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1.
The problem of designing low-energy transfers between the Earth and the Moon has attracted recently a major interest from the scientific community. In this paper, an indirect optimal control approach is used to determine minimum-fuel low-thrust transfers between a low Earth orbit and a Lunar orbit in the Sun–Earth–Moon Bicircular Restricted Four-Body Problem. First, the optimal control problem is formulated and its necessary optimality conditions are derived from Pontryagin’s Maximum Principle. Then, two different solution methods are proposed to overcome the numerical difficulties arising from the huge sensitivity of the problem’s state and costate equations. The first one consists in the use of continuation techniques. The second one is based on a massive exploration of the set of unknown variables appearing in the optimality conditions. The dimension of the search space is reduced by considering adapted variables leading to a reduction of the computational time. The trajectories found are classified in several families according to their shape, transfer duration and fuel expenditure. Finally, an analysis based on the dynamical structure provided by the invariant manifolds of the two underlying Circular Restricted Three-Body Problems, Earth–Moon and Sun–Earth is presented leading to a physical interpretation of the different families of trajectories. 相似文献
2.
Yuan Ren Pierpaolo Pergola Elena Fantino Bianca Thiere 《Celestial Mechanics and Dynamical Astronomy》2012,112(1):1-21
Over the past three decades, ballistic and impulsive trajectories between libration point orbits (LPOs) in the Sun–Earth–Moon
system have been investigated to a large extent. It is known that coupling invariant manifolds of LPOs of two different circular
restricted three-body problems (i.e., the Sun–Earth and the Earth–Moon systems) can lead to significant mass savings in specific
transfers, such as from a low Earth orbit to the Moon’s vicinity. Previous investigations on this issue mainly considered
the use of impulsive maneuvers along the trajectory. Here we investigate the dynamical effects of replacing impulsive ΔV’s with low-thrust trajectory arcs to connect LPOs using invariant manifold dynamics. Our investigation shows that the use
of low-thrust propulsion in a particular phase of the transfer and the adoption of a more realistic Sun–Earth–Moon four-body
model can provide better and more propellant-efficient solution. For this purpose, methods have been developed to compute
the invariant tori and their manifolds in this dynamical model. 相似文献
3.
The distant retrograde orbits (DROs) can serve as the parking orbits for a long-term cis-lunar space station. This paper gives a comprehensive study on the transfer problem from DROs to Earth orbits, including low Earth orbits (LEOs), medium Earth orbits (MEOs), and geosynchronous orbits (GSOs), in the bicircular restricted four-body problem (BR4BP) via optimizations within a large solution space. The planar transfer problem is firstly solved by grid search and optimization techniques, and two types of transfer orbits, direct ones and low-energy ones, are both constructed. Then, the nonplanar transfer problem to Earth orbits with inclinations between 0 and 90 degrees are solved via sequential optimizations based on the planar transfers. The transfer characteristics in the cases of different destination orbit inclinations are discussed for both the direct and the low-energy transfer orbits. The important role of the lunar gravity in the low-energy transfers is also discussed, which can overcome the increase of transfer cost caused by the high inclination of Earth orbits. The distinct features of different transfer scenarios, including multiple revolutions around the Earth and Moon, the exterior phase, and the lunar flyby, are discovered. The energy of transfer orbits is exploited to discuss the effects of close lunar flybys. The results will be helpful for the transfer design in future manned or unmanned return missions, and can also provide valuable information for selecting proper parking DROs for cis-lunar space stations.
相似文献4.
Kenta Oshima Stefano Campagnola Tomohiro Yanao 《Celestial Mechanics and Dynamical Astronomy》2017,128(2-3):303-322
This paper globally searches for low-thrust transfers to the Moon in the planar, circular, restricted, three-body problem. Propellant-mass optimal trajectories are computed with an indirect method, which implements the necessary conditions of optimality based on the Pontryagin principle. We present techniques to reduce the dimension of the set over which the required initial costates are searched. We obtain a wide range of Pareto solutions in terms of time of flight and mass consumption. Using the Tisserand–Poincaré graph, a number of solutions are shown to exploit high-altitude lunar flybys to reduce fuel consumption. 相似文献
5.
This work deals with the structure of the lunar Weak Stability Boundaries (WSB) in the framework of the restricted three and
four body problem. Geometry and properties of the escape trajectories have been studied by changing the spacecraft orbital
parameters around the Moon. Results obtained using the algorithm definition of the WSB have been compared with an analytical
approximation based on the value of the Jacobi constant. Planar and three-dimensional cases have been studied in both three
and four body models and the effects on the WSB structure, due to the presence of the gravitational force of the Sun and the
Moon orbital eccentricity, have been investigated. The study of the dynamical evolution of the spacecraft after lunar capture
allowed us to find regions of the WSB corresponding to stable and safe orbits, that is orbits that will not impact onto lunar
surface after capture. By using a bicircular four body model, then, it has been possible to study low-energy transfer trajectories
and results are given in terms of eccentricity, pericenter altitude and inclination of the capture orbit. Equatorial and polar
capture orbits have been compared and differences in terms of energy between these two kinds of orbits are shown. Finally,
the knowledge of the WSB geometry permitted us to modify the design of the low-energy capture trajectories in order to reach
stable capture, which allows orbit circularization using low-thrust propulsion systems. 相似文献
6.
