I'm aware for over 100 years the reason has been known how impact craters are almost always circular, but my question really is has there been any recent insights in the area? What other topologies are physically possible?

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    $\begingroup$ Well... do you include grazing incidence gouges? These are easy to create with an aerodynamic structure like an airplane, but statistically unlikely for exo-terran objects. $\endgroup$ – Carl Witthoft Mar 5 '18 at 16:10
  • $\begingroup$ Was the formation of the Río Cuarto "craters" ever definitely decided? $\endgroup$ – James K Mar 5 '18 at 19:12

There are elongated craters from grazing impacts, and these can sometimes get rather odd shapes like Schiller on the Moon and Orcus Patera on Mars (the later is a bit contested, it might have formed from something other than an impact).

Double impact craters is another possibility. Some craters occur simultaneously (more direct picture). Splitting impactors is likely the one way of getting truly complex topologies. Most of the time they tend to follow each other, producing crater chains.

If terrain shifts craters may be deformed, and depending on details in the rock they may also get odd shapes. Meteor Crater in Arizona is somewhat squarish.

Craters cannot generate that complex patterns since they are just explosions out from a center and impactors are usually single objects or random clouds. In principle one could arrange asteroids along a trajectory to spell out letters upon impact, but it is an exceedingly unlikely configuration so most impacts will only manage 'O'.

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  • $\begingroup$ A great comprehensive reply which helps broaden the discussion. A thought experiment - take an impact like shoemaker-levy, increase the amount of fragments reduce their separation distance ...what would this produce? $\endgroup$ – Dan Mar 6 '18 at 6:29
  • $\begingroup$ That would make a crater chain. Hmm, I should probably add that to the answer. $\endgroup$ – Anders Sandberg Mar 6 '18 at 9:53
  • $\begingroup$ Actually, you did mention crater chains in your original answer. As you might guess I'm trying to develop this thought experiment in a particular direction...to take it further - imagine a variety of sizes for a disintegrated bolide with the gaps in between consisting of much smaller fragments like gravel, possibly under a power law distribution. what does this impact look like? $\endgroup$ – Dan Mar 8 '18 at 7:44

Impact craters are not always circular. They vary based on the angle of incidence. check Wetumpka crater and this research https://www.sciencedirect.com/science/article/pii/S0032063314001093

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    $\begingroup$ This answer would benefit a lot if you write a few lines explaining what's in that report. Specifically, that noncircular formations are almost exclusively limited to steep slope ground formations. Niven, in Lucifer's Hammer, refers to existing (at that time) studies which show that craters are essentially circular regardless of impact angle for "normal" circumstances. // My reading of your link is that noncircularity depends a lot more on the slope steepness than the relative angle of impact. $\endgroup$ – Carl Witthoft Mar 5 '18 at 19:37

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