Secular perturbations of resonant asteroids

Astronomy and Astrophysics – Astronomy

Scientific paper

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Asteroids, Celestial Mechanics, Equations Of Motion, Long Term Effects, Orbit Perturbation, Jupiter (Planet), Neptune (Planet), Pluto (Planet), Trojan Orbits, Asteroids, Perturbations, Resonance, Astronomy, Celestial Mechanics, Motion, Orbits, Equations Of Motion, Parameters, Eccentricity, Inclination, Perihelion, Procedure, Pluto-Neptune System

Scientific paper

Secular perturbations of asteroids are derived for mean motion resonance cases under the assumptions that the disturbing planets are moving along circular orbits on the same plane and that 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 are derived for given values of two constant parameters, and the variations of the eccentricity and the inclination as functions of the argument of perihelion are graphically estimated. This method is applied to numbered asteroids with commensurable mean motions to estimate the ranges of the variations of orbital elements. The same method is also applied to the Pluto-Neptune system and the results are found to agree with those of numerical integrations and show that the argument of perihelion of Pluto librates around 90 deg.

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