# Air molecules per cubic foot at a certain altitude above the surface

The Earth's and other celestial bodies' atmospheres become thinner the higher you go. Imagine you were able to see atoms/molecules. At what altitude above the Earth's and Mars' surface would you see few enough molecules per cubic foot so you'd be able to count them? If you were, say, 500 miles (805 km) above the Earth's surface, how many air molecules per cubic foot (30 cm³) would you see?

Or, one can ask vice versa: at what altitude above the Earth would you see, say, a 100 air molecules per ft³? Which gas doesn't matter, I'm asking for all atmosphere molecules within the certain volume. And since even interplanetary space isn't perfect vacuum, what would it look like there, e.g. halfway between the Earth and Mars orbit?

• If there's so few molecules that it makes sense to count them, then it probably doesn't make much sense to call the stuff "air." – Solomon Slow Aug 19 '20 at 14:40

The kinds of molecules / atoms and the density of those molecules / atoms as a function of altitude in the Earth's upper atmosphere depends very much on the time of day and the activity of the Sun.

Time of day: The Earth's upper atmosphere has a marked diurnal bulge. The density variation at a constant altitude can vary by an order of magnitude (a factor of ten) just due to the difference between night and day.

Solar activity: One poof from the Sun can make the Earth's upper atmosphere swell by not just one order of magnitude as is seen with the diurnal bulge but multiple orders of magnitude. Satellites in low Earth orbit need to use a good deal more propellant when the Sun's activity is high as compared to now when the Sun is rather quiescent.

To answer your question, there is no one answer to your question. This is part of the reason (perhaps the key reason) why predicting when a satellite in a degrading orbit will re-enter is imprecise. There are multiple models of the Earth's upper atmosphere that vary from fairly simple to ridiculously complex.

On the simple side, I prefer to use the US Naval Research Laboratory's mass spectrometer and incoherent scatter atmosphere model, or NRLMSISE-00 for short. One needs to provide latitude, longitude, date, time of day, and three parameters that indicate recent and current solar activity. And that's on the simple side.

Atoms are small. It's been observed that there are more molecules of water in a teaspoon, than there are teaspoons of water in all the oceans of Earth.

In fact, atoms are so small that even at the very low density of interplanetary space the number of atoms never reaches such low levels that they could be counted. Wikipedia says that the interplanetary medium has about 5 particles per cubic centimetre, or 150000 particles per cubic foot (but quite variable in both time and space). Even in the voids between the galaxies, it is probably over 1000 atoms per cubic foot.

In Low Earth orbit, the density of the air might be $$10^{-15} kg\, m^{-3}$$, which is billions of atoms per cubic foot. (but highly variable, in response to solar activity.)