The attached file demonstrates that there is a predictable relationship between the structural density of a terrestrial body and its none-rotating surface gravity.
Using Newton's gravity law of spherical shells, the geometric relationship between a globe's non-rotating atmospheric gravity gradient δg/δz (T^-2) and the average structural density of the globe can be established.
Titan and Earth have moist condensing volatile atmospheres, whereas Venus and Mars are dry.
Four data points do not make a trend, but any ideas on the impact of latent heat in the process of atmospheric lapse rate formation would be of help.
Thank you.
There is a connection but not directly relation...
A colleague has kindly supplied me with the following reference in which this question is addressed for the planet Venus.
Singh, D., 2019. Venus nightside surface temperature. Scientific reports, 9(1), pp.1-5.
https://www.nature.com/articles/s41598-018-38117-x
In this paper the relationship is given as:-
"The temperature lapse rate in planetary atmosphere is given by:
Lapse rate dT/dz = -g/Cp
where, ‘g’ is acceleration due to gravity, and ‘Cp’ is heat capacity at constant pressure. "
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