Submitted by LoreCriticizer t3_z53aqr in askscience
Quantum_Patricide t1_ixx2zxl wrote
If you are talking about surface gravity, and wanted to calculate the surface gravity of a planet in terms of Earth's gravity (g=(9.81ms^-2), then you couldn't just use the masses of the planets, you'd also need the radii. For example if you wanted to calculate the surface gravity of Mars, 0.38g.
The surface gravity of a planet is calculated as (4/3)*pi*G*density*radius, where G is the universal gravitational constant. If you know the density (mass/volume) and radius of Earth and the planet you're standing on, then the ratio of your planet's surface gravity to Earth's is the ratio of the densities multiplied by the ratio of the radii
or: g_planet/g_earth = (p_planet/p_earth) * (r_planet/r_earth)
More generally, the classical gravitational field at a point due to a distribution of masses is
Div(g) = -4*pi*G*density
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