Calculating oblateness.

[marc]

I've come up with this rough formula for calculating the oblateness of a gas giant.

oblateness = M*rotationPeriod*mass*radius^-3 + C
where M and C are constants to be calculated with the graph below.

Am I on the right track here? Is there a better method or a specific formula I could use?
This is for a system generator so it does not need to be super accurate.

[Evil Dr Ganymede]

If you can wade through the maths, there's a whole ton of stuff about it here: http://scienceworld.wolfram.com/physics/Oblateness.html

(That's generally a really good site for anything scientific)

[marc]

Thanks Dr Evil, that is just what I needed. It looks like I just need to change the exponent of the period to -2. Hopefully I will get a linear graph.
Great site.

[marc]

Oops, repeating myself.

[marc]

I ended up using this formula for calculating the oblateness for the jovians
((-1.05E-15)* rotationPeriod * mass * POW(radius,-3) ) + 0.122
I found it works well for the fictional planets.

I also want to apply oblateness to stars, here is a star with a fairly extreme oblateness hard coded.



I'd like to make the formula a bit more scientific, so that this may perhaps become a new feature of celestia.

Changes to the code are pretty simple, and should only be a few lines if we have the right formula.

Given the parameters celestia has for each star does anyone have any suggestions on a formula? Or links where I can find out? (mh also has a crude mass table).

[Evil Dr Ganymede]

That looks pretty cool. It'd be nifty to be able to apply it to stars and planets in Celestia

[granthutchison]

Oops. Just happened on this thread while searching for something else.
Marc, your equation looks kind of odd to me - just in a handwaving sort of way all your variables seem to be in the wrong places.
As the RotationPeriod goes up, oblateness ought to go down (less centrifugal "force" as the planet rotates more slowly); as the mass goes up, oblateness ought to go down (more gravity holding things spherical); and as the radius goes up oblateness ought to go up (equator further from the centre of gravity and subject to more centrifugal "force"). Your equation seems to have all of these dependencies reversed - or am I reading it wrongly?

It turns out that (all other things being equal) oblateness is proportional to the angular velocity squared and inversely proportional to the density - using your variables of choice:

oblateness = C * [R^3/(M * P^2)]

where C is a constant that depends on the mass distribution of the body in question, so it varies a bit among the gas giants. But you could use the above equation to derive approximate oblatenesses for "Jupiter-like" or "Neptune-like" bodies by just expressing the variables above as multiples of the known values for these bodies.
You can check the logic of this from equations 38 and 40 in the Evil Doctor's link (though there's an error in 38 - the 2 in the divisor shouldn't be there).

Grant