Analytical solutions to the problem of optimizing trajectories in the gravitational field of a spheroidal planet

• Published in: AIP conference proceedings 2024-06, Vol.3119 (1)
• Main Authors: Korshunova, N. A., Ruzmatov, M. I.
• Format: Article
• Language: English
• Subjects: Exact solutions; Gravitational fields; Spheroids; Symmetry; Thrust; Trajectory analysis; Trajectory optimization; Vectors (mathematics)
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/5.0214866

The problem of determining the analytical solutions of the problem of optimizing the trajectories of a point (the center of mass of a spacecraft) in the areas of intermediate thrust in the gravitational field of an axisymmetric spheroidal planet is considered. The conditions for using the potential of the field of two fixed centers in the construction of the gravitational potential of the planet are found. Particular solutions obtained for the problem of minimizing the characteristic velocity in the case of a gravitational field of two fixed centers are applied to determine the solution in the case of a point moving in the gravitational field of an axisymmetric spheroidal planet. The found active areas belong to circular trajectories, the planes of which are perpendicular to the line of centers. The thrust vector lies in the plane normal to the trajectory. The values describing the obtained sections depend on the initial position of the point, on the distance to the axis of symmetry, and on the position of the trajectory plane. For specific values of the position of the trajectory plane, a graphical analysis of the dependences of the quantities characterizing the direction and magnitude of the thrust force on the distance to the axis of symmetry was carried out. The points where the thrust is reversed along the radial and transversal components of the basis vector are determined.