# How do I calculate a planets mass?

by Vetmora
Tags: calculate, fictional, gravity, mass, planets
 P: 177 No, the diameter and orbital radius do not provide enough information to determine the mass or gravity. Both of these values depend on the average density of the planet. However, knowing the mass and diameter of a planet does determine its surface gravity (or vice versa). Specifically (assuming the planet to be spherical), $$M=\frac{\pi{}D^3\rho{}}{6}g=\frac{4GM}{D^2} \Rightarrow{}g=\frac{2\pi{}GD\rho{}}{3}$$. Where G is the universal gravitational constant, M is the mass of the planet, ρ is its average density, and D is its diameter. So, knowing any two of: mass, diameter, average density, and surface gravity is enough to determine the other two.