Planets - Gravity, Mass, Size?

thespiritcoyote April 19, 2011 - 3:52am | How interrelated are the 'big triplet' factors? 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.
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 be accounted for, to make this basic triplet function properly, even given such a low resolution requirment?mustOh humans!! 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? |

TerlObar April 19, 2011 - 5:40am | The surface gravity on a planet (at least one that has a surface) is given by g=GM/r ^{2} where G is the gravitational constant (6.67x10^{-11} m^{3}kg^{-1}s^{-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??r^{3}/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/m ^{3}. The icy moons of the outer planets and the Kuiper Belt and Oort cloud objects have densities on the order of 2000 kg/m^{3}. And the Jovian planets have densities on the order of 1000 km/m^{3}.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. Ad Astra Per Ardua! My blog - Expanding Frontier Webmaster - The Star Frontiers Network & this site Founding Editor - The Frontier Explorer Magazine Managing Editor - The Star Frontiersman Magazine |

thespiritcoyote April 19, 2011 - 7:14am | 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!! 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? |