Martin Lara 《Celestial Mechanics and Dynamical Astronomy》2017,127(3):285-300
This study analyzes a recently discovered class of exterior transfers to the Moon. These transfers terminate in retrograde ballistic capture orbits, i.e., orbits with negative Keplerian energy and angular momentum with respect to the Moon. Yet, their Jacobi constant is relatively low, for which no forbidden regions exist, and the trajectories do not appear to mimic the dynamics of the invariant manifolds of the Lagrange points. This paper shows that these orbits shadow instead lunar collision orbits. We investigate the dynamics of singular, lunar collision orbits in the Earth–Moon planar circular restricted three-body problem, and reveal their rich phase space structure in the medium-energy regime, where invariant manifolds of the Lagrange point orbits break up. We show that lunar retrograde ballistic capture trajectories lie inside the tube structure of collision orbits. We also develop a method to compute medium-energy transfers by patching together orbits inside the collision tube and those whose apogees are located in the appropriate quadrant in the Sun–Earth system. The method yields the novel family of transfers as well as those ending in direct capture orbits, under particular energetic and geometrical conditions. 相似文献
7.
G. Mingotti F. Topputo F. Bernelli-Zazzera 《Celestial Mechanics and Dynamical Astronomy》2011,110(2):169-188
In this paper novel Earth–Mars transfers are presented. These transfers exploit the natural dynamics of n-body models as well as the high specific impulse typical of low-thrust systems. The Moon-perturbed version of the Sun–Earth
problem is introduced to design ballistic escape orbits performing lunar gravity assists. The ballistic capture is designed
in the Sun–Mars system where special attainable sets are defined and used to handle the low-thrust control. The complete trajectory
is optimized in the full n-body problem which takes into account planets’ orbital inclinations and eccentricities. Accurate, efficient solutions with
reasonable flight times are presented and compared with known results. 相似文献
8.
The capture dynamics is an important field in Astronomy and Astronautics. In this paper, the near-optimal lunar capture in the Earth–Moon transfer is investigated under the frame of the planar circular restricted three-body problem. We try to work out how to achieve the permanent lunar capture with the minimum maneuver consumption. This problem is decomposed into two parts: the pre-maneuver part and the post-maneuver part. In the pre-maneuver part, considering the criteria of the gravitational capture, we obtain the minimum pre-maneuver velocity via the numerical backward integration. In the post-maneuver part, using the Poincaré section and the KAM theory, we find the maximum post-maneuver velocity to achieve the permanent capture. Synthesized the results of the two parts, a new method is presented to find the near-optimal maneuver position and the minimum maneuver consumption. The method presented is simple and visible, and can provide abundant capture orbits for the design of low energy Earth–Moon transfers. 相似文献
9.
This paper investigates a method for optimizing multi-rendezvous low-thrust trajectories using indirect methods. An efficient technique, labeled costate transforming, is proposed to optimize multiple trajectory legs simultaneously rather than optimizing each trajectory leg individually. Complex inner-point constraints and a large number of free variables are one main challenge in optimizing multi-leg transfers via shooting algorithms. Such a difficulty is reduced by first optimizing each trajectory leg individually. The results may be, next, utilized as an initial guess in the simultaneous optimization of multiple trajectory legs. In this paper, the limitations of similar techniques in previous research is surpassed and a homotopic approach is employed to improve the convergence efficiency of the shooting process in multi-rendezvous low-thrust trajectory optimization. Numerical examples demonstrate that newly introduced techniques are valid and efficient. 相似文献
10.
