Hill-type stability (cf. closure of the zero-velocity curves in the circular restricted three-body problem) of general hierarchical three-body systems is examined analytically in the case where the total mass of the binary is small in comparison to the mass of the external body (e.g. systems of the type Planet-Satellite-Sun, Planet-Planet-Star, etc.). This is compared with results derived by Szebehely, Markellos and Roy in the Planet-Satellite-Sun case of the circular restricted three-body problem. It is demonstrated how the Hill-type stability is affected by the sense of revolution of the binary, i.e. corotational or contrarotational, and the mass ratio within the binary. The effect of the difference in longitudes of the bodies in their orbits is also examined.read more
Citations
More filters
Journal ArticleDOI
The Hill stability of the possible moons of extrasolar planets
TL;DR: In this paper, the dynamical Hill stability for a full three-body system composed of a binary moving on an inclined elliptical orbit relative to a third body where the binary mass is very small compared with the mass of the third body was derived.
Journal ArticleDOI
Stability criteria for hierarchical triple systems
TL;DR: A summary of stability criteria for hierarchical triple systems over the past few decades is given in this article, where the authors discuss the criteria that are based on the generalisation of the concept of zero velocity surfaces of the restricted three body problem, to the general case.
Journal ArticleDOI
Stability criteria for hierarchical triple systems
TL;DR: This paper discusses the criteria that are based on the generalisation of the concept of zero velocity surfaces of the restricted three body problem, to the general case and presents criteria that have to do with escape of one of the bodies.
Journal ArticleDOI
The Hill stability of binary asteroid and binary Kuiper Belt systems
TL;DR: In this article, the dynamical stability of a bound triple system composed of a binary asteroid system or Kuiper Belt binary system moving on an orbit inclined to a central third body, the Sun, is discussed in terms of Hill stability for the full three-body problem.
Journal ArticleDOI
The Hill stability of inclined small mass binary systems in three-body systems with special application to triple star systems, extrasolar planetary systems and Binary Kuiper Belt systems
TL;DR: In this article, the dynamical stability of a bound triple system composed of a small binary or minor planetary system moving on a orbit inclined to a central third body is discussed in terms of Hill stability for the full three-body problem.
References
More filters
Journal ArticleDOI
Bifurcation points in the planar problem of three bodies
TL;DR: In this paper, an analytical criterion to obtain critical values of the abifurcation point for any given masses of the participating bodies is given, where the critical value is defined by the product of the square of the angular momentum and the total energy.
Journal ArticleDOI
The effects of integrals on the totality of solutions of dynamical systems
TL;DR: In this article, regions of possible motions are established for dynamical systems possessing time-independent Hamiltonians or for systems which are reducible to that form by means of integrals of the motion using only extended point transformations.
Journal ArticleDOI
Stability criteria in many-body systems: I. An empirical stability criterion for co-rotational three-body systems
Journal ArticleDOI
Stability criteria in many-body systems
Ian W. Walker,Archie E. Roy +1 more
TL;DR: In this article, the analytical stability criterion applicable to coplanar hierarchical three-body systems was modified to give an exact representation of Hill-type stability in all such cases, and the dependence of the stability on all orbital parameters was taken into account.
Related Papers (5)
Hill Stability and Distance Curves for the General Three-Body Problem
Christian Marchal,George Bozis +1 more