GamingGlen said:
Is there an equation for this? The only one I found is linear, so my spreadsheet keeps the surface gravity seemingly low for super Earths (which does keep such planets more viable for adventuring on them).
The radius-density relationship is better than scaling exponents. You can derive density from radius and vice-versa. Once you have these two values, you can solve for everything else. Where radius r and density d are expressed in earths (radius and density = 1), the radius-density relationship appears to be:
Ln(2d) = Ln(2) × r and 2d = 2^r
Therefore
d = Exp(r × Ln(2))/2 = 2^r/2 and
r = Ln(2d)/Ln(2)
Watery/icy bodies (icy moons, failed cores, oceanic superterrestrials) have 1/3 to 1/6 of this value (Ceres 0.67, Pluto 0.651, Triton 0.649, Titania 0.574, Charon 0.562, Oberon 0.546, Ganymede 0.531, Titan 0.517, Callisto 0.513, Dione 0.508, Umbriel 0.477, Rhea 0.414, Mimas 0.409, Iapetus 0.365, Enceladus 0.343, Tethys 0.339).
With mass m expressed in earth masses,
m = 0.5 Exp( r × Ln(2) ) × r³ = r³ × 2^r / 2
You can derive radius from mass by working this in reverse, but you need a Lambert power log function.
r = 3 LambertW( Ln(2) / 3×CubeRt(2m) ) / Ln(2)