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In this work, we present a study about the determination of the optimal time–energy cost vector, i.e., flight time and total $${\Delta }V$$ (velocity change) spent in an orbital transfer of a spacecraft from an Earth circular parking orbit to a circular orbit around the Moon. The method used to determine the flight time and total $${\Delta }V$$ is based on the well-known approach of patched conic in which the three-body problem that involves Earth, Moon and spacecraft is decomposed into two ‘two bodies’ problems, i.e., Earth–spacecraft and Moon–spacecraft. Thus, the trajectory followed by the spacecraft is a composition of two parts: The first one, when the spacecraft is within the Earth’s sphere of influence; The second one, when the spacecraft enters into the Moon’s sphere of influence. Therefore, the flight time and total $${\Delta }V$$ to inject the spacecraft into the lunar trajectory and place it around the Moon can be determined using the expressions for the two-body problem. In this study, we use the concept of Pareto Frontier to find a set of parameters in the geometry of patched-conic solution that minimizes simultaneously the flight time and total $${\Delta }V$$ of the mission. These results present different possibilities for performing an Earth–Moon transfer where two conflicting objectives are optimized.

Lagrangian points L4 and L5 lie at 60° ahead of and behind the Moon in its orbit with respect to the Earth. Each one of them is a third point of an equilateral triangle with the base of the line defined by those two bodies. These Lagrangian points are stable for the Earth–Moon mass ratio. As so, these Lagrangian points represent remarkable positions to host astronomical observatories or space stations. However, this same distance characteristic may be a challenge for periodic servicing mission. This paper studies elliptic trajectories from an Earth circular parking orbit to reach the Moon’s sphere of influence and apply a swing-by maneuver in order to re-direct the path of a spacecraft to a vicinity of the Lagrangian points L4 and L5. Once the geocentric transfer orbit and the initial impulsive thrust have been determined, the goal is to establish the angle at which the geocentric trajectory crosses the lunar sphere of influence in such a way that when the spacecraft leaves the Moon’s gravitational field, its trajectory and velocity with respect to the Earth change in order to the spacecraft arrives at L4 and L5. In this work, the planar Circular Restricted Three Body Problem approximation is used and in order to avoid solving a two boundary problem, the patched-conic approximation is considered.

An alternative transfer strategy to send spacecraft to stable orbits around the Lagrangian equilibrium points L4 and L5 based in trajectories derived from the periodic orbits around L1 is presented in this work. The trajectories derived, called Trajectories G, are described and studied in terms of the initial generation requirements and their energy variations relative to the Earth through the passage by the lunar sphere of influence. Missions for insertion of spacecraft in elliptic orbits around L4 and L5 are analysed considering the restricted three-body problem Earth–Moon-particle and the results are discussed starting from the thrust, time of flight and energy variation relative to the Earth.

The diurnal day-night cycle severely limits the Terrestrial solar power. To overcome this limitation, a Solar Power Satellite (SPS) system, consisting of a sunlight reflector and a microwave energy generator-transmitter in formation, is presented in this work. The microwave transmitting satellite (MTS) is placed on a common geostationary orbit (GEO) in the Earth's equatorial plane, and the sunlight reflector uses the solar radiation pressure to achieve quasi-periodic orbits about the MTS, so that the sunlight is always redirected to the MTS, which converts the solar energy in electromagnetic power and transmits it by microwaves to an Earth-receiving antenna. Assuming the sun line direction constant at dierent seasons (i.e. autumn/spring equinoxes and winter and summer solstices), previous studies have shown the existence of a family of displaced ecliptic orbits above or below the equatorial plane of the Earth around a GEO. In this study, the position of the Sun is assumed on the ecliptic plane with a mean obliquity (inclination of Earth's equator with respect to the ecliptic) of 23.5◦. A linear solution as an initial condition for the full equations of motions about a GEO, which yields bounded orbit for the sunlight reflector about the MTS in the Earth-satellite two-body problem with solar radiation pressure. To redirect the sunlight to the MTS, the law of reflection is satisfied by the space mirror attitude.

In the frame of the equilateral equilibrium points exploration, numerous future space missions will require maximization of payload mass, simultaneously achieving reasonable transfer times. To fulfill this request, low-energy non-Keplerian orbits could be used to reach L4 and L5 in the Earth–Moon system instead of high energetic transfers. Previous studies have shown that chaos in physical systems like the restricted three-body Earth–Moon-particle problem can be used to direct a chaotic trajectory to a target that has been previously considered. In this work, we propose to transfer a spacecraft from a circular Earth Orbit in the chaotic region to the equilateral equilibrium points L4 and L5 in the Earth–Moon system, exploiting the chaotic region that connects the Earth with the Moon and changing the trajectory of the spacecraft (relative to the Earth) by using a gravity assist maneuver with the Moon. Choosing a sequence of small perturbations, the time of flight is reduced and the spacecraft is guided to a proper trajectory so that it uses the Moon's gravitational force to finally arrive at a desired target. In this study, the desired target will be an orbit about the Lagrangian equilibrium points L4 or L5. This strategy is not only more efficient with respect to thrust requirement, but also its time transfer is comparable to other known transfer techniques based on time optimization.

Assume a constellation of satellites is flying near a given nominal trajectory around L-4 or L-5 in the Earth-Moon system in such a way that there is some freedom in the selection of the geometry of the constellation. We are interested in avoiding large variations of the mutual distances between spacecraft. In this case, the existence of regions of zero and minimum relative radial acceleration with respect to the nominal trajectory will prevent from the expansion or contraction of the constellation. In the other case, the existence of regions of maximum relative radial acceleration with respect to the nominal trajectory will produce a larger expansion and contraction of the constellation. The goal of this paper is to study these regions in the scenario of the Circular Restricted Three Body Problem by means of a linearization of the equations of motion relative to the periodic orbits around L-4 or L-5. This study corresponds to a preliminar planar formation flight dynamics about triangular libration points in the Earth-Moon system. Additionally, the cost estimate to maintain the constellation in the regions of zero and minimum relative radial acceleration or keeping a rigid configuration is computed with the use of the residual acceleration concept. At the end, the results are compared with the dynamical behavior of the deviation of the constellation from a periodic orbit. (C) 2014 COSPAR. Published by Elsevier Ltd. All rights reserved.