Simple question. Can a crater, theoretically, form inside another crater? Say if a very large one just happened to, by sheer cosmic coincidence, had another smaller meteorite fall inside and impact hard enough to form a smaller crater inside of the crater? Say, half a kilometre inside of a two kilometre large crater?
I am no astronomer by any means, I was just immensely curious if this can actually happen, and if so, how it would work.
Yes, craters can overlap, and they do overlap.
The exact theory of the origin of the Moon is still debated, but from the understanding of the Lunar geologic timescale we can see that it's been there, getting hit for at least 4 billion years. That's plenty of time for craters to being overlapping each other in large numbers.
The ejecta of newer impacts make the contours of the older ones less clear. In fact, crater counting, with attention to the frequency of overlapping craters is actually used to determine the age of a surface, of how long it has been exposed to impacts.
Yes, of course. Lunar surface is filled with overlapping craters. See Vendelinus for example. The relative ages of the craters can be determined by the amount of secondary craters per unit area which overlap on a primary crater. A theoretical study has been made on this. See: Overlapping Lunar Craters by M.S. Podanoffsky, Strolling Astronomer, vol. 20, no. 5–6, 1967 (link)
Even in asteroids, overlapping craters has been observed. Example - Ceres, Vesta
Also see - How overlapping craters are formed?
I know the question is about impact craters, but as it's not precised in the title, and for the sake of completeness: volcanic craters do overlap too. A large eruption can create a large crater, then another, smaller eruption, can create a new, smaller crater inside the old one. There are many examples on Earth, including Santa Ana (El Salvador), Misti (Peru), and Kilimanjaro (Tanzania):
Aerial view of Kibo, the highest cone of Kilimanjaro, showing three nested craters. Photo by Walter Mittelholzer, public domain.
They are called "nested craters" if you want to look for more. On other planets, a famous example is the nested calderas—a type of volcanic crater—of Olympus Mons, the tallest volcano on Mars, with as many as six overlapping structures identified:
This perspective view shows the complex caldera at the summit of Olympus Mons on Mars. CC BY-SA IGO 3.0 ESA/DLR/FU Berlin.
The question is well answered, but here is what has become a classic case in the Martian system. The large (9 km diameter) Stickney crater on the moon Phobos was hit more recently, producing the more sharply defined Limtoc Crater.
Things are not only so, but it is actually an example in math introduction textbooks about the fractals. Fractals are mathematical structures looking similarly in big and small. They have a lot of interesting properties.
Fun thing is that if you only have a photo, it is surprisingly hard to say if it is 10cm or 1000km. Because it looks the same. Some big craters, with more smaller craters over it, and yet more yet smaller craters. Making a picture of the Moon from the Earth with a telescope, or making a picture from 1m height from a probe, it looks the same.
