The Earth's Atmosphere

Chemical Composition:

78% N₂
21% O₂
1% CO₂, H₂O, Ar, Ne, O₃

Why is the atmosphere not H and He (like the Sun, or Jupiter)?
Why is there an atmosphere at all (compare to Mercury, or the Moon)?
What is the pressure/density structure of the atmosphere?

The pressure scale height of an atmosphere (or "how thick is it?")

The pressure of an atmosphere is determined by its weight -- the force of gravity pulling it down. What is this effect called?

From this we know that

Since the atmosphere is very thin, we can assume plane parallel geometry
so that we have instead

Now, we can't assume constant density like we did for the Earth's interior. Gases are compressible, and density and pressure are related by the ideal gas law:

Substituting for density, we get

Rearranging terms, we have the following differential equation:

So let's integrate. P goes from P0 to P as z goes from 0 to z:

and so we get

Let's define the pressure scale height to be

so that we end up with

We see that:

Pressure and density drop as height increases
Scale height defines the distance over which the pressure drops by 1/e = 0.37
Scale height smaller for heavier atoms/molecules.

Example: What is the scale height of the Earth's atmosphere?

It's mostly N₂, so m=2 x 14 x 1.66x10^-27 kg = 4.65x10^-26 kg
and we also have g=9.8 m/s² and T ~ 300 K

so we get H = 9x10³ m = 9 km

Pretty thin...

(Try this at home: What would the scale height be for a hydrogen atmosphere on the Earth?)