A Monte Carlo method for calculating orbits of comets
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**Session 43 -- SL-9, Comets, Solar System**
*Display presentation, Tuesday, 10, 1995, 9:20am - 6:30pm*

## [43.09] A Monte Carlo method for calculating orbits of comets

*J.Q.Zheng, M.J.Valtonen, S.Mikkola (Tuorla Obs), J.J.Matese, P.G.Whitman (USL), H.Rickman (Uppsala Obs)*

The present work is divided into two stages: 1. By using large numbers
(several millions) of accurate orbit integrations with the K-S regularization,
probability distributions for changes in the orbital elements of comets
during encounters with planets are evaluated. 2. These distributions are
used in a Monte Carlo simulation scheme which follows the evolution of orbits
under repeated close encounters. The method is typically about 10000
times faster than the usual integration of orbits, and produces results
which agree statistically with earlier work. We have calculated the orbits
of several million Oort Cloud comets after they have been perturbed by
Galactic tides (or other perturbations) and have entered the inner Solar
System. We find that enough comets are captured from the Oort Cloud by
planetary perturbations in order to explain the present population of
short period comets. If the active lifetime of a comet is not much greater
than 400 orbital revolutions, the median value of cos(i) of the Jupiter
family comets is 0.98, in agreement with observations. Also the inclination
distribution of the Halley type comets, as well as the relative numbers
of Jupiter family, Halley type and long period comets are predicted
correctly by the model. After comets have lost their volatiles they frequently
remain in the inner Solar System as dark bodies and some of them collide
with the planets. The collision rates have been evaluated by \"Opik's method.
We find 0.3--0.9 impacts/Myr by km-size bodies on the Earth. The rate
may be compared with the rate of cratering (20 km or larger in diameter)
which has been estimated to be 1 - 3 per Myr. Thus dead comets originating
from the Oort Cloud may contribute significantly to the terrestrial
cratering rate. Galactic tides cause a periodic modulation of the flux of
Oort cloud comets into the inner Solar System, and we show that the same
periodicity is reflected also in the cratering rate in our results, though
with a time delay and with added noise.

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