Mass of earth's atmosphere

1. Aug 4, 2005

rlmurra2

What is the mass of the earth's atmosphere? The radius of the earth is 6.4E6m.

The only thing I can think of is to subtract something from the mass of the entire earth or something...

2. Aug 4, 2005

Staff: Mentor

The atmosphere is a thin band of gas surrounding a solid/liquid earth, but one can use thin shell method of calculating the thickness of that band.

So V = $\int_{R_i}^{R_o} 4\pi\,\rho(r)\,r^2\,dr$

or V = $4\pi\,R^2\,\int_0^H \rho(z)\,dz$, where R would be the mean radius of the atmosphere referenced from the center of the earth.

Then one needs to integrate as a function of altitude, since density decreases with increase in altitude.

Height of Earth's atmosphere - http://www.rcn27.dial.pipex.com/cloudsrus/atmosphere.html

http://en.wikipedia.org/wiki/Earth's_atmosphere

That should give you enough information.

Last edited by a moderator: Apr 21, 2017
3. Aug 4, 2005

Bystander

Given a radius, can you calculate a surface area? Given an area and a "std." atmospheric pressure can you calculate a total force? Given that force and an "average" value for acceleration of gravity at the earth's surface, can you calculate anything else of interest?

4. Aug 4, 2005

NateTG

Really, how you do this depends on your approach to the problem:

Easy (this is probably what you want to do)- determine the difference in the acceleration due to gravity at the high and low ends of the atmosphere. This will (probably) allow you to make a very nice simplifying assumption so you can get a good approximation quickly and easily using the surface air pressure, the acceleration of gravity, and the surface area of the earth.

Medium - Integrate by shells assuming that the earth is spherical, and the temperature of the atmosphere is constant. Remember that the density is proportional to the pressure.

Hard - Integrate but account for the fact that the earth is a spinning elipsoid and for temperature with respect to lattititude and altititude.