Mass of earth's atmosphere

In summary, to calculate the mass of the Earth's atmosphere, one can use the thin shell method and integrate the density as a function of altitude. This can be simplified by assuming a constant temperature and spherical shape for the Earth. Alternatively, one can account for the Earth's spinning elipsoid shape and varying temperature with latitude and altitude for a more accurate calculation.
  • #1
rlmurra2
19
0
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...
 
Physics news on Phys.org
  • #2
rlmurra2 said:
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 = [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

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

That should give you enough information.
 
Last edited by a moderator:
  • #3
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
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.
 

What is the mass of Earth's atmosphere?

The mass of Earth's atmosphere is approximately 5.1480 x 10^18 kilograms.

How is the mass of Earth's atmosphere calculated?

The mass of Earth's atmosphere is calculated by measuring the density of the air at various altitudes and multiplying it by the volume of the atmosphere.

Why is it important to know the mass of Earth's atmosphere?

Knowing the mass of Earth's atmosphere is important for understanding the planet's overall composition and its impact on the climate and weather patterns.

Has the mass of Earth's atmosphere changed over time?

Yes, the mass of Earth's atmosphere has changed over time due to natural processes such as volcanic eruptions, changes in Earth's orbit, and human activities like burning fossil fuels.

Is the mass of Earth's atmosphere evenly distributed?

No, the mass of Earth's atmosphere is not evenly distributed. The density and pressure of the atmosphere decrease with increasing altitude, meaning that the majority of the mass is concentrated closer to the Earth's surface.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
713
  • Introductory Physics Homework Help
Replies
4
Views
465
  • Introductory Physics Homework Help
Replies
4
Views
963
  • Introductory Physics Homework Help
Replies
11
Views
767
  • Introductory Physics Homework Help
Replies
12
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
880
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
565
  • Introductory Physics Homework Help
Replies
4
Views
434
Back
Top