wrote:
Erik Max Francis wrote:
wrote:
What is the critical escape speed needed to hold atmosphere, and
how
will it depend on the temperature?

Let us take the major Solar System examples, from outside in:

Pluto: 1,18 km per second, approaches to 30 a. u.. Appreciable
nitrogen
atmosphere restricted by freezing.
Triton: 1,45 km per second, orbits at 30 a. u.. Appreciable
nitrogen
atmosphere restricted by freezing.
Titan: 2,64 km per second, orbits at 10 a. u.. A nonfreezing
nitrogen
atmosphere, the inventory being 160 000 Pa.
Io: 2,57 km per second, orbits at 5,2 a. u.. Not much atmosphere.
Europa: 2,03 km per second, orbits at 5,2 a. u.. Not much
atmosphere.
Ganymede: 2,73 km per second, orbits at 5,2 a. u.. Not much
atmosphere.
Callisto: 2,44 km per second, orbits at 5,2 a. u.. Not much
atmosphere.
Mars: 5,03 km per second, orbits at 1.52 a. u.. A freezing carbon
dioxide atmosphere, contains nonfreezing nitrogen inventory of 20
Pa.
Moon: 2,38 km per second, orbits at 1 a. u.. Not much atmosphere.
Earth: 11,2 km per second, orbits at 1 a. u.. Nitrogen atmosphere
of
approximately 80 000 Pa.
Venus: 10,4 km per second, orbits at 0,72 a. u.. Carbon dioxide
atmosphere with nitrogen inventory of about 300 000 Pa.
Mercury: 4,44 km per second, orbits at 0,39 a. u.. Not much
atmosphere.

I wonder if there is any rule between the nitrogen contents of
the
three dense nitrogen atmospheres?

Probably not, but the very nature of atmospheric leakage means that
lighter molecules will leak at a greater rate than heavier ones.
Leakage occurs when the average speed of a molecule is about that
of
escape speed at the exosphere interface. Lighter molecules with
the
same energy have a greater speed, and so the lighter molecules will
tend
to escape at a greater rate than heavier ones.

So it's not surprising that hydrogen and helium are nowhere to be
found
in these terrestrial atmospheres. (For jovian planets like
Jupiter,
that's changed because their enormous gravity now means that the
escape
speed at the exosphere is very high, and so they can retain much
lighter
molecules all the way down to H2.)

So it's not surprising that the atmospheres we see on the list are
nitrogen, carbon dioxide, and oxygen -- with only the Earth having
significant quantities of O2, since that's kept up by life. If
there's
any significant to N2 being listed over CO2 in this list, I'd
expect
it's a chemical favoritism in terms of carbon getting absorbed and
interacted with more readily than nitrogen by the stuff that tends
to

sit around on the surfaces of terrestrial worlds.


Exactly.

However: given the observed inertness of nitrogen, why does Earth
have
4 times less of it than Venus and twice less than Titan?

Also: the first principles computations would show that the
temperature
falls with the square root of distance, and the velocity of a
molecule
of given mass falls with the fourth root of the distance.

Since luminosity is inversely proportional to the square of the
distance, and luminosity is proprotional to the 4th power of the
temperature, temperature falls off with the square of the distance, not
the square root- A planet 4 times as far from the sun will have about
half the absolute temerature- A. McIntire