Earth has about 2^170 atoms. If we ignore the core and mantle, focusing on the crust, surface and atmosphere, we should be able to cram it into IPv6. Even if we add a couple planets and moons in the future. At least if we stop giving each person 18 quintillion IPs just because we once thought encoding MAC addresses in the lower 64 bits was a good idea.

There are 10^80 atoms in the universe, therefore 266 bits are enough to give each a unique identifier. Due to how computers work maybe we can do two numbers: a 32-bit type or area code and a 256-bit counter. Or perhaps we just combine them into a single 272 or 288 or 320-bit number.