Comparisons between the circular restricted three-body and bi-circular four body problems for transfers between the two smaller primaries

Important properties of the dynamics of a spacecraft can be obtained from the Circular Restricted Three Body Problem and the Bi-Circular Bi-planar Four Body Problem. In this work, both systems are compared under the perspective of the costs involved in a transfer between the smaller primaries. An analytical approach shows several properties of the perturbation due to the gravity of the Sun and the motion of the smaller primaries around it over a spacecraft in the region of interest, like its behavior at and around the barycenter or at any point in a circle around the Sun. The costs involved in transfers between the smaller primaries are numerically evaluated and analyzed using the newly developed Theory of Functional Connections. The results show that the influence of this perturbation over the costs is significant for systems like the Sun–Earth–Moon or Sun–Mars–Phobos. On the other hand, it is also shown that this influence may be negligible for other very different systems, like the Sun–Saturn–Titan or Sun–Ida–Dactyl. Maps of perturbation are drawn in the region of interest, which can be used for mission designers. Finally, a new approach to describe the influence of the Sun over the tides of the smaller primaries is proposed under the Four Body Problem model. © 2022, The Author(s)

Applying the perturbative integral in aeromaneuvers around Mars to calculate the cost

The perturbative integral method was applied to quantify the contribution of external forces during a specific interval of time in trajectories of spacecraft around asteroids and under the Luni-solar influence. However, this method has not been used to quantify the contributions of drag in aerocapture and aerobraking. For this reason, the planet Mars is selected to apply this method during an aerogravity-assisted maneuver. Several trajectories are analyzed, making use of a drag device with area to mass ratios varying from 0.0 to 20.0 m2/kg, simulating solar sails or de-orbit devices. The mathematical model is based in the restricted three-body problem. The use of this maneuver makes it possible to obtain the variations of energy in the trajectory, replacing expensive maneuvers based on fuel consumption. To observe the effects of the maneuvers, different values of pericenter velocity and altitude were selected for prograde and retrograde orbits. The innovation of this research is the application of an integral method to quantify the delta-V of the aero gravity maneuver, comparing the cost of the maneuver with the traditional methods of space propulsion. The results allow the identification of orbits with conditions to capture, and the perturbative maps show the velocity variations. © 2022, The Author(s)