Constructive analytical solution of the evolution hill problem |
| |
| Authors: | M A Vashkov’yak |
| |
| Institution: | 1.Keldysh Institute of Applied Mathematics,Russian Academy of Sciences,Moscow,Russia |
| |
| Abstract: | A new analytical solution of the system of differential equations describing secular perturbations and long-period solar perturbations
of mean orbits of outer satellites of giant planets was obtained. As distinct from other solutions, the solution constructed
using von Zeipel’s method approximately takes into account, in the secular part of the perturbing function, the totality of
fourth order with respect to the small parameter m of the ratio of the mean motions of the primary planet and the satellite. This enables us to describe more accurately the
evolution of satellite orbits with large apocentric distances, which in the course of evolution may exceed the halved radius
of the Hill sphere of the planet with respect to the Sun. Among these are the orbits of the two outermost Neptunian satellites
N10 (Psamathe) and N13 (Neso). For these satellites, the parameter m amounts to 0.152 and 0.165, respectively. Different from a purely analytical solution, the proposed solution requires preliminary
calculations for each satellite. More precisely, in doing so, we need to construct some simple functions to approximate more
complex ones. This is why we use the phrase “constructive analytical.” To illustrate the solution, we compare it with the
results of the numerical integration of the strict motion equations of the satellites N10 and N13 over time intervals 5–15
thousand years. |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
