Search for and Study of Nearly Periodic Orbits in the Plane Problem of Three Equal-Mass Bodies

Details Search for and Study of Nearly Periodic Orbits in the Plane Problem of Three Equal-Mass Bodies Search for and Study of Nearly Periodic Orbits in the Plane Problem of Three Equal-Mass Bodies

Sep 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005astl...31..634m&link_type=abstract

Astronomy Letters, vol. 31, Issue 9, p.634-644

Astronomy and Astrophysics

Astronomy

Celestial Mechanics - Periodic Orbits - Three-Body Problem

Scientific paper

We analyze nearly periodic solutions in the plane problem of three equal-mass bodies by numerically simulating the dynamics of triple systems. We identify families of orbits in which all three points are on one straight line (syzygy) at the initial time. In this case, at fixed total energy of a triple system, the set of initial conditions is a bounded region in four-dimensional parameter space. We scan this region and identify sets of trajectories in which the coordinates and velocities of all bodies are close to their initial values at certain times (which are approximately multiples of the period). We classify the nearly periodic orbits by the structure of trajectory loops over one period. We have found the families of orbits generated by von Schubart’s stable periodic orbit revealed in the rectilinear three-body problem. We have also found families of hierarchical, nearly periodic trajectories with prograde and retrograde motions. In the orbits with prograde motions, the trajectory loops of two close bodies form looplike structures. The trajectories with retrograde motions are characterized by leafed structures. Orbits with central and axial symmetries are identified among the families found.

Affiliated with

Also associated with

No associations

Rating

Search for and Study of Nearly Periodic Orbits in the Plane Problem of Three Equal-Mass Bodies 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 Search for and Study of Nearly Periodic Orbits in the Plane Problem of Three Equal-Mass Bodies, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Search for and Study of Nearly Periodic Orbits in the Plane Problem of Three Equal-Mass Bodies will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1302006