Computation of families of periodic orbits and bifurcations around a massive annulus

Tresaco, Eva; Elipe, A.; Riaguas, Andrés

doi:10.1007/s10509-011-0925-1

Cited by 39 publications

(4 citation statements)

References 33 publications

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“…Previous studies have continued the periodic orbit and found period-doubling bifurcations as well as pseudo period-doubling bifurcations of periodic orbit families in the gravitational field of asteroid 216 Kleopatra. This work is quite different from the continuation of the periodic orbit in the gravitational field of a simple-shaped body, such as a finite straight segment (Elipe and Lara 2003), a solid circular ring (Broucke and Elipe 2005), a homogeneous cube (Liu et al 2011), and a massive annulus (Tresaco et al 2012). The continuation of the periodic orbit in the gravitational field of a simple-shaped body can help one to understand the periodic orbit families, bifurcation of periodic orbit families, and stability of orbits around irregular minor celestial bodies.…”

Section: Casesmentioning

confidence: 97%

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Periodic motion near the surface of asteroids

Jiang

Baoyin

Li³

2015

Astrophys Space Sci

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We are interested in the periodic motion and bifurcations near the surface of an asteroid. The gravity field of an irregular asteroid and the equation of motion of a particle near the surface of an asteroid are studied. The periodic motions around the major body of triple asteroid 216 Kleopatra and the OSIRIS-REx mission target-asteroid 101955 Bennu are discussed. We find that motion near the surface of an irregular asteroid is quite different from the motion near the surface of a homoplastically spheroidal celestial body. The periodic motions around the asteroid 101955 Bennu and 216 Kleopatra indicate that the geometrical shapes of the orbits are probably very sophisticated. There exist both stable periodic motions and unstable periodic motions near the surface of the same irregular asteroid. This periodic motion which is unstable can be resonant or non-resonant. The period-doubling bifurcation and pseudo period-doubling bifurcation of periodic orbits coexist in the same gravity field of the primary of the triple asteroid 216 Kleopatra. It is found that both of the period-doubling bifurcations of periodic orbits and pseudo period-doubling bifurcation of periodic orbits have four different paths. The pseudo period-doubling bifurcation found in the potential field of primary of triple asteroid 216 Kleopatra shows that there exist stable periodic orbits near the primary's equatorial plane, which gives an explanation for the motion stability of the triple asteroid 216 Kleopatra's two moonlets, Alexhelios and Cleoselene. spacecraft or moonlet which is orbiting an irregular asteroid can be modeled by a massless particle (Scheeres 2012;Takahashi et al. 2013;Chanut et al. 2014); if the particle is sufficiently far from the irregular asteroid, the asteroid can be approximately modelled as a sphere and the solar gravitation to the particle should be considered; conversely, if the particle is sufficiently close to the irregular asteroid, the irregular asteroidal gravity field provides the decisive effect on the motion of the particle, and the irregular asteroidal gravity field should be considered and the solar gravitation can be neglected (Borisov and Zakharov 2014;Wang et al. 2014).Recently, a few irregular asteroids were selected to analyze motions around them, including asteroids 4 Vesta (Mondelo et al.

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Section: Casesmentioning

confidence: 97%

“…As a periodic orbit continues(Hé non 1965;Tresaco et al 2012), the topological cases of the periodic orbit may change, and period-doubling bifurcation may occur. The period-doubling bifurcation occurs if and only if 2 or 4 Floquet multipliers collide at -1 and leave the original region.…”

mentioning

confidence: 99%

Periodic motion near the surface of asteroids

Jiang

Baoyin

Li³

2015

Astrophys Space Sci

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“…Distribution of six characteristic multipliers of the periodic orbit determines the topological classifications of periodic orbits [35]. The topological classifications of stable periodic orbits [17] have 7 different cases, which is listed in Table 1.…”

Section: Stability Of Periodic Orbitsmentioning

confidence: 99%

Stable periodic orbits for spacecraft around minor celestial bodies

Jiang

Schmidt

et al. 2017

Astrodyn

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We are interested in stable periodic orbits for spacecraft in the gravitational field of minor celestial bodies. The stable periodic orbits around minor celestial bodies are useful not only for the mission design of the deep space exploration, but also for studying the long-time stability of small satellites in the large-size-ratio binary asteroids. The irregular shapes and gravitational fields of the minor celestial bodies are modeled by the polyhedral model.Using the topological classifications of periodic orbits and the grid search method, the stable periodic orbits can be calculated and the topological cases can be determined. Furthermore, we find five different types of stable periodic orbits around minor celestial bodies: (1) stable periodic orbits generated from the stable equilibrium points outside the minor celestial body; (2) stable periodic orbits continued from the unstable periodic orbits around the

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“…For studies on some general features of the dynamics around a massive annulus, like orbit stability for various configurations and the equilibrium of the system, see. e.g., [67,91,92,93,94,95] and [96].…”

Section: Introductionmentioning

confidence: 99%

Orbital Perturbations Due to Massive Rings

Iorio

2012

Earth Moon Planets

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We analytically work out the long-term orbital perturbations induced by a homogeneous circular ring of radius R r and mass m r on the motion of a test particle in the cases (I): r > R r and (II): r < R r . In order to extend the validity of our analysis to the orbital configurations of, e.g., some proposed spacecraft-based mission for fundamental physics like LISA and ASTROD, of possible annuli around the supermassive black hole in Sgr A * coming from tidal disruptions of incoming gas clouds, and to the effect of artificial space debris belts around the Earth, we do not restrict ourselves to the case in which the ring and the orbit of the perturbed particle lie just in the same plane. From the corrections ∆̟ (meas) to the standard secular perihelion precessions, recently determined by a team of astronomers for some planets of the Solar System, we infer upper bounds on m r for various putative and known annular matter distributions of natural origin (close circumsolar ring with R r = 0.02 − 0.13 au, dust ring with R r = 1 au, minor asteroids, Trans-Neptunian Objects). We find m r ≤ 1.4 × 10 −4 m ⊕ (circumsolar ring with R r = 0.02 au), m r ≤ 2.6 × 10 −6 m ⊕ (circumsolar ring with R r = 0.13 au), m r ≤ 8.8 × 10 −7 m ⊕ (ring with R r = 1 au), m r ≤ 7.3 × 10 −12 M ⊙ (asteroidal ring with R r = 2.80 au), m r ≤ 1.1×10 −11 M ⊙ (asteroidal ring with R r = 3.14 au), m r ≤ 2.0×10 −8 M ⊙ (TNOs ring with R r = 43 au). In principle, our analysis is valid both for baryonic and nonbaryonic Dark Matter distributions.

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Computation of families of periodic orbits and bifurcations around a massive annulus

Cited by 39 publications

References 33 publications

Periodic motion near the surface of asteroids

Periodic motion near the surface of asteroids

Stable periodic orbits for spacecraft around minor celestial bodies

Orbital Perturbations Due to Massive Rings

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