Calculating a planet's mass & gravitational pull

[dogscoff]

Hmm, I was *way* off, but now I'm closer. I went back to S_J's original calculation of g = GM/(1000*R)^2
(dunno where I got g=G*m*(r*1000)^3 from)

g = GM/(1000*R)^2
g*(1000*R)^2 = GM
(1000*R)^2 = GM/g
(1000*R) = squareroot(GM/g)
R=(squareroot(GM/g))/1000

In javascript, that comes out as
radius=(Math.sqrt(GRAV*mass)/gravity)/1000

and it works. Sorry for all the fuss, ppl.

[ August 27, 2003, 15:12: Message edited by: dogscoff ]

[Suicide Junkie]

radius=(Math.sqrt(GRAV*mass)/gravity)/1000

Shouldn't you Math.sqrt( grav*mass/gravity ) or somesuch?

[Puke]

GURPS Space (from Steve Jackson Games) used to have work sheets for generating alien planets, that included orbital radius and period, roation, gravity, mass, temerature, etc, etc..

might look for an old copy, or a PDF of the reference sheets Online.

[Ack]

Hmm... I've often wondered about the error associated with using point source gravitational equations. Too lazy to look it up, so maybe someone here knows.

The equations posted here all assume that gravity comes from a point source at the core of a planet. This is fine when you are many, many planet diameters away from a planet. But when you get within some distance, the gravitation effects should be distributed across the planet's height, width, and thickness. The gravitational force that a body feels when within this distance is the vectored sum of all these components. Additionally, each layer of a planet has a different density and therefore differing gravitational contributions.

A second option is that during planet formation, the denser elements settle more towards the planet core. In effect, the bulk of the planet's mass resides in the core. This would make the point source error very small until you've pierced the surface and moved very close to the planet's core.

[dogscoff]

Ack: I don't doubt that these equations have a certain level of innaccuracy built in, but I'm only using them for writing purposes, so I can be sufficiently vague to leave room for correction.
When the program goes up on my website though I fully intend to list all the known areas of innaccuracy. I'll add your comments to my list, thanks=-)

[Suicide Junkie]

Differing densities at various depths does not affect the calculation, assuming that at any particular depth, the density is the same all the way around the planet.
If the density is not the same (ocean water vs rock, say) it still only has a small effect, which is swamped by the effect of the 1000's of km of rock below it.

Distance from the planet surface has the biggest effect.
If you are on top of a mountain, the gravity is lower. While there is a bit more mass directly below you, the 1/r² decrease hits much harder.

However, its still a fraction of a percent change.

You'd need something with an irregular shape, like an asteroid to get decent changes in gravity, but then the gravity is so low to begin with, it really dosen't matter.

Stuff with higher gravity smushes itself into an ovoid ball, and the approximations apply.

[dogscoff]

Wahey! It's finished. Well, not quite finished, but the difficult bit is.

You can put in any combination of variables and it will work out everything it can from them. For example, you could put in radius and mean density to get surface gravity, mass, volume, circumference etc.

Equally though, you could put in surface gravity, circumference and percentage of the surface covered in water and from that derive the radius, mean density and total land area.

On the other hand, you could just tell it how much land and ocean surface there is and the surface gravity and it will give you density, volume, etc etc etc...

You get the idea. If anyone ever needs to design a planet to spec then this could be handy.

All that remains is to validate the input a little more, make the option to compare the figures generated to those of real planets, pretty it up a bit and then I can upload it to my website for everyone to ignore

Thanks for all the help, ppl.