# Homework Help: Mass of the atmosphere

1. Jan 21, 2010

### wrongusername

1. The problem statement, all variables and given/known data
What is the total mass of the earth's atmosphere? The radius of the earth is 6.4 x 10^6 m, and 1 ATM = 10^5 N/m^2

2. Relevant equations
$$F=PA=ma$$

3. The attempt at a solution
$$F_{g}=P_{atm}A_{earth}=m_{atm}g$$

$$m_{atm}=\frac{P_{atm}A_{earth}}{g}=\frac{P_{atm}\pi r^{2}}{g}=\frac{\left(1\times10^{5}Pa\right)\pi\left(6.4\times10^{6}m\right)^{2}}{9.80\frac{m}{s^{2}}}=1\times10^{18}kg$$

I think I'm supposed to account for decreasing gravitational acceleration, but how would I do that? I dunno about the height of the atmosphere. The only thing that saved me from getting this problem wrong was my remembering that the mass of the atmosphere was 5x10^18 kg or something

2. Jan 21, 2010

### D H

Staff Emeritus
Almost right. What is the surface area of a sphere?

3. Jan 21, 2010

### wrongusername

Oh! So I forgot the 4 in front of the pi r2. Thank you!

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