The ` Nice ’ Model. Öpik approximation Planet migration in a planetesimal disk The Nice model Consequences of the Nice Model: Epoch of Late Heavy Bombardment, Kuiper belt and asteroid belt distribution, Trojan asteroid distribution. Öpik approximation.
Planet migration in a planetesimal disk
The Nice model
Consequences of the Nice Model: Epoch of Late Heavy Bombardment, Kuiper belt and asteroid belt distribution, Trojan asteroid distribution
Used to estimate collision probability for 2 objects with orbits that cross
Orbits only cross at points along line where orbital planes intersect
from Wetherill 76
Probability of a collision
per planet’s orbital period
on rate that angular momentum
is passed between planet
and planetesimals, Hx
into formula for M(t)
Tsiganis et al. 05, Nature
Initial conditions: 4 giant planets were initially much closer together. The planetesimal disk was located just outside Uranus and extended from 15-34 AU and was about 35 Mearth
to scattering of planetesimals
a 2:1 mean motion resonance
3 papers appearing in Nature in 2005 + a fourth later
Rapidly changing stability in corotation region during resonances allows capture with a large range of inclinations and eccentricities
Morbidelli et al. 05, Nature
Figure Comparison of the orbital
distribution of Trojans between
model (filled circles) and observations
(dots). The distribution of the simulated Trojans is somewhat skewed towards large libration amplitudes, relative to the observed population. However, a fraction of the planetesimals with the largest amplitudes would leave the Trojan region during the subsequent 4 Gyr of evolution, leading to a better match.
The planetary orbits and the positions of the disk particles. The four giant planets were initially on nearly circular, co-planar orbits with semi-major axes of 5.45, 8.18, 11.5 and 14.2 AU. The dynamically cold planetesimal disk was 35M , with an inner edge at 15.5 AU and an outer edge at 34 AU.
Four different epochs are shown: a, the beginning of planetary migration (100 Myr); b, just before the beginning of LHB (879 Myr); c, just after the LHB has started (882 Myr); and d, 200 Myr later, when only 3% of the initial mass of the disk is left and the planets have achieved their ﬁnal orbits.
Gomes et al. 05, Nature
The cumulative mass of comets (solid curve) and asteroids (dashed curve) accreted by the Moon. We have offset the comet curve so that the value is zero at the time of 1:2 MMR crossing. Thus, 5 x 1021g of comets was accreted before resonant crossing and 9 x 1021g of cometary material would have struck the Moon during the LHB. Gomes et al. 05
Observed KBO objects
Levison, H. F. et al. 08, Icarus, 196, 258
Simulation closely resembles Kuiper belt, and much more so than other models