Secular resonances and the origin of eccentricities of Mars and the asteroids

摘要: Abstract A mechanism is treated for the origin of eccentricities asteroids and Mars: secular resonances associated with dissipation a primitive solar nebula. The nebula modeled as two-dimensional disk; closed-form, convergent integral derived to represent its disturbing function. Dissipation this gives rise “excitation waves”, produced by variable location resonances, which can excite eccentricity Mars, scatter asteroidal through observed ranges. By requiring that these ranges match values functions semimajor axis, one infers: (a) primordial Jupiter Saturn initially had amplitudes different from present-day values, but approached present toward end nebular dissipation; (b) time scale may have been order (few) × 104 years neared completion (but depends on validity linear equations model inherently nonlinear pumping); (c) it reasonable propose common eccentricies Mars asteroids. simple extension also accounts quasi-Gaussian distribution number density eccentricities.