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O C Winter - One of the best experts on this subject based on the ideXlab platform.
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pareto frontier for the time energy cost vector to an earth moon transfer orbit using the Patched Conic approximation
Computational & Applied Mathematics, 2015Co-Authors: F J T Salazar, Elbert E N Macau, O C WinterAbstract: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.
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Pareto Frontier for the time–energy cost vector to an Earth–Moon transfer orbit using the Patched-Conic approximation
Computational and Applied Mathematics, 2015Co-Authors: F J T Salazar, Elbert E N Macau, O C WinterAbstract:In this work, we present a study about the determination of the optimal time–energy cost vector, i.e., flight time and total $${\Delta }V$$ Δ 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 $${\Delta }V$$ Δ 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 $${\Delta }V$$ Δ 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 $${\Delta }V$$ Δ V of the mission. These results present different possibilities for performing an Earth–Moon transfer where two conflicting objectives are optimized.
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alternative transfer to the earth moon lagrangian points l4 and l5 using lunar gravity assist
Advances in Space Research, 2014Co-Authors: F J T Salazar, Elbert E N Macau, O C WinterAbstract:Abstract 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.
Sandro Silva Fernandes - One of the best experts on this subject based on the ideXlab platform.
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A lunar flyby for a tridimensional Earth-to-Earth mission
Acta Astronautica, 2018Co-Authors: Luiz Arthur Gagg Filho, Sandro Silva FernandesAbstract:Abstract The present work formulates an orbital transfer for an Earth-to-Earth mission between non coplanar orbits with different altitudes with a special feature: the occurrence of a lunar flyby during the transfer orbit. This lunar flyby is intended to help change the plane of motion of the spacecraft without fuel consumption. Only two-impulsive trajectories are considered with the velocity increments applied at the initial and final orbits. In order to solve this problem, a 3D Patched-Conic approximation associated with a two-point boundary value problem is proposed. The same transfer problem is formulated considering the spatial circular restricted three-body problem (SCR3BP). The results of the Patched-Conic approximation is compared with the results of the SCR3BP showing a good agreement between the models. This work also determines several trajectories in order to perform a study of the fuel consumption considering several inclinations and altitudes of both initial and final orbits around the Earth. The longitude of the ascending node of the initial orbit, and, the altitude of close approach with the Moon during the flyby are also analyzed. According to the total velocity increment analysis, the changing plane assisted by a lunar flyby can be very favorable. Despite the increase of the time of flight, the saving of fuel is considerable. Indeed, the total velocity increment of this kind of maneuver is in some cases better than the velocity increment provided by the bi-parabolic transfer.
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Minimum fuel trajectories for round trip lunar missions
Computational and Applied Mathematics, 2018Co-Authors: Luiz Arthur Gagg Filho, Sandro Silva FernandesAbstract:In this work, a study about minimum fuel trajectories in a round trip journey to the Moon is presented. It is assumed that the velocity changes are instantaneous, that is, the propulsion system is capable of delivering impulses such that the fuel consumption is represented by the total velocity increment applied to the space vehicle. It is also assumed that the velocity increments are applied tangentially to the terminal orbits, and, the outgoing trip and the return trip are analyzed separately such that the whole mission is performed with four impulses (two impulses in each trip). The mathematical models used to describe the motion of the space vehicle are three: the lunar Patched-Conic approximation; the classic planar circular restricted three-body problem, and, the planar bi-circular restricted four-body problem (PBR4BP). For computing the optimal trajectories, the Sequential Gradient-Restoration Algorithm with constraints is used. The influence of the Sun on round trip lunar missions is analyzed through the PBR4BP model. For all models, the trajectories studied are direct ascent maneuvers, and, both the outgoing and return trips are considered. The results obtained through the different models are compared with each other. The optimal results for the PBR4BP model show that a small reduction of the fuel consumption can be achieved if the initial phase angle of the Sun is chosen properly.
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Optimal round trip lunar missions based on the Patched-Conic approximation
Computational and Applied Mathematics, 2016Co-Authors: Luiz Arthur Gagg Filho, Sandro Silva FernandesAbstract:A study of optimal bi-impulsive trajectories of round trip lunar missions is presented in this paper. The optimization criterion is the total velocity increment. The dynamical model utilized to describe the motion of the space vehicle is a full lunar Patched-Conic approximation, which embraces the lunar Patched-Conic of the outgoing trip and the lunar Patched-Conic of the return mission. Each one of these parts is considered separately to solve an optimization problem of two degrees of freedom. The parameters to be optimized are two: the phase angle of the point at which the space vehicle reaches the edge of the Moon’s sphere of influence and the initial velocity at departure. The Sequential Gradient Restoration Algorithm is employed to achieve the optimal solutions. Analytical and numerical derivatives of expressions describing the lunar Patched-Conic approximations are utilized to ensure the results. The results based on the Patched-Conic approximation show a good agreement with the ones provided by literature, and the solution trajectories proved to be consistent with the image trajectories theorem.
