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Made available in DSpace on 2019-10-06T17:00:11Z (GMT). No. of bitstreams: 0 Previous issue date: 2018-12-01 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Glasgow Caledonian University Terrestrial solar power is severely limited by the diurnal day–night cycle. To overcome these limitations, a Solar Power Satellite (SPS) system, consisting of a space mirror and a microwave energy generator-transmitter in formation, is presented. The microwave transmitting satellite (MTS) is placed on a planar orbit about a geostationary point (GEO point) in the Earth’s equatorial plane, and the space mirror uses the solar pressure to achieve orbits about GEO point, separated from the planar orbit, and reflecting the sunlight to the MTS, which will transmit energy to an Earth-receiving antenna. Previous studies have shown the existence of a family of displaced periodic orbits above or below the Earth’s equatorial plane. In these studies, the sun-line direction is assumed to be in the Earth’s equatorial plane (equinoxes), and at 23. 5 ∘ below or above the Earth’s equatorial plane (solstices), i.e. depending on the season, the sun-line moves in the Earth’s equatorial plane and above or below the Earth’s equatorial plane. In this work, the position of the Sun is approximated by a rectangular equatorial coordinates, assuming a mean inclination of Earth’s equator with respect to the ecliptic equal to 23. 5 ∘ . It is shown that a linear approximation of the motion about the GEO point yields bounded orbits for the SPS system in the Earth–satellite two-body problem, taking into account the effects of solar radiation pressure. The space mirror orientation satisfies the law of reflection to redirect the sunlight to the MTS. Additionally, a MTS on a common geostationary orbit (GEO) has been also considered to reduce the relative distance in the formation flying Solar Power Satellite (FF-SPS). UNESP-Grupo de Dinâmica Orbital e Planetologia School of Engineering University of Glasgow UNESP-Grupo de Dinâmica Orbital e Planetologia FAPESP: 2011/08171-3 FAPESP: 2013/03233-6

Although the Martian environment is very cold (averaging about $-60^{\circ }$ C), highly oxidizing and desiccated, several studies have proposed human colonization of Mars. To carry out this ambitious goal, terraforming schemes have been designed to warm Mars and implant Earth-like life. Mars climate engineering includes the use of orbiting solar reflectors to increase the total solar insolation. In this study, Sun-synchronous solar reflectors orbits with inclination equal or less than $90^{\circ }$ with respect to the orbital plane of Mars are considered to intervene with the Mars’ climate system. With different inclinations, a family of Sun-synchronous solar reflectors orbits distributes azimuthally the energy intercepted by the reflector. The two-body problem is considered, and the Gauss’s form of the variational equations is used to find the conditions to achieve a Sun-synchronous frozen orbit with inclination equal or less than $90^{\circ }$ , taking into account the effects of solar radiation pressure for a perfectly reflecting space mirror and Mars’ $J_{2}$ oblateness perturbation.

The use of space-based orbital reflectors to increase the total insolation of the Earth has been considered with potential applications in night-side illumination, electric power generation and climate engineering. Previous studies have demonstrated that families of displaced Earth-centered and artificial halo orbits may be generated using continuous propulsion, e.g. solar sails. In this work, a three-body analysis is performed by using the circular restricted three body problem, such that, the space mirror attitude reflects sunlight in the direction of Earth’s center, increasing the total insolation. Using the Lindstedt–Poincare and differential corrector methods, a family of halo orbits at artificial Sun–Earth $$\hbox {L}_2$$ points are found. It is shown that the third order approximation does not yield real solutions after the reflector acceleration exceeds 0.245 mm $$\hbox {s}^{-2}$$ , i.e. the analytical expressions for the in- and out-of-plane amplitudes yield imaginary values. Thus, a larger solar reflector acceleration is required to obtain periodic orbits closer to the Earth. Derived using a two-body approach and applying the differential corrector method, a family of displaced periodic orbits close to the Earth are therefore found, with a solar reflector acceleration of 2.686 mm $$\hbox {s}^{-2}$$ .

Several space-based climate engineering methods, including shading the Earth with a particle ring for active cooling, or the use of orbital reflectors to increase the total insolation of Mars for climate warming have been proposed to modify planetary climates in a controller manner. In this study, solar reflectors on Sun-synchronous polar orbits (frozen orbits) normal to the ecliptic plane to the Mars are considered to intervene in the Mars’s climate system.The two-body problem is considered, and the Gauss’ form of the variational equations is used to describe the propagation of the polar orbit, taking into account the effects of solar radiation pressure and Mars’s J2 oblateness perturbation.

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.

Made available in DSpace on 2018-12-11T17:26:44Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-01-01 In this work, we are interested in avoiding large variations in the mutual distances among multiple satellites and also in controlling their geometric configuration around an Earth-Moon triangular point. Previous studies about triangular libration points have determined the existence of zero drift regions with respect to the nominal trajectory, in which the expansion or contraction of the formation never take place. Our goal is to carry out two different control strategies for a formation near a given nominal trajectory around L4: a bang-off-bang control and a minimum weighted total ΔV consumption. A linearization relative to the reference trajectory around the triangular libration point is carried out, and different geometrical possibilities in the zero drift regions are studied. To investigate the influence of the gravitational force of the Sun, the BiCircular Four Body Problem is considered here. According to the results obtained, some meaningful insights to allow a proper design of the geometric configuration of the formation are drawn. UNESP-Grupo de Dinâmica Orbital e Planetologia Instituto Nacional de Pesquisas Espaciais, Av. dos Astronautas 1758 Departament de Matemàtica Aplicada i ETSEIB-UPC, Avda. Diagonal 647 Departament de Matemàtica Aplicada i Anàlisi UB, Gran Vía 585 UNESP-Grupo de Dinâmica Orbital e Planetologia

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.