  A numerical simulation of the Oort cloud is used to explain the observed
orbital distributions and numbers of Jupiter-family and Halley-type
short-period comets. Comets are given initial orbits with perihelion distances
between 5 and 36 AU, and evolve under planetary, stellar and Galactic
perturbations for 4.5 Gyr. This process leads to the formation of an Oort cloud
(which we define as the region of semimajor axes a>1000 AU), and to a flux of
cometary bodies from the Oort cloud returning to the planetary region at the
present epoch. The results are consistent with the dynamical characteristics of
short-period comets and other observed cometary populations: the near-parabolic
flux, Centaurs, and high-eccentricity trans-Neptunian objects. To achieve this
consistency with observations, the model requires that the number of comets
versus initial perihelion distance is concentrated towards the outer planetary
region. Moreover, the mean physical lifetime of observable comets in the inner
planetary region (q<2.5 AU) at the present epoch should be an increasing
function of the comets' initial perihelion distances. Virtually all observed
Halley-type comets and nearly half of observed Jupiter-family comets come from
the Oort cloud, and initially (4.5 Gyr ago) from orbits concentrated near the
outer planetary region. Comets that have been in the Oort cloud also return to
the Centaur (5<q<28 AU, a<1000 AU) and near-Neptune high-eccentricity regions.
Such objects with perihelia near Neptune are hard to discover, but Centaurs
with characteristics predicted by the model (e.g., large semimajor axes, above
60 au, or high inclinations, above 40 degrees) are increasingly being found by
observers. The model predicts that the mean physical lifetime of all comets in
the region q<1.5 AU is less than approximately 200 revolutions.
