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I've been trying to get a decent numerical approximation (curve fit) of Earth's Atmosphere Model, and found what I was looking for at this NASA's web site. However, when checking some basic calculations, the very first formula for stratosphere temperature:

$T = -131.21 + 0.00299 h$

is just simply wrong: When entering a value of 80 km (80000 meters) for $h$, the temperature I get is 107.99°C. This cannot possibly be correct, and it is far from what other on-line engineering resources say (for example, EngineeringToolBox )

Am I doing something wrong, or is the formula incorrect?

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    $\begingroup$ It is disturbing how they deal with physical units... I initially thought, you set the formula up in the wrong way, but it is what they actually write on their homepage :O... Apart from that, I am also confused. 108°C is most definitely wrong. $\endgroup$
    – lmr
    Commented Apr 25, 2019 at 6:50
  • $\begingroup$ So, with this clarified - can anyone point me to a resource where I could find similar equations, but for higher altitudes, up towards outer space? $\endgroup$
    – Mitch99
    Commented Apr 25, 2019 at 7:06
  • $\begingroup$ I have no idea how reliable it is, but you can get the equations for the lines from the Wikipedia plot I linked to that will get you up to 100 km. Keep in mind, though, even the upper atmosphere has some weather. For example, last time I'd heard, the WISE satellite's orbit is decaying slower than expected due to the atmosphere contracting a bit (global warming heats the lower atmosphere, cools the upper atmosphere). $\endgroup$ Commented Apr 25, 2019 at 8:09
  • $\begingroup$ Thanks, sounds good. So basically, for every straight line segment, I'll have a line equation that defines it within those altitude bounds. Is it safe to assume that pressure and density go down to zero at around 40 km altitude? $\endgroup$
    – Mitch99
    Commented Apr 25, 2019 at 18:05

2 Answers 2

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For starters, $80\operatorname{km}$ is outside of the stratosphere (at least, according to the rough graph on wikipedia). Given what's on the slide, I doubt the model applies there. That idea is supported by this graph of temperature and pressure versus altitude that shows the temeprature peaking at the top of the stratosphere.

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  • $\begingroup$ Ah, yes. The temperature takes a wild swing to the other side above 50 km. I thought I was "safe" when they indicated "for h > 25000" but obviously, the formula applies ONLY to stratosphere (up to 50km). I will mark this as an answer - thank you! $\endgroup$
    – Mitch99
    Commented Apr 25, 2019 at 7:02
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Am I doing something wrong, or is the formula incorrect?

I'd say a combination of both.

The formula probably is incorrect for large heights and you did wrong by setting $h = 80000 \text{ m}$ because the given function does not model the temperature correctly.

According to this image

https://upload.wikimedia.org/wikipedia/en/9/9a/EarthAtmosphereBig.jpg

the stratosphere goes up to 50 (or 60) kilometers and your value of 80 km is out of this range.

The model must fail for large $h$ because $T$ will grow without bounds if $h$ increases which is clearly not the case.

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  • $\begingroup$ Thanks - you are also correct, but I indicated Sean's answer as the correct one since it was posted before this one. $\endgroup$
    – Mitch99
    Commented Apr 25, 2019 at 7:03

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