PDAS Home > Contents > Difficult Problems > No fall
Public Domain Aeronautical Software (PDAS)

This question is not as silly as it sounds. The molecules making up the atmosphere have mass and therefore are attracted to the center of the earth by the force of gravity. So, why are they up over our heads instead of down around our feet? I like to answer this by asking another question: If there are ten thousand Pascals of pressure in the atmosphere at sea level, why doesn't this blow the air out into space?

The answer to both questions is that the molecules of air are indeed being pulled toward the center of the earth. But, as they squeeze together as tightly as possible, the resulting pressure pushes them upward. A balance is reached when the atmospheric density varies with altitude in just the right way that gravity and pressure are in static equilibrium.

It is fairly easy to derive the law of hydrostatic equilibrium:

dp/dz = -g * density

which relates the weight density of the atmosphere to the gradient of pressure with height. From this relationship, the perfect gas law and the definition of temperature in the standard atmosphere, one may derive the equations of hydrostatic equilibrium describing the temperature, density and pressure at any altitude in the atmosphere.

You may read the page describing the equations of hydrostatic equilibrium. XHTML+MathML, 12KB or PDF, 69KB.

A related question would be: Since the atmosphere is trying to squeeze as closely as possible to the surface of the earth, how thick is the resulting layer of air? I have a page that addresses this question.

PDAS Home > Contents > Difficult Problems > No fall
Public Domain Aeronautical Software (PDAS)