### What is the minimum mass required so that objects become spherical due to its own gravity?

• Is this minimum mass known? or maybe, is it given in terms of density? If so, how much density is the minimum to have an spherical object due to its own gravity?

You would have to define "objects." Icy bodies start to become round under their own gravity at a certain mass. Rocky planets will take more. Liquids would form a sphere with miniscule mass as I assume gas proto-planets would be round as soon as they have enough gravity to be considered an "object."

The minimum mass to be spherical is a tiny fraction of a gram. A drop of water is spherical. You should ask what is the maximum mass that an object could be and still be non-spherical. This depends on how quickly it is formed, because if there is not sufficient time to cool, it will melt and become round. Planets and asteroids run into this problem.

• This question is more complicated than it seems like it should be!

There is no threshold mass or density beyond which an object becomes perfectly spherical; even supermassive stars are slightly oblong. The only exception is black holes, which are perfectly round up until you reach the quantum level. If we want a simple answer, most guesses are somewhere around $\frac{1}{10000}$ the mass of earth, or $6\cdot10^{20}$ kg, but that is very approximate and depends on the composition of the object.