Highlights• Impactors of different type/size/velocity can produce craters of the same diameter.• Conditions for such "isocraters" are derived from scaling laws, modeled numerically.• Response of interior to isocrater impacts varies strongly between impactor types.• Responses to similar impactors vary strongly with planetary structure.• Observed geophysical anomalies may allow to resolve non-uniqueness of impactor.Abstract 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.where D imp is the diameter of the impactor, and imp the densities of the target and the impactor, v imp is the velocity of the impactor, and g is gravity (e.g., Werner and Ivanov, 2015); following common practice (e.g., Chapman and McKinnon, 1986), we replace the velocity with its vertical component, thus introducing an implicit dependence on the angle θ with the horizontal in this and most of the following equations. The numerical values of the coefficient and exponents vary with certain target properties, especially porosity, and are chosen here to correspond to a frictionless, pore-free material because of our main focus on very large impacts; for porous targets with friction, the constants would be slightly different (see Supplement). Inserting Eq. 2 into Eq. 1 yields D f = 1.3688 imp 1 3 D 0.78 imp v 0.44 imp g 0.22 (3a) for simple craters and D f = 1.3836 imp 0.377 D 0.8814 imp