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Preliminary Analysis of Optimal Round Trip Lunar Missions
Journal of Physics: Conference Series, 2015Co-Authors: L A Gagg Filho, Sandro Silva FernandesAbstract:A study of optimal bi-impulsive trajectories of round trip lunar missions is presented in this paper. The optimization criterion is the total velocity increment. The dynamical model utilized to describe the motion of the space vehicle is a full lunar Patched-Conic approximation, which embraces the lunar Patched-Conic of the outgoing trip and the lunar Patched-Conic of the return mission. Each one of these parts is considered separately to solve an optimization problem of two degrees of freedom. The Sequential Gradient Restoration Algorithm (SGRA) is employed to achieve the optimal solutions, which show a good agreement with the ones provided by literature, and, proved to be consistent with the image trajectories theorem.
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Optimal Two-Impulse Trajectories with Moderate Flight Time for Earth-Moon Missions
Mathematical Problems in Engineering, 2012Co-Authors: Sandro Silva Fernandes, Cleverson Maranhão Porto MarinhoAbstract:A study of optimal two-impulse trajectories with moderate flight time for Earth-Moon missions is presented. The optimization criterion is the total characteristic velocity. Three dynamical models are used to describe the motion of the space vehicle: the well-known Patched-Conic approximation and two versions of the planar circular restricted three-body problem (PCR3BP). In the Patched-Conic approximation model, the parameters to be optimized are two: initial phase angle of space vehicle and the first velocity impulse. In the PCR3BP models, the parameters to be optimized are four: initial phase angle of space vehicle, flight time, and the first and the second velocity impulses. In all cases, the optimization problem has one degree of freedom and can be solved by means of an algorithm based on gradient method in conjunction with Newton-Raphson method.
F J T Salazar - One of the best experts on this subject based on the ideXlab platform.
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pareto frontier for the time energy cost vector to an earth moon transfer orbit using the Patched Conic approximation
Computational & Applied Mathematics, 2015Co-Authors: F J T Salazar, Elbert E N Macau, O C WinterAbstract: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.
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Pareto Frontier for the time–energy cost vector to an Earth–Moon transfer orbit using the Patched-Conic approximation
Computational and Applied Mathematics, 2015Co-Authors: F J T Salazar, Elbert E N Macau, O C WinterAbstract:In this work, we present a study about the determination of the optimal time–energy cost vector, i.e., flight time and total $${\Delta }V$$ Δ 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 $${\Delta }V$$ Δ 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 $${\Delta }V$$ Δ 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 $${\Delta }V$$ Δ V of the mission. These results present different possibilities for performing an Earth–Moon transfer where two conflicting objectives are optimized.
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alternative transfer to the earth moon lagrangian points l4 and l5 using lunar gravity assist
Advances in Space Research, 2014Co-Authors: F J T Salazar, Elbert E N Macau, O C WinterAbstract:Abstract 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.
Elbert E N Macau - One of the best experts on this subject based on the ideXlab platform.
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pareto frontier for the time energy cost vector to an earth moon transfer orbit using the Patched Conic approximation
Computational & Applied Mathematics, 2015Co-Authors: F J T Salazar, Elbert E N Macau, O C WinterAbstract: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.
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Pareto Frontier for the time–energy cost vector to an Earth–Moon transfer orbit using the Patched-Conic approximation
Computational and Applied Mathematics, 2015Co-Authors: F J T Salazar, Elbert E N Macau, O C WinterAbstract:In this work, we present a study about the determination of the optimal time–energy cost vector, i.e., flight time and total $${\Delta }V$$ Δ 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 $${\Delta }V$$ Δ 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 $${\Delta }V$$ Δ 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 $${\Delta }V$$ Δ V of the mission. These results present different possibilities for performing an Earth–Moon transfer where two conflicting objectives are optimized.
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alternative transfer to the earth moon lagrangian points l4 and l5 using lunar gravity assist
Advances in Space Research, 2014Co-Authors: F J T Salazar, Elbert E N Macau, O C WinterAbstract:Abstract 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.
W. Enderson - One of the best experts on this subject based on the ideXlab platform.
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I I A,STUDY OF LUI'?AR lAwlING SITES AMI ASSOCIATED STAY TIMES
2009Co-Authors: W. EndersonAbstract:A study utilizing the results of a Patched Conic approximation was conducted to determine the possible landing sites and associated stay times on the lunar surface that are compatible with the lunar-orbit-rendezvous technique, that is, descent from and return to a vehicle orbiting the moon. Particular emphasis is placed on landing sites that allow a return to the established lunar orbit at all times during the exploration period. Three different landing and take-off maneuvers are considered as well as the effect of variations of the energy and inclination of the earth-to-moon transfer trajectory. Consideration is given to maneuvers that permit the most flexibility in selection of landing sites as well as maneuvers that allow the longest stay time on the lunar surface for a given total plane-change capability. The results of this study indicate that the landing sites and associated stay times are strongly dependent on the inclination of the established lunar orbit as well as the specific landing and take-off maneuvers that are employed. If the inclination of the established lunar orbit is constrained to equal the sum of the landing-site latitude rp and the plane-change capability 6, much versatility exists in the selection of possible landing sites on the lunar surface and in the corresponding stay times. bployment of a plane-change capability during the take-off maneuver allows extended exploration periods and provides an inherent safety factor for the mission. For this case, the landing vehicle caa return to the established lunar orbit at any time during the exploration period