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When you look at other planets and moons in our solar system most of them have lots of craters. If Earth had no vegetation and water would it also look like this image of Charon?

enter image description here

Image Credit: NASA/JHUAPL/SwRI

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Well the oceanic crust get recycled (through subduction), the oldest being only ~200 million year old, and the average, much younger. And on continents it is not just vegetation but dynamic processes such as collision, rifting, erosion etc. that quickly (in geologic time scales) modify the landscape. Even Chicxulub is not obvious if you just look at the topography/bathymetry.

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Without water there would be no multi-billion year history of plate tectonics, no glacial action, and no fluvial erosion, so the Earth would look unrecognizably primitive. But we have an atmosphere, so all the impact crater rims would be subject to aeolian erosion whilst low points, including crater bowls, would have aeolian sedimentary infill. Volcanic activity would be much more obvious, and would also tend to obliterate craters, as it has in numerous other examples in the solar system. Earth would therefore appear as a rather muted, sediment-draped version of the moon.

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No, there are nowhere near this many craters on earth.

I think you're asking if there are lots of craters on earth too, but they're hard to see because of vegetation and the oceans. The answer is 'no'. The main reason is that — thanks to plate tectonics — most of the crust is substantially younger (hundreds of millions of years) than the surface of, say, the moon (billions of years):

The age of continental crust

The ocean floor is mostly less than 200 Ma old:

The age of oceanic crust

This can account for even more of the difference than you might think, because it's thought that bolide impacts were several orders of magnitude more frequent a billion years ago than they are today. There was a lot of detritus in the early solar system!

We also see this surface age effect on the moon itself: the mare (seas) are made of relatively young lava, and have many fewer craters than the older highlands:

Lunar Highlands compared to Mare

Other than the age of the planet's surface, there are some secondary reasons why there are fewer craters on earth:

  • The earth has an atmosphere, in which most particles — things that might make a crater on a planetoid without an atmosphere — break or burn up.
  • The earth has water and weather, resulting in glaciers, frost, rain, and so on — this all acts to erase surface features through erosion.

This is not to say that things don't hit earth — they do, all the time. Just look at this map of recorded bolides over a recent 20 year period (Planetary Science, NASA, via Universe Today):

Recent bolides

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Erosion (especially), viscous relaxation, uplift, crust recycling (in the long term), volcanic activity, filling of the crater with deposits, and distortion by crust deformation (eg earthquakes) are all more important than vegetation, except for very small craters. Other planets and bodies have few or none of these processes.

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