# I How does gravity hold onto the atmosphere

1. Mar 23, 2016

### pauldunnnnnnnn

Gravity seems emense in strength of objects with large mass. So how does the earth hold on to air molecules

2. Mar 23, 2016

### ProfuselyQuarky

Gravity keeps the atmosphere surrounding Earth the same way it keeps everything else on Earth. Some molecules in the upper atmosphere (Ionosphere/Exosphere) do manage to escape Earth's gravitational pull sometimes, though, due to the fact that they continuously are bouncing around really fast.

http://earthsky.org/earth/what-keeps-earths-atmosphere-on-earth

3. Mar 23, 2016

### BvU

Just for the fun of it: what is the mass of a cubic kilometer of air (normal T and p ) ? One metric tonne, a thousand, or a million ?

4. Mar 23, 2016

### ProfuselyQuarky

Are you asking because you don’t know the answer or because you know the answer and you’re seeing if we know?

Last edited: Mar 23, 2016
5. Mar 23, 2016

### BvU

The latter

6. Mar 23, 2016

### ProfuselyQuarky

Well, I don't know, and I'd love if you kindly provided answer . . .

7. Mar 23, 2016

### BvU

Air is mostly nitrogen. Mass of 22.4 liter N2 is 28 gram (standard T p). Let's round off to 22.4 so 1 liter is 1 gram. Now all we have to do is scale up from 1 L (1 dm3) to 1 km3.

8. Mar 23, 2016

### ProfuselyQuarky

That's clever! So the other 20% of elements that air is composed of does not make much of a difference?

9. Mar 23, 2016

### BvU

28 is a pretty good guess . we're talking order of magnitude here: 'answers' provided are three orders of magnitude apart. Not many guess the right one offhand first time.

10. Mar 23, 2016

### ProfuselyQuarky

I see. Thanks for the clarification. That was a fun fact I never thought of before.

11. Mar 24, 2016

### Anand Sivaram

Average molar mass of dry air is 28.97 g/mol
http://https://en.wikipedia.org/wiki/Molar_mass [Broken]

That gives a density of 28.97/22.4 = 1.29 g/L

Last edited by a moderator: May 7, 2017
12. Mar 24, 2016

### BvU

Wiki have it from the engineering toolbox (link in post #9) .
But they decently refer to that in their reference 6.

Did you guess the right order of magnitude at first ?

13. Mar 24, 2016

### ogg

As far as gravity is concerned, there's little difference between a molecule of air, a rock or a planet. They all obey the same Laws of Gravitation. An object close to Earth will "feel" a force towards the center of the Earth of GMm/r² (where G is a constant, M&m are the masses of Earth and the object, and r is the distance between them). This means that if you throw a rock up into the air its vertical velocity will decrease, reach zero, and then it will begin to accelerate downwards. Same thing with an air molecule. Molecules of gas can pretty accurately be described as particles with varying velocities due to collisions between them; when two collide, one may be sped up, the other slowed down, but momentum (and energy) have to be conserved. Within about 10 miles of the surface of the Earth, for most purposes, it is accurate enough to approximate the force acting on a (small (relative to Earth's mass)) object as a constant, g. When talking about what is happening to gas molecules 100 miles above the Earth, that approximation isn't very good. As a molecule of gas rises away from Earth, the force of attraction between it and Earth is getting less and less, so any object given enough of an initial velocity will "escape" from Earth's gravity. But that velocity is pretty high, and few things are traveling that fast. (We ignore air resistance here, because for a molecule of gas, air resistance isn't relevant). Anyway, most of the gas molecules going away from Earth fall back; only a few have teh velocity to escape. (There's also the Solar Wind which can "blow" some molecules away, but talking about that would mean talking about our ionosphere, and we'd get bogged down pretty quick...)

14. Mar 24, 2016

### Anand Sivaram

@BvU That Engineering Toolbox link is very good. I missed seeing it in your post 9... I knew before that the air density is around 1.2kg/m3..But, now only took closer look at that.

15. Mar 24, 2016

### gleem

The escape velocity of a body from the Earth is 11,186 m/s The average velocity of a Nitrogen atom at room temperature is 765 m/sec which has an energy of about .029 eV.. To totally escape it would take a head on collision with a proton of energy of about 3700 ev to impart enough energy to give a nitrogen atom enough velocity to escape if I did my calculations correctly.