Nonlinear Resonances Near the Earth-Moon Equilateral Libration Points

by Hans B. Schechter

Purchase Print Copy

 FormatList Price Price
Add to Cart Paperback $35.00 $28.00 20% Web Discount

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.

This report is part of the RAND Corporation Research memorandum series. The Research Memorandum was a product of the RAND Corporation from 1948 to 1973 that represented working papers meant to report current results of RAND research to appropriate audiences.

Our mission to help improve policy and decisionmaking through research and analysis is enabled through our core values of quality and objectivity and our unwavering commitment to the highest level of integrity and ethical behavior. To help ensure our research and analysis are rigorous, objective, and nonpartisan, we subject our research publications to a robust and exacting quality-assurance process; avoid both the appearance and reality of financial and other conflicts of interest through staff training, project screening, and a policy of mandatory disclosure; and pursue transparency in our research engagements through our commitment to the open publication of our research findings and recommendations, disclosure of the source of funding of published research, and policies to ensure intellectual independence. For more information, visit www.rand.org/about/principles.

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.