At this time, I can't read & comment on previous posts (no time, late on Sunday night), I just want to post some data while it is in my head. I did make an error in transcribing the Mars Atmospheric Density Model, thinking "e" was scientific notation, but I believe it is "e" the mathematical constant, eg, 2.718 ... For my purposes, e(x) is 2.718^x ...
OK, this is giving me big red flags: NASA has sent no less than 3 probes to Mars to measure atmospheric density, they have this data. But where is it? I can't find it, can anyone else find it? This is the most critical set of data anyone can have, and at the low densities on Mars, even small errors have a significant impact on velocities - a little less density, and we are truly dealing with a real vaccuum where Curiosity is not possible, a little more, and NASA can make untrue claims. If we look at:
[
link to www.google.com]
we can see that everybody is saying the atmospheric density of Mars is LESS THAN 1% of EARTH. But if we use the model that NASA provides to the public, we get densities far above 1% ... We can also see that many universities and aerospace organizations have been attempting to figure out the densities at various altitudes right up until the "last minute" - which seems a little risky, because they know it is highly variable at all places all of the time, yet very crucial to any kind of successful outcome. And it is not a linear model.
Anyway, let's see what their public mathematical model produces, from the link previously provided:
First, we know:
0.00237 slugs/ft^3 (Earth, @ sea-level)
0.0000237 slugs/ft^3 (Mars, @ datum, if 1% of Earth's)
Now:
@1ft
14.62*e(-.00003*1)/(1149*((-25.68-.000548*1)+459.7))
.000029
OOPS! That is quite a bit MORE THAN 1%,
eg, .0000237! Why is that?
@1000ft
14.62*e(-.00003*1000)/(1149*((-25.68-.000548*1000)+459.7))
.000028
@5000ft
14.62*e(-.00003*5000)/(1149*((-25.68-.000548*5000)+459.7))
.000025
@10,000ft
14.62*e(-.00003*10000)/(1149*((-25.68-.000548*10000)+459.7))
.000021
@ 25,000ft
14.62*e(-.00003*25000)/(1149*((-25.68-.000548*25000)+459.7))
.000014
@25,000ft (need to switch models at this altitude)
14.62*e(-.00003*25000)/(1149*((-10.34-.001217*25000)+459.7))
.000014
@30,000ft
14.62*e(-.00003*30000)/(1149*((-10.34-.001217*30000)+459.7))
.000012
@50,000ft
14.62*e(-.00003*50000)/(1149*((-10.34-.001217*50000)+459.7))
.000007
@50,000ft (using low altitude model)
14.62*e(-.00003*50000)/(1149*((-25.68-.000548*50000)+459.7))
.000006
OOPS! That's much less than the "high-altitude" model,
why are they giving us a "high-altitude" model that
ADDS EXTRA AIR DENSITY? Why is that? The density
should fall off more rapidly, like light from a bulb,
heat from a heating source, a radio transmission
from an antenna, like gravity, or air pressure out of
a gun, wouldn't you think? Any ideas?
@100,000ft
14.62*e(-.00003*100000)/(1149*((-10.34-.001217*100000)+459.7))
.000001
GRRR! Need more decimal places! I will make 10.
@100,000ft
14.62*e(-.00003*100000)/(1149*((-10.34-.001217*100000)+459.7))
.0000019333
@200,000ft
14.62*e(-.00003*200000)/(1149*((-10.34-.001217*200000)+459.7))
.0000001531
@300,000ft
14.62*e(-.00003*300000)/(1149*((-10.34-.001217*300000)+459.7))
.0000000186
@350,000ft
14.62*e(-.00003*350000)/(1149*((-10.34-.001217*350000)+459.7))
.0000000149
@375,000ft
14.62*e(-.00003*375000)/(1149*((-10.34-.001217*375000)+459.7))
-.0000000235
OOPS! Negative air density at only 71 miles altitude.
OK, so, I guess that is the end of the line for this model.
CONCLUSION: NASA has sent no less than 3 space probes to measure the air density of the Martian atmosphere. Additionally, other institutions and organizations have done much work to make these measurements by other means, and to correct them as much as possible, considering the fluctuating nature of the Martian atmospheric density, and the critical nature of such data. Atmospheric density at various altitudes is probably the most critical set of data one would need for a mission like this, and yet, it is nowhere to be readily found. NASA has put forth a mathematical "model" to describe this data, but the model adds more density to the atmosphere, even in contradiction to the words of NASA's own scientists when interviewed. If anything, NASA would want a model that leans toward more pessimistic values, to ensure greater engineering success, but their model does the opposite, and actually adds density to the atmosphere, not only at low altitudes, but at high altitudes as well. This is not a frivolous misrepresentation, because with such a low air density, fudging the numbers makes a large difference between plausible success, and certain failure.
