Tangential velocity constraint for orbital maneuvers with Theory of Functional Connections.

Maneuvering a spacecraft in the cislunar space is a complex problem, since it is highly perturbed by the gravitational influence of both the Earth and the Moon, and possibly also the Sun. Trajectories minimizing the needed fuel are generally preferred in order to decrease the mass of the payload. A classical method to constrain maneuvers is mathematically modeling them using the Two Point Boundary Value Problem (TPBVP), defining spacecraft positions at the start and end of the trajectory. Solutions to this problem can then be obtained with optimization techniques like the nonlinear least squares conjugated with the Theory of Functional Connections (TFC) to embed the constraints, which recently became an effective method for deducing orbit transfers. In this paper, we propose a tangential velocity (TV) type of constraints to design orbital maneuvers. We show that the technique presented in this paper can be used to transfer a spacecraft (e.g. from the Earth to the Moon) and perform gravity assist maneuvers (e.g. a swing-by with the Moon). In comparison with the TPBVP, solving the TV constraints via TFC offers several advantages, leading to a significant reduction in computational time. Hence, it proves to be an efficient technique to design these maneuvers.

Gravitational perturbations correlated with the asteroid kinetic impact deflection technique.

This paper presents the use of the kinetic impact technique to deflect asteroids that may present some risk of collision with Earth. Within the work to be developed here, we intend to evaluate in more detail the possibility to deflect the orbit of the asteroid 101955 Bennu by applying variations in its velocity ([Formula: see text]v) at different positions along its orbital period and measuring effects of close encounters with planet Earth. We will see that, in a relatively long period of time, the asteroid has several close encounters with the planet, thus suffering a natural gravitational perturbation. With the application of the impulses, the relative distances change, causing variations in the energy of the asteroid and a large variation in the relative distance between the asteroid and Earth over a long period after the impulse. We present results related to the magnitude of the impulse applied, which is important because its defines the mass and velocity of the impactor to be considered. Then, we mapped the positions of the impulses along a period of the orbit of the asteroid. We finish by explaining what happens to the orbit of the asteroid during the periods of gravitational perturbation, since the close encounters amount to "Swing Bys" that intensify the variations of the relative distances between the bodies after the impulse is applied.