On the original distribution of the asteroids: IV. Numerical experiments in the outer asteroid belt

摘要: Abstract We assumed, in 1973, that the asteroids were building blocks of planets and initially distributed approximately uniformly. suggested present distribution was carved out by perturbations Jupiter. To test this hypothesis further, we have now integrated orbits 140 with 14 semimajor axes from 0.63 to 0.76 (in units where aJupiter = 1.0) increments 0.01, at 10 values eccentricity 0.01 0.19 0.02. The integrations extended for 1 million Jovian years (about 12 years) unless asteroid crossed Jupiter's orbit before then. Jupiter an elliptic its varying a 54,000-year period, line apsides rotating 300,000-year period induced secular Saturn. confined plane. In main survey, chose most “unstable” phases relative Jupiter; i.e., apsidal lines separated 180°. There are only 8 8032 reliable between 0.68 0.74. our simulation, 64 90 (71%) equal or larger than 0.680 removed. Of 26 remained, 16 had initial eccentricities less 0.03. Ten remaining a≥0.68 years; 5 became crossers remained. Including these longer integrations, 69 (77%) escaped. However, depletion much reduced those cases when caused conjunctions occur asteroid's perihelion; coincided. found strong correlation Lyapunov exponent crossing time times (and few integrations). If result extrapolates 4.5 billion years, it would indicate perturber, there stable no today.