  Only star clusters that are sufficiently compact and massive survive largely
unharmed beyond 10 Myr. However, their compactness means a high stellar density
which can lead to strong gravitational interactions between the stars. As young
stars are often initially surrounded by protoplanetary disks and later on
potentially by planetary systems, the question arises to what degree these
strong gravitational interactions influence planet formation and the properties
of planetary systems. Here, we perform simulations of the evolution of compact
high-mass clusters like Trumpler 14 and Westerlund 2 from the embedded to the
gas-free phase and study the influence of stellar interactions. We concentrate
on the development of the mean disk size in these environments. Our simulations
show that in high-mass open clusters $80-90\%$ of all disks/planetary systems
should be smaller than 50 AU just due to the strong stellar interactions in
these environments. Already in the initial phases, 3-4 close fly-bys lead to
typical disk sizes within the range of 18-27 AU. Afterwards, the disk sizes are
altered only to a small extent. Our findings agree with the recent observation
that the disk sizes in the once dense environment of the Upper Scorpio OB
association, NGC~2362, and h/$\chi$Persei are at least three times smaller in
size than, for example, in Taurus. We conclude that the observed planetary
systems in high-mass open clusters should also be on average smaller than those
found around field stars; in particular, planets on wide orbits are expected to
be extremely rare in such environments.
