共查询到20条相似文献，搜索用时 15 毫秒
1.
Due to various perturbations, the collinear libration points of the real Earth–Moon system are not equilibrium points anymore.
Under the assumption that the Moon’s motion is quasi-periodic, special quasi-periodic orbits called dynamical substitutes
exist. These dynamical substitutes replace the geometrical collinear libration points as time-varying equilibrium points.
In the paper, the dynamical substitutes of the three collinear libration points in the real Earth–Moon system are computed.
For the points L
1 and L
2, linearized motions around the dynamical substitutes are described, and the variational equations of the dynamical substitutes
are reduced to a form with a near constant coefficient matrix. Then higher order analytical formulae of the central manifolds
are constructed. Using these analytical solutions as initial seeds, Lissajous orbits and halo orbits are computed with numerical
algorithms. 相似文献
2.
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
3.
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
4.
Starting from the identification and classification of a family of fast periodic transfer orbits in the Earth–Moon planar
circular Restricted Three Body Problem (RTBP), and using analytic continuation techniques, we find two unstable periodic orbits
in the Sun–Earth–Moon Quasi-Bicircular Problem (QBCP). The orbits found perform periodic Earth–Moon transfers with a period
of approximately 29.5 days. 相似文献
5.
The Earth–Moon L1 libration point is proposed as a human gateway for space transportation system of the future. This paper
studies indirect transfer using the perturbed stable manifold and lunar flyby to the Earth–Moon L1 libration point. Although
traditional studies indicate that indirect transfer to the Earth–Moon L1 libration point does not save much fuel, this study
shows that energy efficient indirect transfer using the perturbed stable manifold and lunar flyby could be constructed in
an elegant way. The design process is given to construct indirect transfer to the Earth–Moon L1 libration point. Simulation
results show that indirect transfer to the Earth–Moon L1 libration point saves about 420 m/s maneuver velocity compared to
direct transfer, although the flight time is about 20 days longer. 相似文献
6.
The two triangular libration points of the real Earth–Moon system are not equilibrium points anymore. Under the assumption
that the motion of the Moon is quasi-periodic, one special quasi-periodic orbit exists as dynamical substitute for each point.
The way to compute the dynamical substitute was discussed before, and a planar approximation was obtained. In this paper,
the problem is revisited. The three-dimensional approximation of the dynamical substitute is obtained in a different way.
The linearized central flow around it is described. 相似文献
7.
D. J. Scheeres 《Celestial Mechanics and Dynamical Astronomy》1998,70(2):75-98
Starting from the four-body problem a generalization of both the restricted three-body problem and the Hill three-body problem
is derived. The model is time periodic and contains two parameters: the mass ratio ν of the restricted three-body problem
and the period parameter m of the Hill Variation orbit. In the proper coordinate frames the restricted three-body problem
is recovered as m → 0 and the classical Hill three-body problem is recovered as ν → 0. This model also predicts motions described
by earlier researchers using specific models of the Earth–Moon–Sun system. An application of the current model to the motion
of a spacecraft in the Sun perturbed Earth–Moon system is made using Hill's Variation orbit for the motion of the Earth–Moon
system. The model is general enough to apply to the motion of an infinitesimal mass under the influence of any two primaries
which orbit a larger mass.
Using the model, numerical investigations of the structure of motions around the geometric position of the triangular Lagrange
points are performed. Values of the parameter ν range in the neighborhood of the Earth–Moon value as the parameter m increases
from 0 to 0.195 at which point the Hill Variation orbit becomes unstable. Two families of planar periodic orbits are studied
in detail as the parameters m and ν vary. These families contain stable and unstable members in the plane and all have the
out-of-plane stability. The stable and unstable manifolds of the unstable periodic orbits are computed and found to be trapped
in a geometric area of phase space over long periods of time for ranges of the parameter values including the Earth–Moon–Sun
system.
This model is derived from the general four-body problem by rigorous application of the Hill and restricted approximations.
The validity of the Hill approximation is discussed in light of the actual geometry of the Earth–Moon–Sun system.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
8.
