# Maximizing the vertical range of livable air pressure

In Larry Niven's short story "Bordered in Black", there's a planet (Sirius B-IV) with much lower gravity than Earth. As a result, the planet has a gentler atmospheric pressure gradient, i.e., the air pressure changes less over the same vertical distance. Because of this, the planet had clouds as high as 130 kilometers.

It got me thinking: there's a world I've been building for some time that has an extreme vertical component to its geography, with some features being hundreds (and in one extreme case, thousands) of miles tall. It occurred to me a while ago that air pressure would be a serious problem in this setting, since most of that vertical space, although not necessarily the upper- or lower-most extremes, is meant to be habitable. I initially decided to handwave it away, judging the problem to be insurmountable.

Now Niven has reignited my interest in finding a scientific explanation for this. Using real physics, what are some good explanations for a range of livable air pressure extending over several hundred vertical miles? If this isn't possible, what's the largest vertical distance over which air pressure can remain can livable?

Side note: the ground is made out of handwavium. I am not breaching the topic of how hundred-mile-tall features exist in this world. The air on the other hand, being breathable, is normal nitrogen-oxygen, and thus requires an explanation for its behavior.

The suggested "cure": lower (a lot!) surface gravity (i.e.: have either a smaller planet or a lighter core... or both) is mandatory in your case because mountains "several hundred vertical miles" would otherwise collapse under their own weight and thin air is the last of your (scientific) concerns.

There are good geological reasons why tallest peak on Mars (mt.Olympus) is significantly (>20%) taller than any Earth counterpart.

What you propose is quite extreme and I sincerely do not think is achievable without resorting to some "magic".

What You should be concerned, though are other factors I don't know if You accounted for:

• temperature: decreases with altitude and is the main reason why high ranges are "not inhabitable".
• human body can adapt to very extreme pressure ranges, given time.
• if your mountain ranges get higher than troposphere you'll get no atmospheric precipitations, which means: no water!
• high mountain ranges, on Earth, aren't inhabitable mostly due to cold desert climate well before lack of oxygen becomes a problem.
• all above would be mitigated by lower gravity.
• very low gravity means no iron core, which, in turn means no magnetic shield for solar wind.
• Good point... I forgot that higher gravity means lower mountains... – L.Dutch - Reinstate Monica Aug 3 '17 at 7:50

Not easy to give a straight answer.

The approximated formula to calculate pressure vs hight is the following

$p = p_0 exp(-g Mh/R_0T_0)$

Where $p_0$ is the pressure, $g$ is the gravity, $M$ is the molar mass of dry air and $T_0$ is the temperature, all at "sea" level, while h is the height and $R_0$ is the universal gas constant.

Playing with g is risky, as lowering g will also lower the capability of the planet to keep an atmosphere.

You can better use the properties of the exponential decay to "slow" down for great values of h, in this case, and going almost horizontal. If you put your survivability zone in that area of high h you can extend it for really large height differences.

See the chart below: dropping 20 kPa (100 to 80) happens in 2000 meters if you start from sea level, it takes 3000 meters if you start from 4000 meters (60 to 40).

The "trick" is increasing your $p_0$ so that your livable pressure is shifted at high heights. The problem is that to increase your $p_0$ you need to increase your g, which being also in the exponent influence the drop rate. Also an higher g will make your mountains lower.

But, nevertheless, this can explain how the pressure is livable on wider ranges.

• You don't need to increase $g$ to increase $p_0$. You can instead simply add more atmosphere. $g$ also does not, by itself, do anything to help or hinder holding an atmosphere. Escape velocity is far more relevant. You can hold an atmosphere with very low gravity and very high escape velocity, if you have a planet with a very low density, as evidenced by, e.g., Saturn, which holds onto hydrogen just fine (which Earth can't do) despite having a "surface" gravity barely a smidge higher than Earth's. – Logan R. Kearsley Aug 6 '17 at 2:15
• @LoganR.Kearsley, adding atmosphere adds mass, and adding mass increases g... – L.Dutch - Reinstate Monica Aug 6 '17 at 4:08
• If you're inside the atmosphere, no it doesn't. Shell theorem. If you're outside the atmosphere, the difference is negligible. Venus's atmosphere, for example, is over 90 times more massive than Earth's, but it's still a rounding error in computing Venus's gravity. – Logan R. Kearsley Aug 6 '17 at 14:50