Nonlinear Resonances Near the Earth-Moon Equilateral Libration Points
An application of Hamiltonian mechanics to the three-dimensional nonlinear stability analysis of a body at the libration points L4 and L5 about 245, 000 miles from both the Earth and the Moon, in the presence of the solar field. The objective was to determine if any stable periodic orbits are possible at either point. Contrary to the prediction of classical linear stability analysis disregarding the effect of the Sun, one stable equilibrium solution is found: a clockwise coplanar elliptic orbit around L4 with a major axis about 120,000 miles long oriented at right angles to the line from Earth to L4. For orbital stability, the orbit must be traversed at a rate very near the particle's faster natural coplanar frequency; the maximum permissible amplitude of the slower orbital mode is about 2450 miles. Of particular interest, the particle's motion is synchronized with the motion of the Sun as it appears in the rotating reference frame.