I'll answer by asking another question: why doesn't gravity make the atmosphere fall down to the ground? The atmosphere is in hydrostatic balance, in which the pressure force exactly counteracts the force of gravity.
Imagine drawing an imaginary box in the air, which holds a cube of atmosphere 1 meter on each side. Near Earth's surface, that much air has a mass of 1 kilogram, so gravity exerts a force of
F(grav) = M*g = 1 kg * -9.8 m/s^2 = -9.8 Newtons(it's less than zero because gravity pushes downward instead of upward.)
Now, air pressure exerts a force on the bottom of the box equal to the pressure there times the area of the box's top (1 square meter)
Fp(bottom) = P(bottom)*AreaSimilarly, the force on the top of the box is
Fp(top) = -P(top)*Area(again, negative because it's acting downward)
Since the atmosphere has almost no vertical motion, Newton's third law says the sum of these forces must be zero:
F(grav) + Fp(bottom) + Fp(top) = 0 -M*g + P(bottom)*1m^2 - P(top)*1m^2 = 0 P(top) = P(bottom) - M*g/Area
Or, plugging in numbers,
P(top) = P(bottom) - 9.8 Newtons/m^2The air pressure must decrease by 9.8 Newtons/m^2 per meter we ascend in the atmosphere. Since the pressure is 10,000 N/m^2 at the surface, this would mean that the atmosphere is about 10 km thick.
That's roughly true, but the ideal gas law says that the density of a gas decreases as its pressure decreases. So as we stack these cubes of air atop one another, the mass of each cube decreases as we go up, so the top-bottom pressure difference is less for each cube. The net result is that the pressure decreases exponentially with height: it becomes about 1/3 as big for every 10 kilometers we ascend, but never actually reaches zero. Once you get high enough, the atmosphere is so thin it's indistinguishable from the particles making up outer space. Most college physics textbooks which use calculus will show the math behind this exponential drop in pressure. The distance over which the pressure drops by a factor of e=2.72 is called the scale height, equal to about 8 kilometers.
