An Asymptotic Solution for the Trojan Case of the Plane Elliptic Restricted Problem of Three Bodies
Abstract
The planar motion of a Trojan asteroid is considered within the framework of the elliptic restricted threebody problem. The solution is derived asymptotically to second order taking the square root of the JupiterSun mass ratio and the orbital eccentricity of Jupiter as first order quantities. The results are given in explicit form for the coordinates as functions of the true anomaly of Jupiter including both short and long periodic terms resulting from the orbital accentricity of Jupiter.
 Publication:

Celestial Mechanics
 Pub Date:
 April 1977
 DOI:
 10.1007/BF01228428
 Bibcode:
 1977CeMec..15..367E
 Keywords:

 Asteroids;
 Equations Of Motion;
 Orbital Mechanics;
 Three Body Problem;
 Trojan Orbits;
 Asymptotic Methods;
 Eccentricity;
 Jupiter (Planet);
 Long Term Effects;
 Mass Ratios;
 Solar Orbits;
 Astronomy