The Trojan Manifold in the System Earth-Moon

Deprit, André; Henrard, Jacques; Palmore, Julian; Price, J. F.; Sadler, D. H.

doi:10.1093/mnras/137.3.311

Cited by 31 publications

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“…This bifurcation generates a new domain new domain inside of which the orbits librate around the fixed point close to (θ, u) = (180˚, 0) (see Fig.2f). A similar result was found by Deprit et al (1967) for an Earth-Moon like system in the circular case (ε = 1/81). In the RF, the authors showed that the short period families L s 4 and L s 5 terminate on a periodic orbit of L 3 (see the outline in Fig.4).…”

Section: The Averaged Problemsupporting

confidence: 87%

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On the co-orbital motion in the planar restricted three-body problem: the quasi-satellite motion revisited

Pousse

Robutel

Vienne

2017

Celest Mech Dyn Astr

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International audienceIn the framework of the planar and circular restricted three-body problem, we consider an asteroid that orbits the Sun in quasi-satellite motion with a planet. A quasi-satellite trajectory is a heliocentric orbit in co-orbital resonance with the planet, characterized by a non zero eccentricity and a resonant angle that librates around zero. Likewise, in the rotating frame with the planet it describes the same trajectory as the one of a retrograde satellite even though the planet acts as a perturbator. In the last few years, the discoveries of asteroids in this type of motion made the term " quasi-satellite " more and more present in the literature. However, some authors rather use the term " retrograde satellite " when referring to this kind of motion in the studies of the restricted problem in the rotating frame. In this paper we intend to clarify the terminology to use, in order to bridge the gap between the perturbative co-orbital point of view and the more general approach in the rotating frame. Through a numerical exploration of the co-orbital phase space, we describe the quasi-satellite domain and highlight that it is not reachable by low eccentricities by averaging process. We will show that the quasi-satellite domain is effectively included in the domain of the retrograde satellites and neatly defined in terms of frequencies. Eventually, we highlight a remarkable high eccentric quasi-satellite orbit corresponding to a frozen ellipse in the heliocentric frame. We extend this result to the eccentric case (planet on an eccentric motion) and show that two families of frozen ellipses originate from this remarkable orbit

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Section: The Averaged Problemsupporting

confidence: 87%

“…Representation of the result ofDeprit et al (1967) in the RF: the merge of the short period families L s 4 and L s 5 with L 3 and bifurcation of the latter that becomes stable.…”

mentioning

confidence: 99%

On the co-orbital motion in the planar restricted three-body problem: the quasi-satellite motion revisited

Pousse

Robutel

Vienne

2017

Celest Mech Dyn Astr

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“…In this case which corresponds to the Earth-Moon System the families L~ and L~, have been studied by Deprit et al (1967).…”

Section: Resultsmentioning

confidence: 99%

Vertical stability of periodic solutions around the triangular equilibrium points

Perdios

Zagouras

1991

Celestial Mech Dyn Astr

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Abstract. The vertical stability character of the families of short and long period solutions around the triangular equilibrium points of the restricted three-body problem is examined. For three values of the mass parameter less than equal to the critical value of Routh (/~R) i.e. for # = 0.000953875 (Sun-Jupiter), # = 0.01215 (Earth-Moon) and/~ =/1R = 0.038521, it is found that all such solutions are vertically stable. For # > PR vertical stability is studied for a number of 'limiting' orbits extended to/~ = 0.45. The last limiting orbit computed by Deprit for # = 0.044 is continued to a family of periodic orbits into which the well known families of long and short period solutions merge. The stability characteristics of this family are also studied.

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“…is well known that in the R3BP families of such orbits exists around the so called equilibrium points L 4 and L 5 , if the value of the mass parameter is less than the Routh's critical value [24]. In the classical work [9], we can find a deep analysis of the behaviour of the orbits obtained by numerical continuation of the infinitesimal Lyapunov orbits around L 5 and the evolution of such families is shown as the Jacobi constant changes its value. It is worth mentioning that the evolution of analogous families in our case inherits some behavior of the R3BP and the full R4BP [1].…”

Section: 5mentioning

confidence: 99%

Families of periodic orbits in the planar Hill’s four-body problem

Burgos-Garcia

2016

Astrophys Space Sci

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In this work we perform a numerical exploration of the families of planar periodic orbits in the Hill's approximation in the restricted four body problem, that is, after a symplectic scaling, two massive bodies are sent to infinity, by mean of expanding the potential as a power series in m 1/3 3 , (the mass of the third small primary) and taking the limit case when m 3 → 0. The limiting Hamiltonian depends on a parameter µ (the mass of the second primary) and possesses some dynamical features from both the classical restricted threebody problem and the restricted four-body problem. We explore the families of periodic orbits of the infinitesimal particle for some values of the mass parameter, these explorations show interesting properties regarding the periodic orbits for this problem, in particular for the Sun-Jupiter-asteroid case. We also offer details on the horizontal and vertical stability of each family.2010 Mathematics Subject Classification. 70F15, 70F16.

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The Trojan Manifold in the System Earth-Moon

Cited by 31 publications

References 0 publications

On the co-orbital motion in the planar restricted three-body problem: the quasi-satellite motion revisited

On the co-orbital motion in the planar restricted three-body problem: the quasi-satellite motion revisited

Vertical stability of periodic solutions around the triangular equilibrium points

Families of periodic orbits in the planar Hill’s four-body problem

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