Stability of Motions of Asteroids
Secular perturbations of asteroids are derived under assumptions that the disturbing planets are moving along circular orbits on the same plane and, for mean motion resonance cases, that the critical arguments are fixed at stable equilibrium points. Under these assumptions the equations of motion are reduced to those of one degree of freedom with the energy integral. Then equi-energy-curves on (2g — X) plane (g and X being respectively, the argument of perihelion and (1-e2)½) are derived for given values of the two constant parameters, the semi-major axis and Θ=(1-e2)½cosi, and the variations of the eccentricity and the inclination as functions of the argument of perihelion are graphically estimated. In fact this method is applied to all the numbered asteroids to estimate the ranges of the variations of orbital elements. By comparing the dynamical properties of the asteroids numerically derived with those of periodic comets, it is concluded that the energy values which are the averaged Hamiltonian are generally lower for the asteroids than those for the comets, and, therefore, that for most of the asteroids any very close approach to Jupiter can be avoided by various mechanisms, one of which is due to the properties derived by the present secular perturbation theory. By such a dynamical property the difference between the motions of asteroids and comet types is defined.
KeywordsEccentric Orbit Secular Term Stable Equilibrium Point Resonant Case Main Belt
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