How Is the Mass of Earth's Atmosphere Calculated?

[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...

 

[Astronuc]

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

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.

 

[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?

 

[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.