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Homework Help: Mass of earth's atmosphere

  1. Aug 4, 2005 #1
    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. jcsd
  3. Aug 4, 2005 #2


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    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 = [itex]\int_{R_i}^{R_o} 4\pi\,\rho(r)\,r^2\,dr[/itex]

    or V = [itex]4\pi\,R^2\,\int_0^H \rho(z)\,dz[/itex], 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


    That should give you enough information.
    Last edited by a moderator: Apr 21, 2017
  4. Aug 4, 2005 #3


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    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?
  5. Aug 4, 2005 #4


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    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.
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