Quasi-conservative Integration Method for Restricted Three-body Problem

Abstract The simplest restricted three-body problem, in which two massive points and a massless point particle attract one another according to Newton’s law of inverse squares, has pulsating Hill’s regions where the moves inside closed surrounding only points. Until now, no numerical integrator is known maintain these regions, making it challenging reproduce phenomenon gravitational capture particles. In this article, we propose second-order that preserves accurately simulate phenomenon. Our based on logarithmic Hamiltonian leapfrog method developed by Mikkola Tanikawa features parameter adjusted preserve approximation an invariant integration relation problem. We analytically numerically clarify following properties: (i) retains collinear triangular Lagrangian solutions regardless eccentricity relative orbit points, (ii) same Hill stability criterion for satellite-type motion as original (iii) conserves Jacobi integral zero eccentricity.