定点在日-地(月)系L1点附近的探测器的发射及维持 总被引：1，自引：0，他引：1
在限制性三体问题中共线平动点附近的运动虽然是不稳定的,但可以是有条件稳定的,该动力学特征使得一些有特殊目的的探测器只需消耗较少的能量即可定点在这些点附近(如ISEE-3、SOHO).以日-地(月)系的L1点为例,根据其附近的运动特征,探讨定点探测器的发射与轨道控制问题,给出了相应的数值模拟结果,为工程上的实现提供理论依据. 相似文献
9.
Marco Giancotti Mauro Pontani Paolo Teofilatto 《Celestial Mechanics and Dynamical Astronomy》2014,120(3):249-268
Several families of periodic orbits exist in the context of the circular restricted three-body problem. This work studies orbital motion of a spacecraft among these periodic orbits in the Earth–Moon system, using the planar circular restricted three-body problem model. A new cylindrical representation of the spacecraft phase space (i.e., position and velocity) is described, and allows representing periodic orbits and the related invariant manifolds. In the proximity of the libration points, the manifolds form a four-fold surface, if the cylindrical coordinates are employed. Orbits departing from the Earth and transiting toward the Moon correspond to the trajectories located inside this four-fold surface. The isomorphic mapping under consideration is also useful for describing the topology of the invariant manifolds, which exhibit a complex geometrical stretch-and-folding behavior as the associated trajectories reach increasing distances from the libration orbit. Moreover, the cylindrical representation reveals extremely useful for detecting periodic orbits around the primaries and the libration points, as well as the possible existence of heteroclinic connections. These are asymptotic trajectories that are ideally traveled at zero-propellant cost. This circumstance implies the possibility of performing concretely a variety of complex Earth–Moon missions, by combining different types of trajectory arcs belonging to the manifolds. This work studies also the possible application of manifold dynamics to defining a suitable, convenient end-of-life strategy for spacecraft placed in any of the unstable orbits. The final disposal orbit is an externally confined trajectory, never approaching the Earth or the Moon, and can be entered by means of a single velocity impulse (of modest magnitude) along the right unstable manifold that emanates from the Lyapunov orbit at \(L_2\) . 相似文献
10.
Yu Cheng Gerard Gómez Josep J. Masdemont Jianping Yuan 《Celestial Mechanics and Dynamical Astronomy》2017,128(4):409-433
This paper is devoted to the study of the transfer problem from a libration point orbit of the Earth–Moon system to an orbit around the Moon. The transfer procedure analysed has two legs: the first one is an orbit of the unstable manifold of the libration orbit and the second one is a transfer orbit between a certain point on the manifold and the final lunar orbit. There are only two manoeuvres involved in the method and they are applied at the beginning and at the end of the second leg. Although the numerical results given in this paper correspond to transfers between halo orbits around the \(L_1\) point (of several amplitudes) and lunar polar orbits with altitudes varying between 100 and 500 km, the procedure we develop can be applied to any kind of lunar orbits, libration orbits around the \(L_1\) or \(L_2\) points of the Earth–Moon system, or to other similar cases with different values of the mass ratio. 相似文献
11.
Yijun Lian Gerard Gómez Josep J. Masdemont Guojian Tang 《Celestial Mechanics and Dynamical Astronomy》2013,115(2):185-211
In this paper we study the dynamics of a massless particle around the L 1,2 libration points of the Earth–Moon system in a full Solar System gravitational model. The study is based on the analysis of the quasi-periodic solutions around the two collinear equilibrium points. For the analysis and computation of the quasi-periodic orbits, a new iterative algorithm is introduced which is a combination of a multiple shooting method with a refined Fourier analysis of the orbits computed with the multiple shooting. Using as initial seeds for the algorithm the libration point orbits of Circular Restricted Three Body Problem, determined by Lindstedt-Poincaré methods, the procedure is able to refine them in the Solar System force-field model for large time-spans, that cover most of the relevant Sun–Earth–Moon periods. 相似文献
12.
