A commenter on another site with the handle ‘Agent009’ has come up with an interesting formula for calculating the environmental lapse rate on three solar system bodies with atmospheres. Talkshoppers might offer some ideas as to why it works. H/T to Stuart ‘Oldbrew’ for flagging this one up.
I’ve been trying to solve a puzzle… dry adiabatic lapse rate is normally calculated as following:
Γ = g·M/cp
where Γ is lapse rate, g is surface gravity acceleration, M is mole mass and cp is molar heat capacity.
However, if you calculate this for Earth, you arrive at 9.77 K/km, but actual environmental lapse rate, as defined in the ISA, is 6.49 K/km, which is about 9.77 * 0.665. So, I decided to take a look at how this works on Venus and Titan – the only two other worlds in the Sol System that actually have tropospheres.
On Venus (assuming tropopause at 55 km), the average lapse rate is about 7.9 K/km, but the above formula gives you 10.46 K/km, which means that you must multiply the result by 0.756 to get the actual value. On Titan (assuming tropopause at 42 km), actual average lapse rate appears to be around 0.5 K/km, but predicted lapse rate is 1.26 K/km – which gives you the coefficient 0.427. So I’ve been trying to figure what this mysterious coefficient depends upon – and, I think, I’ve found it. The following expression gives you almost exactly those numbers (using SI units, that is):
³√(12·g·M·(1/R – 1/cp))
where R is the ideal gas constant.