The construction of intermediate orbits of the asteroids of the Hecuba family with an electronic computer.
Abstract
A method is described for constructing the solutions of the differential equations of motion for the restricted twodimensional circular threebody problem applied to asteroids of the Hecuba group on the assumption that the average motions of an asteroid and Jupiter are commensurable or nearly so. An averaging scheme is described, and a meansquare approximation of the first integrals of the averaged problem is obtained with the aid of trigonometric polynomials in a multiple anomaly (D). For each asteroid, explicit expressions for the averaged elements and the time are obtained as functions of D. The formulas obtained serve as the intermediate orbit for constructing the perturbation theory of resonance asteroids.
 Publication:

Akademiia Nauk Azerbaidzhanskoi SSR Doklady
 Pub Date:
 1975
 Bibcode:
 1975DoAze..31...16S
 Keywords:

 Asteroids;
 Orbit Calculation;
 Solar Orbits;
 Three Body Problem;
 Computer Techniques;
 Equations Of Motion;
 Numerical Integration;
 Orbit Perturbation;
 Perturbation Theory;
 Astronomy