The Instability Transition for the Restricted 3-Body Problem. III. The Lyapunov Exponent Criterion

Details The Instability Transition for the Restricted 3-Body Problem. III. The Lyapunov Exponent Criterion The Instability Transition for the Restricted 3-Body Problem. III. The Lyapunov Exponent Criterion

2011-06-24

arxiv.org/abs/1106.5062v1

Astronomy and Astrophysics

Astrophysics

Solar and Stellar Astrophysics

10 pages, 8 figures, 3 tables; accepted by Astronomy and Astrophysics

Scientific paper

We establish a criterion for the stability of planetary orbits in stellar binary systems by using Lyapunov exponents and power spectra for the special case of the circular restricted 3-body problem (CR3BP). The centerpiece of our method is the concept of Lyapunov exponents, which are incorporated into the analysis of orbital stability by integrating the Jacobian of the CR3BP and orthogonalizing the tangent vectors via a well-established algorithm originally developed by Wolf et al. The criterion for orbital stability based on the Lyapunov exponents is independently verified by using power spectra. The obtained results are compared to results presented in the two previous papers of this series. It is shown that the maximum Lyapunov exponent can be used as an indicator for chaotic behaviour of planetary orbits, which is consistent with previous applications of this method, particularly studies for the Solar System. The chaotic behaviour corresponds to either orbital stability or instability, and it depends solely on the mass ratio of the binary components and the initial distance ratio of the planet relative to the stellar separation distance. Our theoretical results allow us to link the study of planetary orbital stability to chaos theory noting that there is a large array of literature on the properties and significance of Lyapunov exponents. Although our results are given for the special case of the CR3BP, we expect that it may be possible to augment the proposed Lyapunov exponent criterion to studies of planets in generalized stellar binary systems, which is strongly motivated by existing observational results as well as results expected from ongoing and future planet search missions.

Affiliated with

Also associated with

No associations

Rating

The Instability Transition for the Restricted 3-Body Problem. III. The Lyapunov Exponent Criterion 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 The Instability Transition for the Restricted 3-Body Problem. III. The Lyapunov Exponent Criterion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Instability Transition for the Restricted 3-Body Problem. III. The Lyapunov Exponent Criterion will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-144446