An invariant relation in the elliptic restricted problem of three bodies with an application to Trojan asteroids
Abstract
An invariant relation generalizing the Jacobi integral to the elliptic restricted three body problem is derived on the basis of the classical perturbation theory and by making use of the energy and angular momentum integrals. But the relation contains a nonintegrable term becoming integrable only in a few special cases. In the case of perturbed triangular solutions the relation reduces to an approximate integral valid in the vicinity of L1 and L5. In case of a small mass ratio of primaries the relation is reducible to another approximate integral valid for planetarytype motions. In the limit of zero orbital eccentricity of the primaries the relation yields the Jacobi integral. The approximate integral for the perturbed triangular solutions is applied to the case of the SunJupiterTrojan Asteroid system and reduced to the ecliptic as a reference plane to make contact with observations, allowing the Jacobi constant J to be calculated to four decimals for any Trojan.
 Publication:

Ph.D. Thesis
 Pub Date:
 1978
 Bibcode:
 1978PhDT.........1V
 Keywords:

 Asteroids;
 Elliptic Functions;
 Jacobi Integral;
 Three Body Problem;
 Trojan Orbits;
 Approximation;
 Celestial Mechanics;
 Orbit Perturbation;
 Perturbation Theory;
 Planetary Orbits;
 Solar Orbits;
 Astrophysics