A planet made from denser material than Earth might have equal gravity to Earth but a smaller radius. How small can a planet be and still have Earth gravity?

Ideally it should be habitable by humans, so not made of anything dangerous, radioactive or unstable.


The surface gravity of a planet is very close to $$g=\frac{4\pi G}{3}\rho r.$$ With $g$ to be kept constant, and $\frac{4\pi G}{3}$ a constant, we need $\rho_Pr_P=\rho_Er_E$, or $$r_P=\frac{\rho_E}{\rho_P}r_E,$$ with $\rho_E=5.515 \mbox{ g}/\mbox{cm}^3$ the mean density of Earth, $r_E=6371.0 \mbox{ km}$ the mean radius of Earth, $\rho_P=22.59\mbox{ g}/\mbox{cm}^3$ the density of densest natural element osmium, and $r_P$ the radius of the fictive osmium planet.

Hence $$r_P=\frac{5.515}{22.59}r_E=0.2441~r_E=1555\mbox{ km}.$$

Some compression of the core of an osmium planet due to pressure is neglected.

| improve this answer | |
  • $\begingroup$ Wow that's really small on the planet scale. $\endgroup$ – TheBluegrassMathematician Apr 30 '14 at 1:56
  • $\begingroup$ Yeah, that is small; that's half the size of Mercury. $\endgroup$ – LDC3 Apr 30 '14 at 2:10
  • $\begingroup$ Notably, despite having the same surface gravity of Earth, this "osmium-earth" has less than 0.1 times the mass. $\endgroup$ – zaratustra Apr 30 '14 at 15:23
  • $\begingroup$ Why would osmium be the limit though? Neutron stars are much denser. I realize you can't make a planet out of neutron star material, but surely there are things denser than osmium? $\endgroup$ – user21 Feb 21 '15 at 16:04
  • $\begingroup$ There's probobly not anything denser than Osmium in this context. Certainly there's denser material, even in our solar-system. The density at the core of our sun is about 150 g/CM3, but that's only possible under enormous pressure. The density of a white dwarf is much greater than that and the density of a neutron star, much greater still, but if you're talking about 1 earth gravity, neutron star material or white dwarf material would probobly be unstable and fly apart. There are some theories that say it could maintain integrity, but that's uncertain and I think unlikely $\endgroup$ – userLTK Apr 21 '15 at 9:03

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.