MadSci Network: Astronomy
Query:

Re: Do we know the atmospheric pressure near the bottom of the 'Valley of the M

Date: Fri Apr 10 12:12:12 1998
Posted By: Matthew Buynoski, Senior Member Technical Staff,Advanced Micro Devices
Area of science: Astronomy
ID: 891488980.As
Message:

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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