  Impactors of different types and sizes can produce a final crater of the same
diameter on a planet under certain conditions. We derive the condition for such
"isocrater impacts" from scaling laws, as well as relations that describe how
the different impactors affect the interior of the target planet; these
relations are also valid for impacts that are too small to affect the mantle.
The analysis reveals that in a given isocrater impact, asteroidal impactors
produce anomalies in the interior of smaller spatial extent than cometary or
similar impactors. The differences in the interior could be useful for
characterizing the projectile that formed a given crater on the basis of
geophysical observations and potentially offer a possibility to help constrain
the demographics of the ancient impactor population. A series of numerical
models of basin-forming impacts on Mercury, Venus, the Moon, and Mars
illustrates the dynamical effects of the different impactor types on different
planets. It shows that the signature of large impacts may be preserved to the
present in Mars, the Moon, and Mercury, where convection is less vigorous and
much of the anomaly merges with the growing lid. On the other hand, their
signature will long have been destroyed in Venus, whose vigorous convection and
recurring lithospheric instabilities obliterate larger coherent anomalies.
