Re: "The Scarcity of Life Bearing Planets"

Vince Morgan wrote:
"Wod" <wod@xxxxxxx> wrote in message
news:5082c$491da6a4$4f85fc3$14599@xxxxxxxxxxxxxxxx
"The Scarcity of Life Bearing Planets"

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[snip]
In order for a molecule of gas to be lost to the planet, it must
acquire a thermal velocity greater than the planet's escape velocity.
This
must occur at an altitude at which the atmosphere is sufficiently thin so
that it does not strike other molecules while escaping. (This occurs
above
the altitude where the effects of diffusion are significant.) The rate at
which atmospheric gases are lost to space is determined almost entirely
by
the rate of energy input from the Sun and by the escape velocity of the
planet at the top of its atmosphere The rate of atmosphere loss is
virtually
independent of the amount of atmosphere the planet owns at any instant of
time.

I disagree. One would think that the larger the atmosphere (diameter),
the
higher the orbital velocity in it's outer regions.
Not that the atmosphere, or the upper regions of it, is 'in orbit' but it
will have greater angular momentum and therefore less thermal energy is
required for it to attain escape velocity.

Escape velocity is sqrt(2) times the circular orbit velocity for
any orbit radius.

The circular orbit velocity at radius r for a planet with gravitational
parameter u ( where u = G*M, M being the mass of the planet, atmosphere
included), is

Vcirc = sqrt(u/r)

So higher radii have lower orbital velocities and escape velocities.

It's the thermal velocity (kinetic energy) versus the escape velocity
that counts for gas loss.




.

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