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I am looking to find the reason: why air pressure decreases with altitude? Has it to do with the fact that gravitational force is less at higher altitude due to the greater distance between the masses? Does earth’s spin cause a centrifugal force? Are the molecules at higher altitude pushing onto the molecules of air at lower altitudes thus increasing their pressure? Is the earths air pressure higher at the poles than at the equator?

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  • $\begingroup$ Pressure is a force. So is gravity, but you can have either one without the other. $\endgroup$ Commented Dec 21, 2020 at 13:56
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    $\begingroup$ Lie on the floor. Then have someone lie on top of you. Then someone on top of them. Repeat until you're buried under 100 people. Why does the person at the bottom feel more squished than the person on top? $\endgroup$
    – J...
    Commented Dec 21, 2020 at 17:47
  • $\begingroup$ Since there is no air pressure on the moon there should be decrease of the pressure with altitude starting at least at some point... but that's not physics, it's math... $\endgroup$ Commented Dec 21, 2020 at 19:27
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    $\begingroup$ Because there are more air on top when you are at low altitude versus less air when you are at high altitude. $\endgroup$ Commented Dec 21, 2020 at 22:19
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    $\begingroup$ @J... My cats have been performing that experiment for years. I'm still waiting to read about their scientific conclusions. $\endgroup$ Commented Dec 22, 2020 at 22:04

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The air pressure at a given point is the weight of the column of air directly above that point, as explained here. As altitude increases, this column becomes smaller, so it has less weight. Thus, points at higher altitude have lower pressure.

While gravitational force does decrease with altitude, for everyday purposes (staying near the surface of the Earth), the difference is not very large. Likewise, the centrifugal force also does not have significant impact.

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    $\begingroup$ Or piling a bunch of rocks on top of you, or straw on a camel's back :-) $\endgroup$
    – jamesqf
    Commented Dec 21, 2020 at 16:59
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    $\begingroup$ @CarlWitthoft Note the air pressure decreases (approximately) exponentially with the altitude, while the water pressure increases (approx.) linearly with depth. The air pressure variation depends on temperature, i.e. the larger the temperature the slower the pressure drop. This answer is correct, but a bit incomplete in this sense. $\endgroup$ Commented Dec 21, 2020 at 19:55
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    $\begingroup$ "While gravitational force does decrease with altitude, for everyday purposes (staying near the surface of the Earth), the difference is not very large." – At the ISS, gravity is still ~90% of surface gravity, is a good landmark number to keep in mind. Clearly, atmospheric pressure is almost non-existent, which hints at the fact that the two are unrelated. $\endgroup$ Commented Dec 22, 2020 at 0:53
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    $\begingroup$ Maybe a helpful analogy: imagine a large tower of springs stacked on each other standing upright. The bottom springs will be compressed more than the top ones, because the bottom ones carry the weight of the top ones (but not vice versa). In this analogy, the compression of the spring is the same principle as the air pressure at a given altitude. The more you put on top of it, the more it gets compressed/pressurized. $\endgroup$
    – Flater
    Commented Dec 22, 2020 at 1:55
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    $\begingroup$ Now I feel like air pressure should drop when I go indoors, since then most of the column of air above me is being held up by the building's roof, rather than my own body :) $\endgroup$ Commented Dec 22, 2020 at 3:49
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I edited this question on the first day, in response to a few comments that pointed out a misunderstanding, but it didn't register. I sincerely apologize for that.

As pointed out by other answers, the pressure due to any fluid, compressible or not, increases with depth. This is due to the greater mass and thus weight of the fluid above.

What's interesting is that the pressure of water increases linearly with depth, while that of air does not.

The gravitational field strength drops down to only 88% even at the height of the ISS. The drop in pressure has more to do with the fact that unlike water, air is a compressible fluid. As you move further down the atmosphere, there is a greater weight of air above pushing down on the air below, so the density, and thus the air pressure, increases. Basically, the density $\rho$ is a function of $h$. so you have to integrate density over the height instead of simply multiplying.

$$P=g\int\rho\mathrm{d}h$$

or $$P=\int g\rho\mathrm{d}h$$ if you want to account for the change in gravitational field, however small

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    $\begingroup$ Doesn't matter if is compressible or not - water pressure also increases with the depth. $\endgroup$ Commented Dec 21, 2020 at 9:05
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    $\begingroup$ Yes, compressibility only means that increases faster than linearly with depth. It increases exponentially with depth for an ideal (isothermal) atmosphere. $\endgroup$ Commented Dec 21, 2020 at 17:01
  • $\begingroup$ I'm not super confident in this argument but I think putting $g$ inside the integral isn't necessary - it goes down as $1/r^2$, and the column 'directly above' (actually radially outwards from earth's centre) increases in area as $r^2$ as $h$ increases $\endgroup$
    – llama
    Commented Dec 21, 2020 at 17:01
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    $\begingroup$ Bad answer. The higher you go, the less atmosphere there is above you, the less it weighs, so the pressure diminishes. Arguments about compressibility affect the exact rate that pressure decreases with altitude, but are irrelevant to the fact that it does decrease. $\endgroup$ Commented Dec 22, 2020 at 3:05
  • $\begingroup$ Please see edir $\endgroup$ Commented Dec 22, 2020 at 9:41
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As you go higher, there are less air molecules (less weight) on a given area this is basically one reason why it decreases.

