Chaos and cometary clouds in the solar system

Petrosky, Tomio

doi:10.1016/0375-9601(86)90673-0

Cited by 78 publications

(85 citation statements)

References 3 publications

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“…The fact that it is comets that are considered in Ref. 8, but not DMP's, is obviously of no importance for this conclusion. The minimum value of r a is defined by the maximum w ch ∼ r p /r a value which can be reach by an injected DMP during its chaotic motion.…”

Section: Density Of Dark Mattermentioning

confidence: 94%

“…8. According to the numerical calculations of Ref. 8, in the case of Jupiter the values of the semi-major axes r a for the resulting trajectories belong to the interval 10 3 -10 4 au for q/r p = 4 -6. The fact that it is comets that are considered in Ref.…”

Section: Density Of Dark Mattermentioning

confidence: 97%

“…It was pointed out and partly analyzed (though for the capture of comets, but not of DMP's), by Petrosky in Ref. 8 and Chirikov and Vecheslavov in Ref. 9.…”

Section: Dimensional Estimate For Mass Of Captured Dark Mattermentioning

confidence: 99%

“…The kick function F (φ) was computed in Ref. 8 for the case when a comet (or DMP) and a planet move in one plane and when the perihelion distance q > r p . In this case F (φ) = (m p /M )β(q/r p ) sin φ and the function β(x) ≈ 26 exp(−4x 3/2 /3 √ 2)/x 1/4 so that β(1) ≈ 10.…”

Section: Dynamical Approachmentioning

confidence: 99%

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Capture of Dark Matter by the Solar System

Khriplovich

Shepelyansky

2009

Int. J. Mod. Phys. D

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We study the capture of galactic dark matter by the Solar System. The effect is due to the gravitational three-body interaction between the Sun, one of the planets, and a dark matter particle. The analytical estimate for the capture cross-section is derived and the upper and lower bounds for the total mass of the captured dark matter particles are found. The estimates for their density are less reliable. The most optimistic of them give an enhancement of dark matter density by about three orders of magnitudes compared to its value in our Galaxy. However, even this optimistic value remains below the best present observational upper limits by about two orders of magnitude.

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Section: Density Of Dark Mattermentioning

confidence: 94%

Section: Density Of Dark Mattermentioning

confidence: 97%

“…It was pointed out and partly analyzed (though for the capture of comets, but not of DMP's), by Petrosky in Ref. 8 and Chirikov and Vecheslavov in Ref. 9.…”

Section: Dimensional Estimate For Mass Of Captured Dark Mattermentioning

confidence: 99%

Section: Dynamical Approachmentioning

confidence: 99%

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Capture of Dark Matter by the Solar System

Khriplovich

Shepelyansky

2009

Int. J. Mod. Phys. D

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“…We expect to have chaotic regions for this Hamiltonian since it is well known that a small time-periodic perturbation imposed on the Kepler problem creates a chaotic region with an erratic behavior near the parabolic orbit of the Kepler problem (see [21]). …”

Section: The Cp Problemmentioning

confidence: 99%

Phase space structure of the hydrogen atom in a circularly polarized microwave field

Barrabés

Ollé

Borondo

et al. 2012

Physica D: Nonlinear Phenomena

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We consider the problem of the hydrogen atom interacting with a circularly polarized microwave field, modeled as a perturbed Kepler problem. A remarkable feature of this system is that the electron can follow what we term erratic orbits before ionizing. In an erratic orbit the electron makes multiple large distance excursions from the nucleus with each excursion being followed by a close approach to the nucleus, where the interaction is large. Here we are interested in the mechanisms that explain this observation. We find that the manifolds associated with certain hyperbolic periodic orbits may play an important role, despite the fact that, in some respects, the dynamics is almost Keplerian. A study of some relevant invariant objects is carried out for different system parameters. The consequences of our findings for ionization of an electron by the external field are also discussed.

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The Evolution of Long-Period Comets

Wiegert

Tremaine

1999

Icarus

174

210

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We study the evolution of long-period comets by numerical integration of their orbits, a more realistic dynamical approach than the Monte Carlo and analytic methods previously used to study this problem. We follow the comets from their origin in the Oort cloud until their final escape or destruction, in a model solar system consisting of the Sun, the four giant planets and the Galactic tide. We also examine the effects of nongravitational forces as well as the gravitational forces from a hypothetical solar companion or circumsolar disk. We confirm the conclusion of Oort and other investigators that the observed distribution of long-period comet orbits does not match the expected steady-state distribution unless there is fading or some similar physical process that depletes the population of older comets. We investigate several simple fading laws. We can match the observed orbit distribution if the fraction of comets remaining observable after m apparitions is ∝m −0.6±0.1 (close to the fading law originally proposed by Whipple 1962); or if approximately 95% of comets live for only a few (∼6) returns and the remainder last indefinitely. Our results also yield statistics such as the expected perihelion distribution, distribution of aphelion directions, frequency of encounters with the giant planets and the rate of production of Halley-type comets.

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Chaos and cometary clouds in the solar system

Cited by 78 publications

References 3 publications

Capture of Dark Matter by the Solar System

Capture of Dark Matter by the Solar System

Phase space structure of the hydrogen atom in a circularly polarized microwave field

The Evolution of Long-Period Comets

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