Sun-perturbed earth-to-moon transfers with low energy and moderate flight time

Yagasaki, Kazuyuki

doi:10.1007/s10569-004-0406-8

Cited by 63 publications

(38 citation statements)

References 21 publications

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“…23,25). Hence, the equations of motion for the spacecraft can be written as (Yagasaki 2004): The bicircular model is a good approximation for the Earth-Moon-Sun system. The eccentricity of the Earth's orbit about the Sun (e earth = 0.016) and that of the Moon's orbit around the Earth (e moon = 0.054), are, in fact, very small and the lunar orbital plane is inclined by only 5 • with respect to the ecliptic plane.…”

Section: Equation Of Motionmentioning

confidence: 99%

Earth–Moon Weak Stability Boundaries in the restricted three and four body problem

Romagnoli

Circi

2008

Celest Mech Dyn Astr

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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.

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Section: Equation Of Motionmentioning

confidence: 99%

Earth–Moon Weak Stability Boundaries in the restricted three and four body problem

Romagnoli

Circi

2008

Celest Mech Dyn Astr

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“…Introduction. The notion of weak stability boundary (WSB) was first introduced heuristically by Belbruno in 1987 for designing fuel efficient space missions and was proven to be useful in applications [2,3,4,12,13,6,45,33,14,35,22,7,39,38,44]. The WSB can be used to construct low energy transfers to the Moon, requiring little or no fuel for capture into lunar orbit.…”

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confidence: 99%

Weak Stability Boundary and Invariant Manifolds

Belbruno¹,

Gidea²,

Topputo³

2010

SIAM J. Appl. Dyn. Syst.

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Abstract. The concept of weak stability boundary has been successfully used in the design of several fuel efficient space missions. In this paper we give a rigorous definition of the weak stability boundary in the context of the planar circular restricted three-body problem, and we provide a geometric argument for the fact that, for some energy range, the points in the weak stability boundary of the small primary are the points with zero radial velocity that lie on the stable manifolds of the Lyapunov orbits about the libration points L 1 and L 2 , provided that these manifolds satisfy some topological conditions. The geometric method is based on the property of the invariant manifolds of Lyapunov orbits being separatrices of the energy manifold. We support our geometric argument with numerical experiments.Key words. Weak Stability Boundary, Lyapunov Orbits, Invariant Manifolds AMS subject classifications. 70F15, 70F07, 37D101. Introduction. The notion of weak stability boundary (WSB) was first introduced heuristically by Belbruno in 1987 for designing fuel efficient space missions and was proven to be useful in applications [2,3,4,12,13,6,45,33,14,35,22,7,39,38,44]. The WSB can be used to construct low energy transfers to the Moon, requiring little or no fuel for capture into lunar orbit. The first application for an operational spacecraft occurred in 1991 with the rescue of the Japanese mission Hiten. WSB was also applied in ESA's spacecraft SMART-1 in 2004 (see [40]). The WSB technique will be applied again in ESA's mission BepiColombo to explore planet Mercury in 2013 (see [25]), and in some upcoming NASA missions.A different methodology of designing fuel efficient trajectories, based on hyperbolic invariant manifolds, was proposed in [1,26,28,29,30,31], and was successfully applied in several space missions (see also [18,19,20,21]). In some of these works it has been suggested that the hyperbolic invariant manifold method can be used to explain the trajectories obtained through the WSB method. Supporting this assertion, García and Gómez present in [22] numerical explorations that suggests that, for some range of energies, the WSB is contained in the closure of the union of the stable manifolds of the periodic orbits about two of the equilibrium points of the planar circular restricted three-body problem.In this paper we use the separatrix property of the invariant manifolds of the periodic orbits about the equilibrium points to argue that, under some conditions, the points on the stable manifolds are WSB points. We support our geometrical argument with numerical experiments. Our result, corroborated with the result in [22], demonstrates, by double inclusion, that, for some range of energies, the WSB coincides with the set of points on the stable manifolds with zero radial velocity and negative Kepler energy relative to the small primary.In Section 2 we give some background on the planar circular restricted three-body problem. In Section 3 we define the WSB as follows: in the context of the planar circular r...

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“…In contrast, in the present work we found periodic orbits which, besides being moderately fast, perform repeated passages around the primaries. Moreover, it must be noted that Bollt and Meiss (1995) and Yagasaki (2004a) only address the Earth-Moon RTBP, and though the most recent work (Yagasaki, 2004b) introduces the Sun perturbation, it does it through the BCP. In contrast, in this work we addressed the problem in the frame of the QBCP, which is a far more realistic model.…”

Section: Discussionmentioning

confidence: 99%