Planets - Gravity, Mass, Size?

thespiritcoyote's picture
thespiritcoyote
April 19, 2011 - 3:52am

How interrelated are the 'big triplet' factors?
Is there a quick 'rule-of-thumb' that can account for these on a sliding scale?

Consider that Gravity needs no more than a two decimal point granularity, and is used in the basic mechanic effects with only a one decimal point granularity.


Planets
 Gravity Mass  Size
 0.10 0.10 0.10
 0.20 ? ?
 0.30 ? ?
 0.40 ? ?
 ... ... ...
 1.0 1.0 1.0
 ... ... ...
 1.60 ? ?
 1.70 ? ?
 1.80 ? ?
 1.90 ? ?
 ... ... ...
Obviously a simple chart does not work, all the variables need to be more dynamic...

But can it be simplified close enough, to match the single-decimal-point granularity of SF's planetary gravity statistic?
Are there other factors that must be accounted for, to make this basic triplet function properly, even given such a low resolution requirment?

Oh humans!! Innocent We discover a galactic community filled with multiple species of aliens, and the first thing we think about is "how can we have sex with them?".
~ anymoose, somewhere on the net...

so...
if you square a square it becomes a cube...
if you square a cube does it become an octoid?
Comments:

TerlObar's picture
TerlObar
April 19, 2011 - 5:40am
The surface gravity on a planet (at least one that has a surface) is given by g=GM/r2 where G is the gravitational constant (6.67x10-11 m3kg-1s-2), M is the mass of the planet, and r is the planet's radius.  But the mass, M, is also given by M=4??r3/3 where ? is the mean density of the planet.  Plugging this in gives g=4G??r/3.  So your triple is really gravity, radius and density.

Terrestrial (rocky) planets like the Earth and Mars have densities on the order of 5500 kg/m3.  The icy moons of the outer planets and the Kuiper Belt and Oort cloud objects have densities on the order of 2000 kg/m3.  And the Jovian planets have densities on the order of 1000 km/m3.

You could construct a table but it would have to be more than three columns, it would need to be a grid.  the column header would be radius, the row header would be density and the values in the cells would be the gravity of the planet.
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thespiritcoyote's picture
thespiritcoyote
April 19, 2011 - 7:14am
Foot in mouth

Would HAVE to construct a grid, was pretty much my thought too.
I know the math works, but how do we get it into a simple format, for those who are under the impression that a slide-rule is a complicated tool.

simplified to,
 the single decimal Gravity constant that is already used in the rules
 the size (in a single decimal of earth diameters preferably, so a second radian to diameter chart isn't neccessary)
 the density/mass (not the same thing I know but mass is a bit more usefull as a system mechanic value, though neither is necessary for much in a common use mechanic, and density would probably work fine.)
 
  So you suggest a grid-table... where if you know what gravity you are looking for, you look for the the two numbers that match, and then convert between radians and diameters on a second chart.
 If you know what diameter, you convert to radians, then check what gravities work at what densities.
 Can't really think of a reason you would want to start with densities or masses of earth, but it is a plausable unforseen necessity.

cumbersome, but if it is unavoidable.... it might work... I was hoping for something a little more intuitive.
though I realize that my rationale sets a counter intuitive requirment from the perspective of the typical random planetary generator.
Oh humans!! Innocent We discover a galactic community filled with multiple species of aliens, and the first thing we think about is "how can we have sex with them?".
~ anymoose, somewhere on the net...

so...
if you square a square it becomes a cube...
if you square a cube does it become an octoid?