We had the gravity discussion just a few months ago, I was under the impression G was largely a 'done deal', that planetary density was a minor factor compared to sheer size.
So G would be largely determined simply by world size with a few things like 'superdense neutronium core placed by Grandfather's prankster kids and powered up' type anomalies.
Gravity varies significantly by average density of body.
G = M/D²
G in gravities
M in earths
D distance in earth radii
All expressed in earths.
Mass = r³d
r = radius
d = density
Both can be expressed in earths.
Substituting into the formula to get surface g's
G = r³d/r²
Simplifying
G = rd
Noting that comets have densities of between 0.6 and 2 g/cm³, and Earth is about 5.5, expressing cometary density in earths is 0.1 to 0.36 or so...
Note that the inner core is about 13 g/cm³, or 2.3 D
e, outer core between 10 and 12 g/cm³, and the mantle about 3 and 5 g/cm³, and the ocean between 1.4 and 1.01 g/cm³..
Simplifying for playability...
So, a metalic core is about 2.4 D
e, liquid outer core about 2 D
e.
The silicate layer is about 0.55 to 1 D
e, let's average and call it 75%
Ices run from about 0.1 to a peak at around 0.25 D
e... (1.4 g/cm³)...
I think I can cobble up a calculator in Javascript to do it easily enough...
but not tonight. Tonight I'll use a calculator.
If we assume similar proportions... radii and density (in earths) for an approximation
Earth inner solid core 1220km 2.4 D
e 0.16 M
eEarth liquid outer core 3400 km, 2 D
e 0.29 M
eEarth surface 6,371km, 0.75 D
e 0.63 M
eI get about 0.94 M
e, which means I need a better estimate on the density.
But note, for a simpler methodology...
G= {[0.86*(S/8)³]+[1.15*(S
core/8)³]}/S²
Here's a handy table of Masses (in Earth Masses) by proportion of metallic core.
| | | | | | | | | | | | | | | | | | | | | | | |
UWP Size | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 0 | 0 | 0 | 0.02 | 0.06 | 0.14 | 0.28 | 0.49 | 0.77 | 1.15 | 1.64 | 2.25 |
1 | 0 | 0 | 0.02 | 0.06 | 0.15 | 0.28 | 0.49 | 0.77 | 1.15 | 1.64 | 2.25 | | | | | | | | | | | | |
2 | 0.01 | 0.02 | 0.03 | 0.07 | 0.16 | 0.29 | 0.5 | 0.78 | 1.16 | 1.65 | 2.26 | | | | | | | | | | | | |
3 | 0.04 | 0.05 | 0.06 | 0.11 | 0.19 | 0.33 | 0.53 | 0.82 | 1.19 | 1.68 | 2.29 | | | | | | | | | | | | |
4 | 0.11 | 0.11 | 0.12 | 0.17 | 0.25 | 0.39 | 0.59 | 0.88 | 1.26 | 1.74 | 2.35 | | | | | | | | | | | | |
5 | 0.21 | 0.21 | 0.23 | 0.27 | 0.35 | 0.49 | 0.69 | 0.98 | 1.36 | 1.84 | 2.45 | | | | | | | | | | | | |
6 | 0.36 | 0.36 | 0.38 | 0.42 | 0.5 | 0.64 | 0.84 | 1.13 | 1.51 | 2 | 2.6 | | | | | | | | | | | | |
7 | 0.57 | 0.57 | 0.59 | 0.63 | 0.71 | 0.85 | 1.05 | 1.34 | 1.72 | 2.21 | 2.82 | | | | | | | | | | | | |
8 | 0.85 | 0.85 | 0.87 | 0.91 | 0.99 | 1.13 | 1.34 | 1.62 | 2 | 2.49 | 3.1 | | | | | | | | | | | | |
9 | 1.21 | 1.21 | 1.23 | 1.27 | 1.35 | 1.49 | 1.7 | 1.98 | 2.36 | 2.85 | 3.46 | | | | | | | | | | | | |
10 | 1.66 | 1.66 | 1.68 | 1.72 | 1.8 | 1.94 | 2.15 | 2.43 | 2.81 | 3.3 | 3.91 | | | | | | | | | | | | |
[tc=11]Metal Core Size[/tc]
[TR]
So, in finding the mass, multiply it by 8, then divide by the UWP size, and you get surface gravity.
http://frigg.physastro.mnsu.edu/~eskridge/astr102/density.jpg