Marco Giancotti Mauro Pontani Paolo Teofilatto 《Celestial Mechanics and Dynamical Astronomy》2012,114(1-2):55-76
Analysis and design of low-energy transfers to the Moon has been a subject of great interest for many decades. This paper is concerned with a topological study of such transfers, with emphasis to trajectories that allow performing lunar capture and those that exhibit homoclinic connections, in the context of the circular restricted three-body problem. A fundamental theorem stated by Conley locates capture trajectories in the phase space and can be condensed in a sentence: “if a crossing asymptotic orbit exists then near any such there is a capture orbit”. In this work this fundamental theoretical assertion is used together with an original cylindrical isomorphic mapping of the phase space associated with the third body dynamics. For a given energy level, the stable and unstable invariant manifolds of the periodic Lyapunov orbit around the collinear interior Lagrange point are computed and represented in cylindrical coordinates as tubes that emanate from the transformed periodic orbit. These tubes exhibit complex geometrical features. Their intersections correspond to homoclinic orbits and determine the topological separation of long-term lunar capture orbits from short-duration capture trajectories. The isomorphic mapping is proven to allow a deep insight on the chaotic motion that characterizes the dynamics of the circular restricted three-body, and suggests an interesting interpretation, and together corroboration, of Conley’s assertion on the topological location of lunar capture orbits. Moreover, an alternative three-dimensional representation of the phase space is profitably employed to identify convenient lunar periodic orbits that can be entered with modest propellant consumption, starting from the Lyapunov orbit. 相似文献
11.
Priscilla Sousa-Silva Maisa O. Terra Matteo Ceriotti 《Astrophysics and Space Science》2018,363(10):210
This contribution deals with fast Earth–Moon transfers with ballistic capture in the patched three-body model. We compute ensembles of preliminary solutions using a model that takes into account the relative inclination of the orbital planes of the primaries. The ballistic capture orbits around the Moon are obtained relying on the hyperbolic invariant structures associated to the collinear Lagrangian points of the Earth–Moon system, and the Sun–Earth system portion of the transfers are quasi-periodic orbits obtained by a genetic algorithm. The trajectories are designed to be good initial guesses to search optimal cost-efficient short-time Earth–Moon transfers with ballistic capture in more realistic models. 相似文献
12.
Homotopy methods have been widely utilized to solve low-thrust orbital transfer problems, however, it is not guaranteed that the optimal solution can be obtained by the existing homotopy methods. In this paper, a new homotopy method is presented, by which the optimal solution can be found with probability one. Generalized sufficient conditions, which are derived from the parametrized Sard’s theorem, are first developed. A new type of probability-one homotopy formulation, which is custom-designed for solving minimum-time low-thrust trajectory optimization problems and satisfies all these sufficient conditions, is then constructed. By tracking the continuous zero curve initiated by an initial problem with known solution, the optimal solution of the original problem is guaranteed to be solved with probability one. Numerical demonstrations in a three-dimensional time-optimal low-thrust orbital transfer problem with 43 revolutions is presented to illustrate the applications of the method. 相似文献
13.
Elisa Maria Alessi Gerard Gómez Josep J. Masdemont 《Celestial Mechanics and Dynamical Astronomy》2010,107(1-2):187-207
It is known that most of the craters on the surface of the Moon were created by the collision of minor bodies of the Solar System. Main Belt Asteroids, which can approach the terrestrial planets as a consequence of different types of resonance, are actually the main responsible for this phenomenon. Our aim is to investigate the impact distributions on the lunar surface that low-energy dynamics can provide. As a first approximation, we exploit the hyberbolic invariant manifolds associated with the central invariant manifold around the equilibrium point L 2 of the Earth–Moon system within the framework of the Circular Restricted Three-Body Problem. Taking transit trajectories at several energy levels, we look for orbits intersecting the surface of the Moon and we attempt to define a relationship between longitude and latitude of arrival and lunar craters density. Then, we add the gravitational effect of the Sun by considering the Bicircular Restricted Four-Body Problem. In the former case, as main outcome, we observe a more relevant bombardment at the apex of the lunar surface, and a percentage of impact which is almost constant and whose value depends on the assumed Earth–Moon distance dEM. In the latter, it seems that the Earth–Moon and Earth–Moon–Sun relative distances and the initial phase of the Sun θ 0 play a crucial role on the impact distribution. The leading side focusing becomes more and more evident as dEM decreases and there seems to exist values of θ 0 more favorable to produce impacts with the Moon. Moreover, the presence of the Sun makes some trajectories to collide with the Earth. The corresponding quantity floats between 1 and 5 percent. As further exploration, we assume an uniform density of impact on the lunar surface, looking for the regions in the Earth–Moon neighbourhood these colliding trajectories have to come from. It turns out that low-energy ejecta originated from high-energy impacts are also responsible of the phenomenon we are considering. 相似文献
14.
15.
