The applicability of evolutions obtained from linearized averaged resonant equations with non-gravitational effects for dynamics of dust particles at a solution of resonant condition
Year: 2015
Type: preprint
Abstract: The linearzition solution of averaged resonant equations for planar circular restricted three-body problem with non-gravitational effect is derived. The averaged resonant equations are derived from Lagrange's planetary equations with added terms in order to include of the non-gravitational effects. The derived solution depends on that whether the non-gravitational effects act rotationally symmetrically around the star. The solution has the standard form with time dependence in exponential, quadratic, linear and constant terms. It is investigated how well the linearization solution describes real solution obtained from an equation of motion by a comparison of frequency found analytically and numerically. Since the differential equations describing the evolution in the mean motion resonance are averaged, the applicability of the linearization solution depends on the averaging. The assumption used in the derivation of the averaged resonant equations is that the orbit of dust particle does not change during of the averaging. The assumption implies for the mean motion resonances that the linearization solution describes the real evolution with best accordance close to the solution of resonant condition ($da / dt$ $=$ 0). At the solution of resonant condition is the semimajor axis maximal or minimal and the resonant angular variable has approximately linear time dependence in the libration period. The variations of other orbital elements at the solution of resonant condition shifts the best accordance from the maxima or mimima of the semimajor axis. If the initial condition are chosen close to the resonant condition, then practically all simple oscillatory evolutions can be suitable well approximated. Due to this property frequencies of stationary solutions can be correctly determined from the linearization solution.
Source: arXiv (Cornell University)
Author: P. Pástor
Language: English
Subfield: Aerospace Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2784375955