Accurate formula for calculating environmental lapse rate on three worlds

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.

Evgeny Yantovski: Thomas Gold and the Future of Methane as a Fuel

H/T to @IntrepidWanders for this paper, which lays out in clear terms the argument for abiotic oil/gas. I’ll post the second half next.

Saturn seen across a sea of methane on Titan. Artists impression. Credit: NASA/JPL Gregor Kervina

Evgeny Yantovski
Independent researcher
Elsass str. 58, D-52068 Aachen, Germany

Abstract
Thomas Gold was a main participant and contributor in the controversy between the biogenic
and abiogenic theories of the origin of hydrocarbons, a controversy launched by the abiogenic
views of Mendeleev and supported by other Russian and Ukrainian authors. The great success
of Gold’s forecasts is illustrated by a photo of the methane seas on the cold planetary body
Titan. Recently Scott et al.’s experiment on methane formation at high pressure suggests a
possibility of methane formation in the mantle. Some thermodynamic equilibrium
calculations suggest a possible exothermic reaction of carbon dioxide with fayalite producing
methane. In this view, carbon could play the role of an energy carrier from fayalite to
methane and then to a power plant and in a closed cycle be reinjected in Earth. Fayalite
becomes a fuel, with methane the energy carrier. Methane is then a renewable energy source.
The search for methane in Earth and resoluton of its origins deserve more efforts than ever
before.