MOTION OF THE FRAGMENTS OF BINARY COMETS AND ASTEROIDS
Yu. A. Chernetenko
Institute of Theoretical Astronomy of RAS,
nab.Kutuzova, 10, Saint-Petersburg, 191187, Russia
The aim of this paper is to derive the averaged equations of
the motion of the fragments of a binary small body, a comet or an
asteroid, taking into account its heliocentric orbital motion. The
small body is supposed to consist of two fragments which are mass
points attracting one another. The motion of the fragments is
perturbed by the attraction of a third mass point, the Sun.
Basic assumptions are the following.
a) The ratio of the mutual fragment distance, r, to the
heliocentric distance of the binary body, d, is small, and
the expansion of the perturbing function R in terms of the
r/d parameter is restricted with the terms containing the
second and the third harmonics.
b) The period of the orbital revolution of fragments is small as
compared with the period of the orbital revolution of the
perturbing body, and within one revolution of the fragments
around their centre of masses the perturbing function is the
linear function of the mean anomaly of the third body.
The lawfulness of this approach is controlled by numerical
intergation of the averaged and nonaveraged equations. The formulae
obtained are compared with the formulae by Lidov M.L. [1].
[1] Lidov M.L.,1962. The evolution of orbits of artificial satellites
of planets under the action of gravitational perturbations of
external bodies. Planet. Space Sci., Vol.9, pp.719-759.