2020/11/27 by Sergey Ershkov, Sergey V. Ershkov, Ershkov, Sergey +2
Engineering · Physics and Astronomy · #Astro and Planetary Science #Cosmology and Gravitation Theories #Spacecraft Dynamics and Control #msc:70F07 #msc:70F15 #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.2012.04501
18 pages, 3 Figures; Key words: Bi-elliptic restricted problem of four bodies, Sitnikov-type solution; arXiv admin note: text overlap with arXiv:2011.05776
arxiv created 2020/12/24 · arxiv updated 2020/12/25
In this paper, we present a new ansatz for approximated solving equations of motion of the infinitesimal mass m in case of bi-elliptic restricted problem of four bodies (BiER4BP) (where three primaries M1, M2, M3 are rotating around their common centre of mass on elliptic orbits with hierarchical configuration M3 < M2 << M1). A new type of the solving procedure is implemented here to obtain the coordinates of the infinitesimal mass m. Meanwhile, the system of equations of motion has been successfully explored with respect to the existence of semi-analytical (approximated) way for presentation of the solution. We obtain as follows: 1) the solution for coordinates x, y = 0, 0 is approximately satisfied both the first and second equations of motion if we take into consideration assumption M3, M2 << M1, 2) the expression for coordinate z(f) is given by the equation of 2-nd order, which describes Sitnikov-type approximated solution. It means that test particle is moving along the z-axis, outward the common barycenter of the system (but perpendicular to the plane of the mutual rotation of all the primaries).