  It is possible that the formation of the Oort Cloud dates back to the
earliest epochs of solar system history. At that time, the Sun was almost
certainly a member of the stellar cluster, where it was born. Since the solar
birth cluster is likely to have been massive (1000--10 000 Msol), and therefore
long-lived, an issue concerns the survival of such a primordial Oort Cloud. We
have investigated this issue by simulating the orbital evolution of Oort Cloud
comets for several hundred Myr, assuming the Sun to start its life as a typical
member of such a massive cluster. We have devised a synthetic representation of
the relevant dynamics, where the cluster potential is represented by a King
model, and about 20 close encounters with individual cluster stars are selected
and integrated based on the solar orbit and the cluster structure. Thousands of
individual simulations are made, each including 3 000 comets with orbits with
three different initial semi-major axes. Practically the entire initial Oort
Cloud is found to be lost for our choice of semi-major axes (5 000--20 000 au),
independent of the cluster mass, although the chance of survival is better for
the smaller cluster, since in a certain fraction of the simulations the Sun
orbits at relatively safe distances from the dense cluster centre. For the
range of birth cluster sizes that we investigate, a primordial Oort Cloud will
likely survive only as a small inner core with semi-major axes < 3 000 au. Such
a population of comets would be inert to orbital diffusion into an outer halo
and subsequent injection into observable orbits. Some mechanism is therefore
needed to accomplish this transfer, in case the Oort Cloud is primordial and
the birth cluster did not have a low mass. From this point of view, our results
lend some support to a delayed formation of the Oort Cloud, that occurred after
the Sun had left its birth cluster.
