Using the theory of functional connections to create periodic orbits with a linear variable thrust

• Autor(a) principal: de Almeida, Allan Kardec
• Data de Publicação: 2023
• Outros Autores: Prado, Antonio F.B.A., Mortari, Daniele
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10773/38065
• topic: Two point boundary value problem; Periodic non-Keplerian orbits; Theory of functional connections; Astrodynamics; Aerospace engineering

This paper shows that the Theory of Functional Connections (TFC) can be used to find the thrust (given by a sub-optimal linear control law) required to create and maintain periodic orbits, like resonant orbits with the rotation of the Earth. Thus, the satellite will be located at the same position in the sky over the surface of the Earth every day, despite the perturbations. This facilitates the predictions of its motion and, thus, its tracking. The perturbations considered are: the J2 term of the Earth’s gravitational potential and the gravitational presence of the Sun and the Moon. The proposed approach is applied to two distinct periodic orbits. The first is an 8 hours periodic orbit while the second is a 24 hours geosynchronous periodic orbit. The fuel costs to maintain periodicity are evaluated and compared with other two methods: in the first method the perturbations are perfectly canceled by a variable thrust and in the second method a two-impulsive maneuver is applied as also obtained using TFC. Comparisons with the other two methods show that the one proposed in this paper can be used to lower the fuel costs.