Optimal Guidance for Quasi‐planar Lunar Ascent

The minimum‐time controls (thrust pitch angle and thrust yaw angle) for the three‐dimensional transfer of a constant‐thrust rocket from one state to another over a flat moon are used to develop guidance laws for operation over a spherical moon. The objective is to evaluate the effect of making approximations on the size of the thrust pitch angle on the suitability of the resulting control law as a guidance law. After assuming small out‐of‐plane motion (small yaw angle), three pitch angle control laws (exact, first‐order, and zeroth‐order) are developed. The three laws are employed in the sample and hold guidance of a lunar ascent vehicle. All three laws satisfy the final conditions and give essentially the same pitch and yaw control histories. Since the zeroth‐order law can be obtained completely analytically (no iteration processes), it merits consideration for ascent guidance.