In this paper, the lunar gravity assist (LGA) orbits starting from the Earth are investigated in the Sun–Earth–Moon–spacecraft restricted four-body problem (RFBP). First of all, the sphere of influence of the Earth–Moon system (SOIEM) is derived. Numerical calculation displays that inside the SOIEM, the effect of the Sun on the LGA orbits is quite small, but outside the SOIEM, the Sun perturbation can remarkably influence the trend of the LGA orbit. To analyze the effect of the Sun, the RFBP outside the SOIEM is approximately replaced by a planar circular restricted three-body problem, where, in the latter case, the Sun and the Earth–Moon barycenter act as primaries. The stable manifolds associated with the libration point orbit and their Poincaré sections on the SOIEM are applied to investigating the LGA orbit. According to our research, the patched LGA orbits on the Poincaré sections can efficiently distinguish the transit LGA orbits from the non-transit LGA orbits under the RFBP. The former orbits can pass through the region around libration point away from the SOIEM, but the latter orbits will bounce back to the SOIEM. Besides, the stable transit probability is defined and analyzed. According to the variant requirement of the space mission, the results obtained can help us select the LGA orbit and the launch window. 相似文献
13.
There exist cislunar and translunar libration points near the Moon, which are referred to as the LL 1 and LL 2 points, respectively. They can generate the different types of low-energy trajectories transferring from Earth to Moon. The time-dependent analytic model including the gravitational forces from the Sun, Earth, and Moon is employed to investigate the energy-minimal and practical transfer trajectories. However, different from the circular restricted three-body problem, the equivalent gravitational equilibria are defined according to the geometry of the instantaneous Hill boundary due to the gravitational perturbation from the Sun. The relationship between the altitudes of periapsis and eccentricities is achieved from the Poincaré mapping for all the captured lunar trajectories, which presents the statistical feature of the fuel cost and captured orbital elements rather than generating a specified Moon-captured segment. The minimum energy required by the captured trajectory on a lunar circular orbit is deduced in the spatial bi-circular model. The idea is presented that the asymptotical behaviors of invariant manifolds approaching to/traveling from the libration points or halo orbits are destroyed by the solar perturbation. In fact, the energy-minimal cislunar transfer trajectory is acquired by transiting the LL 1 point, while the energy-minimal translunar transfer trajectory is obtained by transiting the LL 2 point. Finally, the transfer opportunities for the practical trajectories that have escaped from the Earth and have been captured by the Moon are yielded by the transiting halo orbits near the LL 1 and LL 2 points, which can be used to generate the whole of the trajectories. 相似文献
14.
In this paper, we study the existence of libration points and their linear stability when the three participating bodies are axisymmetric and the primaries are radiating, we found that the collinear points remain unstable, it is further seen that the triangular points are stable for 0<μ<μ c , and unstable for where , it is also observed that for these points the range of stability will decrease. In addition to this we have studied periodic orbits around these points in the range 0<μ<μ c , we found that these orbits are elliptical; the frequencies of long and short orbits of the periodic motion are affected by the terms which involve parameters that characterize the oblateness and radiation repulsive forces. The implication is that the period of long periodic orbits adjusts with the change in its frequency while the period of short periodic orbit will decrease. 相似文献
15.
This paper is devoted to the study on applying numerical techniques to accurately compute and robustly extend the libration point orbits (LPOs). A new methodology is proposed exploiting the hyperbolic dynamics of the collinear libration points. Numerical tools are developed to facilitate the efficient computation process, which are applicable to realistic force models and inherently parallelizable. Extensive numerical explorations in the Earth–Moon system are carried out, revealing the delicate structures of nested island chains and bounded chaotic motions on the center manifold. Numerical results confirm that the proposed approach can handle the computations of various types of LPOs in a unified manner and is operational over a wide range of energy levels. LPOs obtained with this approach offer a broad range of future mission possibilities in an extended vicinity of the collinear libration points. 相似文献
16.
