# Weight of Earth's atmosphere?

## Main Question or Discussion Point

Greetings,

I was thinking about gravity on Earth. From what I know, if you are standing on the Earth's surface, all the mass of the Earth below you will pull you downwards (or more correctly, it warps the space above you which pushes you down snug to the ground). But then I thought about the atmosphere above you and how it tries to pull you upwards, in contrast to the earth's gravity. So my question is, if the Earth's atmosphere suddenly evaporated off the Earth in an instant (just assume this), we wouldn't find it more difficult to walk up stairs and such wouldn't we? And by how much? Do we know how much the Earth weighs and how much the atmosphere weighs, approximately? For now, lets disregard gravity from the moon and sun.

Cheers.

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The atmosphere is approximately symmetrical, so it doesn't attract you (upwards or downwards).
But we can't forget Archimedes: we are immersed in the atmosphere.
So, you have to consider the weight of the air your body displaces, and this will be the upward force on you.
Without the air, you would weight about 0.13% more.

russ_watters
Mentor
If you're talking about gravity due to the mass of the atmosphere, Chaos, that is negligible. Especially since there is mass of atmosphere above you and below you.

The mass of the atmosphere is approximately equal to the atmospheric pressure times the surface area of the earth (divided by g).

4,987,588,284,000,000,000 kgs is my best guess for what the atmosphere weighs

rbj
4,987,588,284,000,000,000 kgs is my best guess for what the atmosphere weighs

lessee, 14.696 lbs in-2 x 4 $\pi$ x (6378100 m x 39.37 in/m)2 = 1.165 x 1019 lbs.

hmmmm. that's fewer pounds than you have kg. i normally thought that a kg is bigger than a lb. are you sure that's right?

Gokul43201
Staff Emeritus
Gold Member

lessee, 14.696 lbs in-2 x 4 $\pi$ x (6378100 m x 39.37 in/m)2 = 1.165 x 1019 lbs.

hmmmm. that's fewer pounds than you have kg.
No, it's not. You have an extra zero. The two numbers are within 5% of each other.

Gokul43201
Staff Emeritus
Gold Member
But then I thought about the atmosphere above you and how it tries to pull you upwards, in contrast to the earth's gravity.
Treat the atmosphere as a thick spherical shell, with you living on its inside surface. What does Gauss' law tell you about the force you will feel from it?

Treat the atmosphere as a thick spherical shell, with you living on its inside surface. What does Gauss' law tell you about the force you will feel from it?
Yes, I thought about Gauss' law after I posted the question and realized the atmosphere's G would simply cancel out. It was intereting to learn in Fernbac's post that the air your displace with your body has a minute effect on the G you experience.

The weight of the atmosphere can be used to push dust and other bits of crap into a bag; it's called a vacuum cleaner.

Borek
Mentor
If you're talking about gravity due to the mass of the atmosphere, Chaos, that is negligible.
I thinks it is not negligible, it just cancels out. IIRC if you are inside a sphere you are pulled down only by the part of the sphere that is below you (so if you are inside the Earth - say 1000 km from the mass center - you are attracted only by the 1000 km radius sphere, as if everything else didn't exist).