It is considered the problem of the spaceship descending on the Moon (cosmic body without atmosphere) with spending a minimum amount of the fuel. The mathematical model represents an optimal control problem. It’s solved by application of the Lagrange principle and the maximum principle of Pontreaghin. The investigation of the problem with Lagrange method it is difficult because it needs application of numerical methods with a high precision and knowledge in several fields of mathematics and physics, also. However we obtain numerical results that illustrates the possibility for the cosmic ship to descend, respecting the proposed beginning requirements (the initial mass of fuel, height, velocity, etc.). It is presented the program for lunar descending simulation process in Mathematica 7.0. The formulas and numerical results, obtained during the theoretical analysis of the problem, are program fundamentals.