Physics – Accelerator Physics
Scientific paper
Mar 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987cemec..42..355h&link_type=abstract
Celestial Mechanics, Volume 42, Issue 1-4, pp. 355-368
Physics
Accelerator Physics
Scientific paper
In this article we treat analytically the problem of finding stability limits ofP-type orbits (=direct nearly circular orbits surrounding both primaries) in double stars. The model used is the circular restricted three body problem; in that sense the results are not valid for binaries in eccentric orbits. But as the chosen model is often used in dynamical descriptions of the problem we can compare our results with other ones derived in earlier studies with semianalytical or just numerical methods. Our stability analysis uses known and well established methods of nonlinear dynamics; they are especially used with great success in accelerator physics. The two methods, namely first the semi-analytical one and second the analytical one, are described in all detaila. In the first one the unknown planetary orbit has to be substituted by a circular reference orbit in the equations of motion; this leads to linear second order differential equations. These Hill type differential equations are then analyzed according to the properties of the trace of the transfer matrix. In the second method the frequency of the reference orbit is varied according to the nonlinear perturbations and two Mathieu equations are derived. They are now also analyzed according to their stability properties. Finally stability limits of radii of nearly circular planetary orbits are derived as functions of the mass parameters of the primaries. The results are now compared with existing studies of the problem in question for the whole range of the mass parameters μ of the primaries. It comes out that for small mass parameters the analytic expression is rather accurate. For the range between 0.1 and 0.5 the limiting critical orbit seems to be underestimated compared to existing results and our own numerical integrations. It is a good confirmation of the validity of the method that we observe the appearance of a small instability strip well inside the stable zone found also by other people.
Dvorak Rudolf
Hagel Johannes
No associations
LandOfFree
An Analytical Study of Stable Planetary Orbits in the Circular Restricted 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 An Analytical Study of Stable Planetary Orbits in the Circular Restricted Problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An Analytical Study of Stable Planetary Orbits in the Circular Restricted Problem will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1454838