J.-B. Caillau B. Daoud J. Gergaud 《Celestial Mechanics and Dynamical Astronomy》2012,114(1-2):137-150
The circular restricted three-body problem is considered to model the dynamics of an artificial body submitted to the attraction of two planets. Minimization of the fuel consumption of the spacecraft during the transfer, e.g. from the Earth to the Moon, is considered. In the light of the controllability results of Caillau and Daoud (SIAM J Control Optim, 2012), existence for this optimal control problem is discussed under simplifying assumptions. Thanks to Pontryagin maximum principle, the properties of fuel minimizing controls is detailed, revealing a bang-bang structure which is typical of L1-minimization problems. Because of the resulting non-smoothness of the Hamiltonian two-point boundary value problem, it is difficult to use shooting methods to compute numerical solutions (even with multiple shooting, as many switchings on the control occur when low thrusts are considered). To overcome these difficulties, two homotopies are introduced: One connects the investigated problem to the minimization of the L2-norm of the control, while the other introduces an interior penalization in the form of a logarithmic barrier. The combination of shooting with these continuation procedures allows to compute fuel optimal transfers for medium or low thrusts in the Earth–Moon system from a geostationary orbit, either towards the L 1 Lagrange point or towards a circular orbit around the Moon. To ensure local optimality of the computed trajectories, second order conditions are evaluated using conjugate point tests. 相似文献
16.
Kazuyuki Yagasaki 《Celestial Mechanics and Dynamical Astronomy》2004,90(3-4):197-212
We construct a spacecraft transfer with low cost and moderate flight time from the Earth to the Moon. The motion of the spacecraft
is modeled by the planar circular restricted three-body problem including a perturbation due to the solar gravitation. Our
approach is to reduce computation of optimal transfers to a non-linear boundary value problem. Using a computer software called
AUTO, we solve it and continue its solutions numerically to obtain the optimal transfers. Our result also shows that the use of
the solar gravitation can further lower the transfer cost drastically. 相似文献
17.
Alejandro M. Leiva Carlos Bruno Briozzo 《Celestial Mechanics and Dynamical Astronomy》2008,101(3):225-245
Starting from 80 families of low-energy fast periodic transfer orbits in the Earth–Moon planar circular Restricted Three Body
Problem (RTBP), we obtain by analytical continuation 11 periodic orbits and 25 periodic arcs with similar properties in the
Sun–Earth–Moon Quasi-Bicircular Problem (QBCP). A novel and very simple procedure is introduced giving the solar phases at
which to attempt continuation. Detailed numerical results for each periodic orbit and arc found are given, including their
stability parameters and minimal distances to the Earth and Moon. The periods of these orbits are between 2.5 and 5 synodic
months, their energies are among the lowest possible to achieve an Earth–Moon transfer, and they show a diversity of circumlunar
trajectories, making them good candidates for missions requiring repeated passages around the Earth and the Moon with close
approaches to the last. 相似文献
18.
P. V. Kazmerchuk 《Solar System Research》2018,52(7):630-635
Several well-studied problems for optimizing low-thrust spacecraft trajectories are solved using the modified linearization method (MLM). The results are compared with the results obtained by other authors. On this basis, conclusions are drawn on the possible use of the modified linearization method for optimizing low-thrust spacecraft trajectories. 相似文献
19.
Robert A. Jacobson William F. Powers 《Celestial Mechanics and Dynamical Astronomy》1977,15(2):161-189
Future space missions to the outer planets may depend upon the use of low-thrust propulsion systems. As these planets are decidedly oblate, the question of the effect of that oblateness on a low-thrust trajectory is of some interest. In this paper the problem of optimal energy increase is attacked under the assumption that the coefficients for the second zonal harmonic, i.e.,J
2, and the nondimensional thrust acceleration are the same order of magnitude. Using a two variable asymptotic expansion technique, a near optimal control program is generated and the first order uniformly valid approximation for the corresponding trajectory is obtained. Tangential thrust is shown to be a good near-optimal thrust program even in the presence of oblateness effects. The optimal control program is found to be oscillatory and quite similar to the optimal control for energy increase in an inverse square gravitational field.This research was supported by the National Aeronautics and Space Administration under Grant NGR-23-005-329. 相似文献
20.
Imaging of low-energy neutral atoms (LENAs) in the vicinity of the Moon can provide wide knowledge of the Moon from the viewpoint of plasma physics and planetary physics. At the surface of the Moon, neutral atoms are mainly generated by photon-stimulated desorption, micrometeorite vaporization and sputtering by solar wind protons. LENAs, the energetic neutral atoms with energy range of 10-500 eV, are mainly created by sputtering of solar wind particles. We have made quantitative estimates of sputtered LENAs from the Moon surface. The results indicate that LENAs can be detected by a realistic instrument and that the measurement will provide the global element maps of sputtered particles, which substantially reflect the surface composition, and the magnetic anomalies. We have also found that LENAs around dark regions, such as the permanent shadow inside craters in the pole region, can be imaged. This is because the solar wind ions can penetrate shaded regions due to their finite gyro-radius and the pressure gradient between the solar wind and the wake region. LENAs also extend our knowledge about the magnetic anomalies and associated mini-magnetosphere systems, which are the smallest magnetospheres as far as one knows. It is thought that no LENAs are generated from mini-magnetosphere regions because no solar wind may penetrate inside them. Imaging such void areas of LENAs will provide another map of lunar magnetic anomalies. 相似文献