A maneuver called "Aero-Gravity Assisted" is known in the literature to increase the energy gains given by a close approach between a spacecraft and a planet using the atmosphere of the planet. In a sequence of studies related to this problem, the present paper studies close approaches between a spacecraft and the Earth, in situations where the passage is close enough to the surface of the Earth such that the spacecraft crosses its atmosphere. The dynamical model considers the atmosphere of the Earth, in terms of drag and lift, the gravitational fields of the Earth and the Sun, assumed to be points of mass, and the spacecraft. The Earth and the Sun are assumed to be in circular coplanar orbits around their common center of mass. The equations of motion are the ones given by the circular planar restricted three-body problem with the addition of the forces generated by the atmospheric drag and lift. The primary objective is to map the variations of energy of the orbits of the spacecraft due to this close approach. The results show how the atmosphere affects the trajectory of the spacecraft, generating situations where the variation of energy changes sign with respect to the gravity part of the maneuver or where they have a zero net result, based in the equilibrium

This paper considers the problem of out of plane orbital maneuvers for station keeping of satellites. The main idea is to consider that a satellite is in an orbit around the Earth and that it has its orbit is disturbed by one or more forces. Then, it is necessary to perform a small amplitude orbital correction to return the satellite to its original orbit, to keep it performing its mission. A low thrust propulsion is used to complete this task. It is important to search for solutions that minimize the fuel consumption to increase the lifetime of the satellite. To solve this problem a hybrid optimal control approach is used. The accuracy of the satisfaction of the constraints is considered, in order to try to decrease the fuel expenditure by taking advantage of this freedom. This type of problem presents numerical difficulties and it is necessary to adjust parameters, as well as details of the algorithm, to get convergence. In this versions of the algorithm that works well for planar maneuvers are usually not adequate for the out of plane orbital corrections. In order to illustrate the method, some numerical results are presented.

The main goal of the present paper is to study the lifetime of orbits around moons that are in elliptic motion around their parent planet. The lifetime of the orbits is defined as the time the orbit stays in orbit around the moon without colliding with its surface. The mathematical model used to solve this problem is the second order expansion of the potential of the disturbing planet, assumed to be in an elliptical orbit. The results are presented in maps showing the lifetime of the orbit as a function of its initial inclination and eccentricity. The only perturbation acting on the orbit of the spacecraft is assumed to be the gravity of the planet, so the problem is solved by studying the orbital evolution of the spacecraft perturbed by a third body in an elliptical orbit. The region of inclination above the critical value of the third-body perturbation (around 63 • ) is studied, since below that value the orbits survive for a long time. The influence of the eccentricity of the primaries is also investigated, assuming a hypothetical system that has the same mass parameter and sizes of the Earth-Moon system, but the eccentricity can be in the range 0.0-0.2.

Space missions to visit small bodies of the Solar System are important steps to improve our knowledge of the Solar System. Usually those bodies do not have well known characteristics, as their gravity field, which make the mission planning a difficult task. The present paper has the goal of studying orbits around the triple asteroid 2001SN 263 , a Near-Earth Asteroid (NEA). A mission to this system allows the exploration of three bodies in the same trip. The distances reached by the spacecraft from those three bodies have fundamental importance in the quality of their observations. Therefore, the present research has two main goals: (i) to develop a semi-analytical mathematical model, which is simple, but able to represent the main characteristics of that system; (ii) to use this model to find orbits for a spacecraft with the goal of remaining the maximum possible time near the three bodies of the system, without the need of space maneuvers. This model is called ''Precessing Inclined Bi-Elliptical Problem with Radiation Pressure" (PIBEPRP). The use of this model allow us to find important natural orbits for the exploration of one, two or even the three bodies of the system. These trajectories can be used individually or combined in two or more parts using orbital maneuvers.

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