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This is not really a realistic scenario; an astronomer would first figure out the mass and volume, and THEN calculate the density based on these pieces of information.


Anyway, first you would get the volume, as density / mass. Then, from the volume, you can calculate the radius, using the formula of a sphere. This will only work for fairly large asteroids; for smaller ones it would be a very rough approximation - small asteroids usually have irregular shapes.

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Q: How do you find the diameter of an asteroid knowing its density and mass?
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