From the barometric formula, one can get the relation between the pressure and altitude. It's defined as

$$P = P_{0}e^{-\frac{mgh}{kT}}$$

so the relation between pressure and altitude is $P\propto e^{-h}$. Thus, as we go to higher altitudes pressure will exponentially decrease.

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  • $\begingroup$ Pedantically speaking that's not $P \propto e^{-h}$ (in fact, $e^{-h}$ doesn't even technically make sense). To be correct you should say that $\log(P/P_0) \propto -h$ (or just say the entire statement, or introduce the notion of scale height, or something). $\endgroup$
    – Ian
    Commented Dec 22, 2020 at 19:56
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Has it to do with the fact that gravitational force is less at higher altitude due to the greater distance between the masses?

The gravitational force does decrease as you go higher up, but that's not the reason. The pressure would still be greater at the bottom even in some weird physics where gravity got stronger further from the surface.

Does earth’s spin cause a centrifugal force?

It does, but again, that's not part of the reason.

Are the molecules at higher altitude pushing onto the molecules of air at lower altitudes thus increasing their pressure?

Yes. That is exactly the answer.

Is the earths air pressure higher at the poles than at the equator?

No. Even if the effective gravity is different, air at sea level will flow from where there is more pressure to where there is less until it balances out. Of course, pressure changes due to weather but over time I believe seal level pressure is the same around the world.

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Edit: After researching a bit more, I've edited my answer to be significantly more accurate.

In short - air pressure is the result of the cumulative force that air molecules act on objects below them due to Earth's gravity. The higher the altitude, the less air molecules there are to act a force below them, and therefore, there's less air pressure at higher altitudes.

So, even though

Molecules further away from the earth have less weight (because gravitational attraction is less) ... they are also ‘standing’ on the molecules below them, causing compression. Those lower down have to support more molecules above them and are further compressed (pressurised) in the process. [Source]

A more technical way to approach the question would be looking at the general formula for pressure: $$p=\frac{F}{A}$$ Where $p$ is the pressure, $F$ is the force that causes the pressure, and $A$ is the area of the surface on contact, we can understand that (assuming $A$ is constant), as $F$ increases, so does $p$.

As for the effect of Earth's spin on air pressure, it is miniscule, as explained here.

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You can check the following link from Wikipedia this is what I learned during the undergraduate education in thermodynamics course. You can relate ideal gas law and Bernoulli's principles without introducing kinetic terms (hydrostatic approximation only). Thus, you get an equation that also depends on the temperature. Gravitational acceleration is fairly the same considering the depth of atmosphere. So, it can only be a correction to the atmospheric model rather than the main principle.

I guess also you can include centrifugal force in the gravitational acceleration, because they are in the opposite direction (Be aware that centrifugal force is just an imaginary force that you may add to the equation.). You can imagine the radius of Earth and compare it to the depth of atmosphere to guess if the radius dependent terms such as gravity or centrifugal force is important with respect to other changes in your equation. If you want to do a precise calculation to compare two regions, the poles and the equator, you can add the centrifugal acceleration part too.

The air certainly pushes down the other air molecules, thus increase the pressure. It is the same principle (Bernoulli's) that is applied also in the pressure change in liquids.

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The weight of the column of air pressing down on the air below seems to be an incomplete answer because if that were true then the inside a building would have less pressure because the roof is holding up the air above it. I think the downward pressure causes the air to be compacted together from all sides (pressurizing it) - so the air in the building is at the same pressure as outside the building.

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  • $\begingroup$ This does not provide an answer to the question. Once you have sufficient reputation you will be able to comment on any post; instead, provide answers that don't require clarification from the asker. - From Review $\endgroup$
    – Miyase
    Commented May 2, 2023 at 16:16
  • $\begingroup$ the roof is holding up the air above it. It depends on how big diameter of air column is. If it's big enough to fit whole house inside,- so that roof "holds" only part of air column,- then due to the fact that house isn't sealed and air can flow into it through various holes and cracks,- pressure from air column "gets" into house as well. Btw, not all roofs also are sealed,- some have ventilation openings, etc. Only inside of tightly sealed box/container is independent of outside pressure. $\endgroup$ Commented May 6, 2023 at 20:39

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