On the Stability of Resonant Asteroid Orbits

Hadjidemetriou, John D.; Ichtiaroglou, S.

doi:10.1007/978-94-009-7214-8_18

Cited by 10 publications

(13 citation statements)

References 12 publications

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“…We shall consider some well known asteroids, computing the measure of stability S, introduced by Szebehely (1978) and corresponding to the criteria defined by Hill (1878). The results obtained are confirmed by the computations of Hadjidemetriou and Ichtiaroglou (1983) In the Hilda group some (Hilda, Ismene, Bononia) show S< 0 while others (Chicago, Normannia) show S > 0 ; they correspond to a resonance of 2/3 with libration cycles of 250 to 300 years. The resonance 2/3 is represented by branches B. and B of Fig.…”

Section: Introductionmentioning

confidence: 55%

“…The Hecuba group shows S > 0 corresponding to a resonance 1/2, and can be identified on the stable branch A of Fig. 1 (Hadjidemetriou and Ichtiaroglou, 1983). The Hestia type of asteroids also present S> 0 and correspond to stable orbits with non-zero eccentricity at resonance 1/3.…”

Section: Introductionmentioning

confidence: 91%

“…This paper is an application of the criteria of stability defined and employed in the papers by Szebehely et al (1983),and Hadjidemetriou and Ichtiaroglou (1983); it is the result of discussions among the authors previously mentioned.…”

Section: Introductionmentioning

confidence: 99%

“…The resonance 2/3 is represented by branches B. and B of Fig. 1 of Hadjidemetriou and Ichtiaroglou (1983).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Stability of Some Asteroids

Vicente¹

1983

International Astronomical Union Colloquium

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The utilization of two different stability criteria, namely, Hill's modified stability criterium and the method of surface of section, has been employed for asteroid orbits. The idea is to compute different criteria of stability for the same asteroids in order to compare the results and see the practical interest of the computations for researches about evolutionary trends of individual asteroids, groups and families of asteroids.

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Section: Introductionmentioning

confidence: 55%

Section: Introductionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

“…The resonance 2/3 is represented by branches B. and B of Fig. 1 of Hadjidemetriou and Ichtiaroglou (1983).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Stability of Some Asteroids

Vicente¹

1983

International Astronomical Union Colloquium

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“…A detailed analysis of families of periodic orbits in the planar circular restricted problem and their stability was performed by Hadjidemetriou & Ichtiaroglou (1984) for µ = 0.001. Moreover, a review of different types of periodic orbits is given in Hadjidemetriou (1988).…”

Section: Introductionmentioning

confidence: 99%

The dynamics of the 1:2 resonant motion with Neptune in the 3D elliptic restricted three-body problem

Kotoulas¹

2005

A&A

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Abstract. We study the planar and the three-dimensional 1:2 resonant motion with Neptune (N1:2) in the framework of the elliptic restricted three-body problem. We examine the dynamics at the 1:2 mean motion resonance with Neptune in a hierarchy of models: the planar circular, the planar elliptic, the three-dimensional circular and the three-dimensional elliptic restricted three body problem. We start from the planar circular model in which we compute families of symmetric periodic orbits with stable and unstable segments. Using the circular planar model as the basic model, we proceed to more realistic models, namely the planar elliptic and the 3D circular problem. Families of symmetric periodic orbits of the above models bifurcate from the families of periodic orbits of the planar circular problem. Moreover, we compute families of symmetric periodic orbits in the 3D elliptic restricted three-body problem. These new families bifurcate from the families of periodic orbits of the planar elliptic and the 3D circular problem. The stability of all orbits is studied and the structure of the phase space is discussed in detail.

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Periodic Orbits

Hadjidemetriou

1984

The Stability of Planetary Systems

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On the Stability of Resonant Asteroid Orbits

Cited by 10 publications

References 12 publications

The Stability of Some Asteroids

The Stability of Some Asteroids

The dynamics of the 1:2 resonant motion with Neptune in the 3D elliptic restricted three-body problem

Periodic Orbits

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