On final evolutions in the restricted planar parabolic three-body problem

Details On final evolutions in the restricted planar parabolic three-body problem On final evolutions in the restricted planar parabolic three-body problem

May 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006cemda..95..173a&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 95, Issue 1-4, pp. 173-200

Astronomy and Astrophysics

Astronomy

1

Restricted Three-Body Problem, Final Evolutions, Heteroclinic Orbits

Scientific paper

In this paper, we prove the existence of special type of motions in the restricted planar parabolic three-body problem, of the type exchange, emission-capture, and emission-escape with close passages to collinear and equilateral triangle configuration, among others. The proof is based on a gradient-like property of the Jacobian function when equations of motion are written in a rotating-pulsating reference frame, and the extended phase space is compactified in the time direction. Thus a phase space diffeomorphic to [-π/2, π/2]× {mathbb C}backslash \{-μ_1, μ_2\}× {mathbb C} -coordinates (θ, ζ, ζ') is obtained with the boundary manifolds θ = ± π/2 corresponding to escapes of the binaries when time tends to ± ∞. It is shown there exists exactly five critical points on each boundary, corresponding to classic homographic solutions. The connections of the invariant manifolds associated to the collinear configurations, and stable/unstable sets associated to binary collision on the boundary manifolds, are obtained for arbitrary masses of the primaries. For equal masses extra connections are obtained, which include equilateral configurations. Based on the gradient-like property, a geometric criterion for capture is proposed and is compared with a criterion introduced by Merman (1953b) in the fifties, and an example studied numerically by Kocina (1954).

Affiliated with

Also associated with

No associations

Rating

On final evolutions in the restricted planar parabolic three-body problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On final evolutions in the restricted planar parabolic three-body problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On final evolutions in the restricted planar parabolic three-body problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1005794