Get a copy of What If? 2 and Randall’s other books at: https://xkcd.com/booksMore serious answers to absurd questions at: https://what-if.xkcd.com/How long w...
Actually, even if the density was constant, the earth would turn into a black hole when it reached about 1.925 * 10^13 times its original mass, since the mass of a black hole is proportional to its radius, whereas the mass of the earth in this scenario grows proportional to radius cubed. This should happen around 371 years (?) after starting.
(Please check my calculations, I’m not 100% sure.)
Actually, even if the density was constant, the earth would turn into a black hole when it reached about 1.925 * 10^13 times its original mass, since the mass of a black hole is proportional to its radius, whereas the mass of the earth in this scenario grows proportional to radius cubed. This should happen around 371 years (?) after starting.
(Please check my calculations, I’m not 100% sure.)