Physics
Scientific paper
Jan 1988
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988ltdb.conf..277p&link_type=abstract
NATO Advanced Study Institute on Long-Term Dynamical Behaviour of Natural and Artificial N-Body Systems, p. 277 - 288
Physics
Four-Body Problem: Restricted, Four-Body Problem: Minor Planets
Scientific paper
The hierarchical system of restricted problems is described as the generalization of the classical restricted problem of three bodies. This is followed by a special example consisting of two interacting asteroids as influenced by the gravitational effects of the Sun and Jupiter. This binary asteroid problem is first represented in the synodic Sun-Jupiter system as a two-plus-two-body restricted problem and the existence of a generalized Jacobian integral is shown. After this a simplified and approximate system is introduced where closed surfaces of zero velocity limit the possible range of motion of the asteroids and under certain conditions allow the analytical proof of stability of the system. This stability is equivalent to establishing analytically the possibility of existence of binary asteroids and supports the presently questionable observational findings. In addition, the analytical stability investigations describe the possible behaviour of binary asteroids and assist the observers to locate them.
Pojman J.
Szebehely Vector
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