system
Given the following post, respond as if you're commenting on Reddit:
human
If the Earth was shrunken down to the size of a marble but still had the same mass, would it form a black hole? How much mass would a marble need to have to form a black hole?
gpt
We don't exactly know how big a black hole is. The math says it has zero volume (a singularity), but we don't know what happens to the physics in these situations. What we do know is, given a certain amount of mass, how big the radius is of the sphere that encompasses the region from which light can't escape.

This radius is called the Schwarzschild radius and it is given by the expression 2 G M / c^2 (G = Gravitational constant, M = mass, c = speed of light). If the object is smaller than its Schwarzschild radius, then it's a black hole.

Plugging in the numbers for Earth gives a value of 8.8 mm. This is around the size of a large marble.