The "Sphere of Influence" of the Moon is not really spherical
A tool often employed in the early stages of space mission design is the patched conics approximation. In this formalism, a trajectory is approximated by a sequence of two-body orbits, defined with respect to an appropriately changing primary body, according to the updated position of the spacecraft. The validity of this approach rests on the assumption that in each portion of the trajectory the acceleration of the spacecraft mostly arises from the gravitational attraction by a single body, which dominates over all the other perturbations. For instance, to an excellent degree of approximation, the motion of an interplanetary probe is mostly governed by solar gravity, except when in the immediate vicinity of a planet. The "Sphere of Influence" (SOI) of a celestial body with respect to a distant, major primary is formally defined below. At the lowest order of approximation, the SOI is a sphere centered on the secondary body, and of radius $R_S = D \, \left(\frac{m}{M}\right)^{2...