Do individual molecules in a gas like the Earth’s atmosphere travel in parabolas?
I know that there are many collisions in such a gas, but in between collisions, I would guess that gravity should effect the motion of the particles. However, I’m having a tough time visualizing how this would result in air currents. Is it just that the velocity of the particles in a gas dwarfs the gravitational acceleration so they might as well be traveling in straight lines? Or are air currents composed of particles that are all traveling on tiny significantly parabolic arcs?
Very tiny parabolic arcs, I suppose, in between collisions — which are going to happen quite frequently in a gas as dense as the Earth’s atmosphere. I think the mean free path length in 1 standard atmosphere is something on the order of 10[sup]-7[/sup] meters.
For any gas there is a parameter called ‘mean free path.’ This is the average distance a moleculte of the gas can travel before it hits another particle. In 11.4 liters of air at 0 C and 1 atmosphere of pressure there are 6.02*10[sup]23[/sup]molecules of air. You can compute the average distance between them from there. Or you can google mean free path for air and I’ll bet you find it somewhere in a reference. My crude computation comes up with a mean free path of .007 mm and the mean particle speed is pretty high so gravity doesn’t have a lot of time to affect the particles path before there is a collision with another particle.
The average velocity for an oxygen molecule at o C and 1 atmosphere pressure is about 460 m/sec. So the mean time between collisions would be about 1.4*10[sup]-10[/sup] or 0.14 nanoseconds. So the paths would be exceedingly small segments of ellipses.
And by the way, in my previous post that mean free path is 0.007 cm, and not mm.
To put it in numbers, if the path were horizontal, it deviates from a straight line by about 10[sup]-19[/sup] meters. That’s one billionth of the size of a water molecule. In most cases you’d be justified in approximating it as a straight line.
Air currents are the aggregate motion of many zillions of air molecules occupying a large macroscopic space. Individual molecules within a moving air mass are themselves still moving in the same way as before: in tiny little paths, extremely close to straight lines (as so far discussed), interrupted by frequent collisions. The parabolic or elliptical shape of the individual paths isn’t significant.
That’s for air certainly. For a much sparser fluid — such as the interstellar medium, or even the plasma outside the Earth’s atmosphere — the mean free path length might be long enough that you could theoretically “see” the orbital arc of a molecule’s trajectory. That’s assuming you could watch an individual molecule moving around, which you can’t actually.
Oh sure. You start making approximations there and pretty soon the Planet Earth Simulator is going to be telling you that the planet is shaped like a banana, the rain in Spain falls in the mountains, and and that the Libertarians are going to sweep the 2008 Presidential elections. Just program it right! It’s just a simple quadratic, for Og’s sake!
