Skip to main content
SearchLoginLogin or Signup

Three-body Stability Limit at Infinite Time

Presentation #310.04 in the session Dynamical Dances in Space.

Published onOct 20, 2022
Three-body Stability Limit at Infinite Time

The long term stability limit is of interest in two-planet systems of arbitrary mutual inclinations and eccentricities. When such a system is viewed as an inner binary and an outer third body, the most important parameter for the stability of the system is the pericenter of the outer orbit measured in the units of the inner binary semi-major axis. We present an analytical expression for the smallest value of the pericenter which guarantees the stability of the system. We call this value the stability limit. We show that the stability limit is a function of time, in addition to be a being a function of the mutual inclinations and the two eccentricities. At the limit of infinite time, the expression converges to a well defined limiting value. We show by computer experiments that the infinite time limit is applicable to wide range initial orbital elements. We also discuss some interesting resonance regions in the parameter space where the stability limit is about twice as large as in the standard expression.

No comments here