Equations needed for a theoretical water planet

krd

I'm looking for some equations to look at an idea I have. (I haven't seriously touched a physics equation in years - I have studied it but have forgotten nearly everything).


A crude model of a hypothetical planet completely covered in water, with no initial atmosphere, but with gravity and a constant solar flux. (It doesn't have to be water - I'd like to be able to switch it with other chemicals - and the model can be very crude - it doesn't have to account of everything - the solar flux and absorption of the water or vapour doesn't have to be precise - purely energy in, phase changes - temperatures - no absorption spectra etc)

Starting with no atmosphere. The solar flux heats the water creating vapour. The vapour is formed into an atmosphere, effected by gravity. Its' dense and warmer at lower altitudes, at higher altitudes less dense an cooler - where the water condenses at a specific height and precipitates. And starts the cycle again.

The equation model I'd like to put together will show a simple system in equilibrium - where there is a constant rainfall and temperature and gas density gradient through the atmosphere.

What I would especially like to see is the hypothetical sea level temperature. I have a rough idea, which I would like to see if the equations will bear out:

Given a planet completely made of water or any other single compound (could be hydrogen), with a constant solar flux, but disregarding weather effects caused by rotation. At sea level, there would be a constant in relation to temperature and pressure(or vapour density), regardless of the size of the planet or solar flux.

I think it's simpler than it sounds - but I'm way too scratchy to remember the equations I need or how to manipulate them.


(Does a planet with a constant solar flux - regardless of atmosphere - reach an energy equilibrium with itself and outer space. I assume it does. What would the equations be, that would give me the surface temperature - or the equations to show how its' equilibrium works)

Any equation to get me started would be great. Thanks

Capt'n Midnight

the planet WILL have an atmosphere

it's the vapour pressure of water at the temperature of the water,



from simulations done on ringworlds there will be atmosphere over most of the planet. ringworlds are tidally locked to the sun - so one hemisphere is towards the sun the other away - and you DO NOT get the sudden temp changes like Crematoria on Chronicles of Riddick because the gas carries heat to /from the halves, because of wind and turbulance and stuff


Now you can compare the known atmospheres of the planets/moons to see what happens as the inital point of the simulation, eg: mars has a very tenuous atmosphere , what are it's temps and variations towards the poles ?



What is the temp profile in earth's oceans ?

you model will need to take into account that 4 degrees is the maximum density of water. for most (but not all) other substances the fact that solids are denser than liquids means that oceans of other substances will probably be solid ( depending on pressure and what have you ) and only the surface may be liquid.



Or or course it may be like Europa with a covering of ICE and the main heat source is from inside

cores of any large planet will be solid - it's just a matter of pressure to figure how far down you need to go, - what initial temp will you use for the core ?

Neptune has a surface gravity of 1.17
Saturn has a surface gravity of 0.92

both are larger than earth ( and the higher escape velocity means 's an excellent place for a penal colony since no one is coming back up the gravity well any time soon ) and might be useful to compare to the imagined water planet