Families of Asymmetric Periodic Orbits in the Restricted Three-body Problem

Details Families of Asymmetric Periodic Orbits in the Restricted Three-body Problem Families of Asymmetric Periodic Orbits in the Restricted Three-body Problem

Oct 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008em%26p..103...25p&link_type=abstract

Earth, Moon, and Planets, Volume 103, Issue 1-2, pp. 25-42

Other

1

Asymmetric Orbit, Critical Orbit, Homoclinic Orbit, Levi-Civita Regularization, Periodic Orbit, Restricted Three-Body Problem

Scientific paper

This paper studies the asymmetric solutions of the restricted planar problem of three bodies, two of which are finite, moving in circular orbits around their center of masses, while the third is infinitesimal. We explore, numerically, the families of asymmetric simple-periodic orbits which bifurcate from the basic families of symmetric periodic solutions f, g, h, i, l and m, as well as the asymmetric ones associated with the families c, a and b which emanate from the collinear equilibrium points L 1, L 2 and L 3 correspondingly. The evolution of these asymmetric families covering the entire range of the mass parameter of the problem is presented. We found that some symmetric families have only one bifurcating asymmetric family, others have infinity number of asymmetric families associated with them and others have not branching asymmetric families at all, as the mass parameter varies. The network of the symmetric families and the branching asymmetric families from them when the primaries are equal, when the left primary body is three times bigger than the right one and for the Earth Moon case, is presented. Minimum and maximum values of the mass parameter of the series of critical symmetric periodic orbits are given. In order to avoid the singularity due to binary collisions between the third body and one of the primaries, we regularize the equations of motion of the problem using the Levi-Civita transformations.

Affiliated with

Also associated with

No associations

Rating

Families of Asymmetric Periodic Orbits in the Restricted 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 Families of Asymmetric Periodic Orbits in the Restricted Three-body Problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Families of Asymmetric Periodic Orbits in the Restricted Three-body Problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1699766