[X] My Assistant

[scalbers]

A neat paper by Jonathan Fortney shows this ratio to scale (approximately) with sqrt(Rp/H), with Rp being the planet radius and H the scale height. Both indeed decrease this effect for Pluto.

If we assume the scale height of Pluto's atmosphere is 60km and the aerosols have the same height as the gas, then I was able to get a few numbers in the course of comparing various airmass equations. Earth would be about 39 airmasses in the horizontal and Pluto would be 6.4. These numbers would be doubled when looking at grazing incidence from space as in the NH images. I'd still like to come up with a formula for an isothermal atmosphere (exponential density decrease with height) by integrating the thin shell relationship over height and to compare this with the other formulations in Wikipedia. On the other hand, the isothermal case is within just a few percent of the homogeneous (constant density with height) case.

To check the scale height and see why it is much higher than Earth, we might evaluate this expression for Earth and Pluto:

H = kT/mg

H is scale height
T is temperature (a representative value since this varies with height)
k is Boltzmann's constant
m is molecular mass
g is gravitational acceleration

The Wikipedia link above shows this worked example for Earth:

Taking T = 288.15 K, k = 1.3806488x10-13 J/K, m = 28.9644×1.6605×10−27 kg, and g = 9.80665 m/s2 yields H = 8345m

Roughly speaking, if pluto has .07 Earth's gravity and the same T and similar m we'd get about 120km scale height. If the scale height is 60km, then the temperature would still end up being ~140K. So we can check how much the temperature increases with height over the surface value of 44K.

There are other atmosphere posts in the Near Encounter thread as well (e.g. posts #1238 and #1252).