Simple mass distribution for the lunar potential.

A set of twenty-one point masses gravitationally equivalent to the L1 lunar potential model is presented. By construction, the equivalence is valid only in a region of space 'sampled' by Apollo spacecraft. That region is taken to be a finite, torus-shaped shell. When used in place of the L1 model for Apollo 12 lunar orbit determination, the solution set gives spacecraft positions identical to within about 100 m. The solution is developed in two steps: first the L1 potential is examined to determine favorable mass locations, and then the mass values are computed to force an optimum matching of the L1 potential. Therefore the solution set is 'artificial.' It is related to the moon's actual mass distribution only in its similar gravitational effects in a limited region of space.