Analysis of the trajectory of spacecraft return from the lunar surface to a given region of the Earth

The paper describes a method developed for designing the trajectory of a spacecraft flight from the lunar surface to a given area of the Earth’s surface and analyzes a single-pulse flight scheme, in which the trajectory of a take-off lunar rocket is approximated by a single velocity pulse. The characteristics of the spacecraft entry into the Earth’s atmosphere are chosen so as to ensure that the conditions along the entry corridor during the ballistic entry are met and to ensure the landing of the reentry vehicle at a given point on the Earth’s surface. The criterion for optimizing the trajectory of the spacecraft return to the Earth is considered to be the value of the impulse that provides the spacecraft launch from the lunar surface. The method relies on the analysis of an auxiliary problem, the solution of which makes it possible to estimate the main properties of the investigated maneuver and find an initial approximation for the selected characteristics of the optimized trajectory.