If the earth's gravity exerts a net downward gravitational force on all air molecules, how come the molecules don't eventually lose their momentum and all settle down? How is the atmosphere is still miles thick after billions of years?
Answer
First of all, gravity does continually accelerate the air molecules. I don't see how this could make them lose their momentum.
What is the net effect of gravity on the atmosphere? Simple, gravity prevents the atmosphere from flying off in space, and instead it keeps it comfortably wrapped around our planet!
The reason why the atmosphere is still thick after billions of years is because you have two net effects on the air molecules, gravity, which keeps it as close as possible to the ground, and inertia, who has the opposite net effect. So as long as the molecules do not slow down they "orbit" our planet.
The reason is the same as why is the moon orbiting the Earth after billions of years. There's a balance between the kinetic energy of the moon and the gravitational potential energy - or a balance between gravity and inertia.
The other answers give you a summary explanation of what determines the temperature of the atmosphere and hence its molecules' average velocity. The reality is way more complicated as the temperature of the atmosphere is not constant with height and you have to take into account many more factors like varying pressure, convection and so on. Modelling the Earth's atmosphere accurately is very complicated.
In conclusion the basic mechanisms are outlined above. I hope they answer your question.
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