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As far as I can find, the pressure in the valley is not directly
measured, but it can be estimated.
Assumptions: ideal gas law (PV = nRT)
temperature 220K (I chose this, about -50C, as a "typical"
Martian temperature--it varies between 130K and 300K--and
comparable to what you might find on Himalayan mountain
tops. The answer changes with the temperature assumed.).
Isothermal atmosphere (not an especially good assumption for
Earth, although probably not bad for Mars).
Scrambling back to his physics texts, your Mad Scientist finds the formula:
P = Po exp <(-g)(Ro)(y)/Po) where
P is the pressure at altitude y
Po is the pressure at the reference altitude
y is the altitude (it can be plus or minus) from reference altitude
Ro is the density of the atmosphere at reference altitude.
g is the gravitational acceleration, with is 9.8m/sec2 for Earth
and 38% of that, about 3.7m/sec2, for Mars.
Ro for the Earth at sea level at 20C is 1.2 kg/cubic meter. Correcting for
our base temp. of -50C, the Ro of the Earth goes to 1.58kg/m3. Using a base
pressure of 8 millibars for Mars at the lander's altitude (reference alt.
for Mars), then the Ro for Mars is about 0.04 kg/m3. I computed that as
follows
Ro (Mars) = 1.2kg/m3 * (44/14) * (0.008) * (293/223)
Earth std ratio Mars temperature
density of mo- pressure ratio to
at 20C lecular is 0.008 convert std
wts of of Earth Earth density
C02 to at sea lvl to -50C
N2
Now it is a matter of stuffing things into the equation, for the two sets
of conditions on Earth and Mars. When I do that for 10 kilometers of going
up on Earth (roughly the top of Everest) and down 10 kilometers on Mars
(roughly the depth of the valley), then I compute...
P (Earth's highest mountain) appx. 312 millibars
P (Mar's deepest valley) appx. 52 millbars
I leave it to you to decide if these are comparable or not. They differ by
a factor of 6, looked at one way, or by only about 1/4 of an (earth)
atmosphere, looked at another way. There are a lot of assumptions on these
numbers, of course. If you are persistent, you can probably find the actual
air pressure at the top of Everest (I searched all over the web and came up
empty, so evidently my choice of key words is poor). Getting an actual
measurement for Mars could be somewhat more difficult :-) however.
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