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• W1990599228 abstract "view Abstract Citations (38) References (31) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Chaotic Motion in the Outer Asteroid Belt and its Relation to the Age of the Solar System Murison, Marc A. ; Lecar, Myron ; Franklin, Fred A. Abstract Recently, we analyzed a relation, found for chaotic orbits, between the Lyapunov time TL (the inverse of the maximum Lyapunov exponent) and the 'event' time Te (the time at which an orbit becomes clearly unstable). In this paper we treat two new problems. First, we apply this TL - Te relation to numerical integrations of 25 outer-belt asteroids and show that, when viewed in the proper context of a Gaussian distribution of event time residuals, none of the 25 objects exhibit an anomalously short Lyapunov time. The current age of the solar system is approximately three standard deviations or less from the anticipated event times of all these asteroids. We argue that the Lyapunov times of the 25 remaining bodies are each consistent with the age of the solar system, and that we are therefore seeing the remnants of a larger original distribution. The bulk of that population has been ejected by Jupiter, leaving the 'tail members' as present-day survivors. This interpretation is consistent with current understanding of the behavior of trajectories near KAM tori in Hamiltonian systems. In particular, there is no need to invoke a new type of motion or class of dynamical objects to explain the short Lyapunov time scales found for solar system objects. Second, we discuss integrations of 440 fictitious outer-belt asteroids and show that the slope and offset parameters of the TL - Te relation do not change with an increase in Jupiter's mass by a factor of 10, and that the distribution of residuals in log Te is Gaussian. This allows us to sensibly and quantitatively interpret the significance of the Lyapunov time scale. However, the width of the residuals' distribution is a function of mass ratio. Since knowledge of the distribution width is needed in order to interpret the significance of predicted event times, a calibration must be performed at the mass ratio of interest. Publication: The Astronomical Journal Pub Date: December 1994 DOI: 10.1086/117245 Bibcode: 1994AJ....108.2323M Keywords: Asteroid Belts; Astronomical Models; Celestial Mechanics; Chronology; Liapunov Functions; Solar System Evolution; Computerized Simulation; Jupiter (Planet); Mass Distribution; Mass Ratios; Normal Density Functions; Numerical Integration; Astrophysics; SOLAR SYSTEM: GENERAL; CHAOTIC PHENOMENA full text sources ADS |" @default.
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• W1990599228 title "Chaotic motion in the outer asteroid belt and its relation to the age of the solar system" @default.
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