# Would a world filled with water collapse?

I don't know if this is considered off-topic but,

If you took a planet (assumed solid) and filled it with water continuously/non-stop what would eventually happen to the water?

• Would gravity at some point fail to hold the water against the planet?
• Would the bonds of the water assist it and maintain a sort of spherical water planet?
• Adding more and more water would lead to a huge spherical water drop containing a solid core. Ultimately, a black hole would be obtained. Apr 18, 2016 at 18:53
• On a planet the size of Earth , water at depths deeper than 100 km would become a solid due to the pressure. As you add more and more water, that depth below which water is a solid would decrease due to the increasing gravity. Apr 18, 2016 at 18:58
• Depends whether you have any place to dump the heat to... before anything resembling a black hole forms, there would be a star with quite a bit of fusion reactions in your way. Try pouring water onto the sun and see what happens... Apr 18, 2016 at 19:20

Let's ignore the planet in the middle for now and just consider a big drop of water. The mass of water is proportional to the radius cubed:

$$M = \tfrac{4}{3} \pi r^3 \rho$$

and the surface gravitational acceleration is given by:

$$a = \frac{GM}{r^2}$$

so substituting for $M$ we get:

$$a = G\tfrac{4}{3} \pi \rho r$$

So the surface gravity increases as we add more water and $r$ increases. That means every extra bit of water we add is more tightly bound not less tightly bound. You could go on adding water until the whole thing eventually collapsed into a black hole, and there would never come a time when the gravity failed to hold any extra water added.

Though the working get's a little more complicated, exactly the same thing happens for a shell of water surronding a spherical body like a planet. Every additional kilogram of water is more tightly bound not less tightly bound.

• I think I'm missing some basic understanding here, everyone keeps mentioning a black hole. Why would a massive water drop cause a black hole? Apr 18, 2016 at 19:49
• Thank you for the link. I googled it myself but ended up at the Schwardzschild metric which wasn't as helpful haha. Apr 18, 2016 at 19:58
• @JohnRennie: Just a quick clarifying comment on word choice that you probably know. The object collapses into a black hole not when the radius "exceeds" the Schwarzschild radius, but when it LESS than that radius. You need to compress the object into that radius (for example, for the earth you need to squash it into about the size of a golf-ball). Apr 19, 2016 at 0:44