The instability transition for the restricted 3-body problem. II. The hodograph eccentricity criterion

Details The instability transition for the restricted 3-body problem. II. The hodograph eccentricity criterion The instability transition for the restricted 3-body problem. II. The hodograph eccentricity criterion

May 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010a%26a...514a..19e&link_type=abstract

Astronomy and Astrophysics, Volume 514, id.A19

Astronomy and Astrophysics

Astrophysics

1

Binaries: General, Celestial Mechanics, Planetary Systems

Scientific paper

Aims: We present a new method that allows identifying the onset of orbital instability, as well as quasi-periodicity and multi-periodicity, for planets in binary systems. This method is given for the special case of the circular restricted 3-body problem (CR3BP). Methods: Our method relies on an approach given by differential geometry that analyzes the curvature of the planetary orbit in the synodic coordinate system. The centerpiece of the method consists in inspecting the effective (instantaneous) eccentricity of the orbit based on the hodograph in rotated coordinates and in calculating the mean and median values of the eccentricity distribution. Results: Orbital stability and instability can be mapped by numerically inspecting the hodograph and/or the effective eccentricity of the orbit in the synodic coordinate system. The behavior of the system depends solely on the mass ratio μ of the binary components and the initial distance ratio ρ_0 of the planet relative to the stellar separation distance noting that the stellar components move on circular orbits. Our study indicates that orbital instability occurs when the median of the effective eccentricity distribution exceeds unity. This instability criterion can be compared to other criteria, including those based on Jacobi's integral and the zero-velocity contour of the planetary orbit. Conclusions: The method can be used during detailed numerical simulations and in contrast to other methods such as methods based on the Lyapunov exponent does not require a piece-wise secondary integration of the planetary orbit. Although the method has been deduced for the CR3BP, it is likely that it can be expanded to more general cases.

Affiliated with

Also associated with

No associations

Rating

The instability transition for the restricted 3-body problem. II. The hodograph eccentricity 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. II. The hodograph eccentricity 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. II. The hodograph eccentricity criterion will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1889503