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.