On the original distribution of the asteroids

Franklin, F. A.; Lecar, M.; Soper, Paul

doi:10.1016/0019-1035(89)90118-8

Cited by 31 publications

(11 citation statements)

References 8 publications

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“…All orbits located in these zones were temporarily stabilized by MMRs in the time span of over 10 4 years. This period of time is comparable with the mean lifetime of the nonresonant particles in the region among giant planets estimated by Franklin et al (1989). Most of the resonances are observed in the Main Belt and outside Saturn's orbit.…”

Section: Islands Of Temporary Stabilitysupporting

confidence: 83%

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The resonant dynamical evolution of small body orbits among giant planets

Gabryszewski

Wlodarczyk

2003

A&A

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Abstract.Mean motion resonances (MMRs) can lead either to chaotic or regular motion. We report on a numerical experiment showing that even in one of the most chaotic regions of the Solar System -the region of the giant planets, there are numerous bands where MMRs can stabilize orbits of small bodies in a time span comparable to their lifetimes. Two types of temporary stabilization were observed: short period (∼10 4 years) when a body was in a MMR with only one planet and long period (over 10 5 years) when a body is located in overlapping MMRs with two or three planets. The experiment showed that the Main Belt region can be enriched by cometary material in its pre-active state due to temporary resonant interactions between small bodies and giant planets.

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Section: Islands Of Temporary Stabilitysupporting

confidence: 83%

“…The earlier works of Everhart (1973) and Franklin et al (1989) indicate that there are two narrow bands at 7.02 and 7.54 AU where particles can survive longer than 10 6 years. In 1997 Holman (1997) pointed to a region between 24 and 27 AU where low inclined (i ≤ 1 • ) and low eccentric (e ≤ 0.01) objects can survive 1 Gyr.…”

Section: Discussionmentioning

confidence: 90%

The resonant dynamical evolution of small body orbits among giant planets

Gabryszewski

Wlodarczyk

2003

A&A

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“…It has been concluded (Franklin et al 1989;Murray & Dermott 1999) that low-eccentricity, low-inclination orbits between Jupiter and Saturn are unlikely to survive longer than 10 7 years, therefore any object formed in that region during the early stages of the formation of the outer Solar System was ejected long ago. Similar calculations for the Saturn-Uranus zone (Gladman & Duncan 1990;Holman & Wisdom 1993) gave an upper limit for the survival time scale in that region of 10 8 years.…”

Section: Discussionmentioning

confidence: 99%

On the origin of comet C/1999 S4 LINEAR

Marcos

2002

A&A

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Abstract. Current models of the formation of comets in the Solar System assume that the most likely formation site for these pristine objects is in the Uranus-Neptune zone or just beyond with subsequent dynamical ejection by the growing protoplanets to distant orbits to form the Oort cloud. However, the composition of the recently disintegrated comet C/1999 S4 LINEAR suggests that it was most likely formed in the Jupiter-Saturn region (Mumma et al. 2001b;Kawakita et al. 2001). In this paper we argue that cometesimals could easily appear inside exterior resonances resulting from gas drag, between the orbits of Jupiter and Saturn and beyond Saturn, during the formation of these giant planets. Then, the trapped material could evolve into actual comets by means of collisional coagulation, followed by gravitational instability of a layer of macroscopic bodies or two-body accretion. Properties of these objects would be rather different from those found in classical comets formed beyond Neptune as a result of different physicochemical environment. Our results also suggest that temporarily stable cometary belts may have existed in the Jupiter-Saturn region. We also discuss the implications of this scenario on the existence of a bimodal Centaur population.

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“…to be regular (integrable) if c \ 0 and chaotic if c [ 0. The numbers s(t) are called Lyapunov characteristic indicators (LCI ;& Lohinger 1993) and for pracFroeschle , Froeschle , tical calculations it is not possible to take t ] O. Thus, the evolution of s(t) is followed up to some time and we plot log s(t) versus log t. If the curve has a negative constant slope, the system is regular ; if it presents an inÑection of the slope which comes close to 0 and the plot converges to a certain value of s(t), the system is chaotic.…”

Section: Introductionmentioning

confidence: 99%

A Comparison Between Methods to Compute Lyapunov Exponents

Tancredi¹,

Sánchez²,

Roig³

2001

The Astronomical Journal

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Lyapunov characteristic exponents measure the rate of exponential divergence between neighboring trajectories in the phase space. For a given autonomous dynamical system, the maximum Lyapunov characteristic exponent (hereafter LCE) is computed from the solution of the variational equations of the system. There are many dynamical systems in which the formulation and solution of the variational equations is a cumbersome task. In those cases an alternative procedure, Ðrst introduced by Benettin et al., is to replace the variational solution by computing two neighbor trajectories (the test particle and its shadow) and calculating the mutual distance. In this paper, we deal with a comparison between these two di †erent techniques for the calculation of LCE : the variational method and the two-particle method. We point out a problem that can appear when the two-particle method is used, which can lead to a false estimation of a positive LCE. The explanation of this phenomenon can be analyzed in two di †erent situations : (1) for relatively large initial separations the two-particle method is not a good approximation to the solution of the variational equations, and (2) for small initial separations the two-particle method have problems related to the machine precision, even when the separation can be many order of magnitudes larger than the machine precision. We show some examples of false estimates of the LCE that have already appeared in the literature using the two-particle method, and Ðnally we present some suggestions to be taken into account when this method has to be used.

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On the original distribution of the asteroids

Cited by 31 publications

References 8 publications

The resonant dynamical evolution of small body orbits among giant planets

The resonant dynamical evolution of small body orbits among giant planets

On the origin of comet C/1999 S4 LINEAR

A Comparison Between Methods to Compute Lyapunov Exponents

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