This work presents a semi-analytical and numerical study of the perturbation caused in a spacecraft by a third-body using a double averaged analytical model with the disturbing function expanded in Legendre polynomials up to the second order. The important reason for this procedure is to eliminate terms due to the short periodic motion of the spacecraft and to show smooth curves for the evolution of the mean orbital elements for a long-time period. The aim of this study is to calculate the effect of lunar perturbations on the orbits of spacecrafts that are traveling around the Earth. An analysis of the stability of near-circular orbits is made, and a study to know under which conditions this orbit remains near circular completes this analysis. A study of the equatorial orbits is also performed.

Space missions are an excellent way to increase our knowledge of asteroids. Near‐Earth asteroids (NEAs) are good targets for such missions, as they periodically approach the orbit of the Earth. Thus, an increasing number of missions to NEAs are being planned worldwide. Recently, NEA (153591) 2001 SN263 was chosen as the target of the ASTER MISSION – the First Brazilian Deep Space Mission, with launch planned for 2015. NEA (153591) 2001 SN263 was discovered in 2001. In 2008 February, radio astronomers from Arecibo‐Puerto Rico concluded that (153591) 2001 SN263 is actually a triple system. The announcement of ASTER MISSION has motivated the development of the present work, whose goal is to characterize regions of stability and instability of the triple system (153591) 2001 SN263. Understanding and characterizing the stability of such a system is an important component in the design of the mission aiming to explore it. The method adopted consisted of dividing the region around the system into four distinct regions (three of them internal to the system and one external). We performed numerical integrations of systems composed of seven bodies, namely the Sun, Earth, Mars, Jupiter and the three components of the asteroid system (Alpha, the most massive body; Beta the second most massive body; and Gamma, the least massive body), and of thousands of particles randomly distributed within the demarcated regions, for the planar and inclined prograde cases. The results are displayed as diagrams of semi‐major axis versus eccentricity that show the percentage of particles that survive for each set of initial conditions. The regions where 100 per cent of the particles survive are defined as stable regions. We found that the stable regions are in the neighbourhood of Alpha and Beta, and in the external region. Resonant motion of the particles with Beta and Gamma was identified in the internal regions, leading to instability. For particles with I > 45° in the internal region, where I is the inclination with respect to Alpha’s equator, there is no stable region, except for particles placed very close to Alpha. The stability in the external region is not affected by the variation of inclination. We also present a discussion of the long‐term stability in the internal region, for the planar and circular case, with comparisons with the short‐term stability.

An analytical and a numerical study of the perturbation imparted to a spacecraft by a third body is developed. There are several important applications of the present research, such as calculation of the effect of lunar and solar perturbations on high-altitude Earth satellites. The goal is to study the evolution of orbits around some important natural satellites of the solar system, such as the moon, the Galilean satellites of Jupiter, Titan, Titania, Triton, and Charon. There is special interest in learning under which conditions a near-circular orbit remains near circular. The existence of circular, equatorial, and frozen orbits are also considered for a lunar satellite, but the results are valid for any system of primaries by making a time transformation that depends on the masses of the bodies involved. Several plots will show the time histories of the Keplerian elements of the orbits involved. Then, a study is performed to estimate the lifetime of orbits around those natural satellites.

The present paper searches for transfers from the Earth to three of the Kuiper Belt Objects (KBO): Haumea, Makemake, and Quaoar. These trajectories are obtained considering different possibilities of intermediate planet gravity assists. The model is based on the “patched-conics” approach. The best trajectories are found by searching for the minimum total ∆V transfer for a given launch window, inside the 2023-2034 interval, and disregarding the ∆V required for the capture at the target object. The results show transfers with duration below 20 years that spend a total ∆ V under 10 km/s. There is also one trajectory for each of the KBOs with ∆V under 10 km/s and duration below 10 years, using the Jupiter swingby. For the 20-year trajectories, there are also asteroids in the main belt that could be encountered with low additional ∆V , so increasing the scientific return of the mission.

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