Geologic results from the lunar precursor probes.

Abstract

we need to use only one of the arbitrary terms (note that mo and UQ are not arbitrary), setting all other arbitrary terms equal to zero. The choice depends on the requirement that the coefficient of the power of IJL should be near but not much greater than unity. For a mixed boundary-value problem, there are six integrals of motion near the moon: h, I, i, 6, a*, and TQ + /XT; and six near the earth: he = — p, le = n\, i, co, 0, and TQ + fjLTi. Subject to the necessary constraints for a moon-to-earth trajectory, a specified combination of six of the integrals will determine the remaining six (but perhaps not uniquely nor to the same order of accuracy). In general, the method for finding the six unknown integrals involves the simultaneous solution of Eqs. (35-43), (56-58), (73), and (lla) of Ref. 3, subject to the conditions of Eqs. (20) and (22). Since each particular combination of the specified integrals requires a separate analysis, it is not possible to summarize the results as was done for the initial-value problem. References 1 Lagerstrom, P. A. and Kevorkian, J., Trajectories in the Restricted Three-Body Problem/' Journal de Mecanique, Vol. 2, 1963, pp. 189-218. 2 Lagerstrom, P. A. and Kevorkian, J., Numerical Aspects of Valid Asymptotic Approximations for a Class of Trajectories in the Restricted Three-Body Problem/ AIAA Progress in Aeronautics and Astronautics: Celestial Mechanics and Astrodynamics, edited by V. G. Szebehely, Vol. 14, Academic Press, New York, 1964, pp. 3-33. 3 Lagerstrom, P. A. and Kevorkian, J., Nonplanar Earthto-Moon Trajectories in the Restricted Three-Body Problem/' AIAA Journal, Vol. 4, No. 1, Jan. 1966, pp. 149-152. 4 Kevorkian, J. and Lancaster, J. E., An Asymptotic Solution for a Class of Periodic Orbits of the Restricted Three-body Problem/' Astronomical Journal (to be published). 5 Shi, Y. Y. and Eckstein, M. C., Uniformly Valid Asymptotic Solution of Non-Planar Earth-to-Moon Trajectories in the Restricted Four-Body Problem, Astronomical Journal, Vol. 72, 1967, p. 685.