Other
Scientific paper
Feb 1984
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984cemec..32..137w&link_type=abstract
Celestial Mechanics (ISSN 0008-8714), vol. 32, Feb. 1984, p. 137-144.
Other
12
Celestial Mechanics, Jacobi Integral, Many Body Problem, Orbit Perturbation, Sidereal Time, Three Body Problem, Artificial Satellites, Asteroids, Circular Orbits, Comets, Gravitational Effects
Scientific paper
The circular restricted problem of three bodies is briefly described in sidereal and synodic systems using dimensional and non-dimensional variables. This dynamical system is generalized to n ≥ 2 primary bodies with masses Mi, 1 ≤ i ≤ n, interacting with arbitrary force laws. The number of bodies of small mass mα very low Mi not perturbing the primaries is increased from ν = 1 to ν ≥ 1 where 1 ≤ α ≤ ν and the minor bodies are allowed to interact with one another under arbitrary force laws. The primaries influence the motions of the minor bodies with arbitrary force laws. For the case where n = 2, ν ≥ 1, and only gravitational forces act on the system, an integral of the system is derived. It is shown that the energy integral of the general problem of N bodies and the Jacobian integral of the classical restricted problem of three bodies are limiting cases of this integral. The role of the integral in bounding the motion of the minor bodies is discussed.
Szebehely Vector
Whipple Arthur L.
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