This work proposes a Lunar Global Positioning System (LGPS) and a Lunar Global Communication System (LGCS) using two constellations
of satellites on Lissajous trajectories around the collinear L
1 and L
2 libration points in the Earth–Moon system. This solution is compared against a Walker constellation around the Moon similar
to the one used for the Global Positioning System (GPS) on the Earth to evaluate the main differences between the two cases
and the advantages of adopting the Lissajous constellations. The problem is first studied using the Circular Restricted Three
Body Problem to find out its main features. The study is then repeated with higher fidelity using a four-body model and higher-order
reference trajectories to simulate the Earth-Moon-spacecraft dynamics more accurately. The LGPS performance is evaluated for
both on-ground and in-flight users, and a visibility study for the LGCS is used to check that communication between opposite
sides of the Moon is possible. The total ΔV required for the transfer trajectories from the Earth to the constellations and the trajectory control is calculated. Finally,
the estimated propellant consumption and the total number of satellites for the Walker constellation and the Lissajous constellations
is used as a performance index to compare the two proposed solutions. 相似文献
17.
Using inter-satellite range data,the combined autonomous orbit determination problem of a lunar satellite and a probe on some special orbits is studied in this paper.The problem is firstly studied in the circular restricted three-body problem,and then generalized to the real force model of the Earth-Moon system.Two kinds of special orbits are discussed:collinear libration point orbits and distant retrograde orbits.Studies show that the orbit determination accuracy in both cases can reach that of the observations.Some important properties of the system are carefully studied.These findings should be useful in the future engineering implementation of this conceptual study. 相似文献
18.
On the stabilization of the collinear libration points of the restricted circular three-body problem
The possibility of stabilizing the collinear libration points of the circular restricted three-body problem by using an additional jet acceleration (constant in magnitude) is investigated. Three stabilization laws are considered when the jet acceleration is either directed continuously to one of the primariesm
1,m
2 or is parallel to the line joining them. The solution of the problem formulated is based on the method of the driving forces structure analysis created by W. Thomson and P. Tait. It is shown that none of the stabilization laws mentioned ensures the existence of the isolated minimum of changed potential energy, and therefore the secular stability of the collinear libration points is impossible. In the 3rd and 4th paragraphs the possibility of a gyroscopic stabilization of these points is considered. It is shown that the gyroscopic stabilization of the external libration points is possible only when jet acceleration is either directed to the distant mass or is parallel to the line joining the primaries. The necessary and sufficient conditions of the gyroscopic stabilization are given. It is also shown that the internal libration points cannot be stabilized by any of the laws considered. For the Earth-Moon system the numerical data of time-existence of the satellite in the vicinity of the libration point situated near the Moon are given. 相似文献
19.
We study the equilibrium points and the zero-velocity curves of Chermnykh’s problem when the angular velocity ω varies continuously and the value of the mass parameter is fixed. The planar symmetric simple-periodic orbits are determined numerically and they are presented for three values of the parameter ω. The stability of the periodic orbits of all the families is computed. Particularly, we explore the network of the families when the angular velocity has the critical value ω = 2√2 at which the triangular equilibria disappear by coalescing with the collinear equilibrium point L1. The analytic determination of the initial conditions of the family which emanate from the Lagrangian libration point L1 in this case, is given. Non-periodic orbits, as points on a surface of section, providing an outlook of the stability regions, chaotic and escape motions as well as multiple-periodic orbits, are also computed. Non-linear stability zones of the triangular Lagrangian points are computed numerically for the Earth–Moon and Sun–Jupiter mass distribution when the angular velocity varies. 相似文献
20.
M. K. Ammar 《Astrophysics and Space Science》2008,313(4):393-408
In this paper the effect of solar radiation pressure on the location and stability of the five Lagrangian points is studied,
within the frame of elliptic restricted three-body problem, where the primaries are the Sun and Jupiter acting on a particle
of negligible mass. We found that the radiation pressure plays the rule of slightly reducing the effective mass of the Sun
and changes the location of the Lagrangian points. New formulas for the location of the collinear libration points were derived.
For large values of the force ratio β, we found that at β=0.12, the collinear point L3 is stable and some families of periodic orbits can be drawn around it. 相似文献