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This article presents basic procedures for calculating the trajectory of a spaceship that uses only the Earth's atmosphere to reduce its speed, allowing it to land on the Earth's surface successfully. The first flight of the {\tt ARTEMIS} program, which took place from November 16 to December 11 2022, was used as a template for the calculations. All calculations are performed in the symbolic algebra program Maple. To simplify the calculations, forces that have a less significant impact on the shape of the trajectory, such as the gravitational influence of the Sun and Moon, the rotation of the Earth, and its non-spherical shape, were neglected. To conserve space, only the essential components of the solution are shown, given the intensive calculations involved. The commands used to produce the graphics are not included. (English) |
