# Calculating the Mass of Earth's Atmosphere

I am trying to solve the problem below:

Calculate the mass of the Earth's atmosphere given a mean pressure at the surface of $$1.013\times 10^5$$ Pa and $$g=9.81$$ m/s/s.

I have been provided a hint in the textbook to use the hyrdostatic equation. From my understanding, the hyrdostatic equation is of the form $$\frac{\partial p}{\partial z}=-\rho g.$$Here, $$\rho$$ denotes density and thus $$\rho=\frac{m}{v}\implies \frac{\partial p}{\partial z}=-\frac{mg}{v}.$$I am unsure of how to proceed. Any tips would be greatly appreciated.

• I have derived the following for the entire atmosphere $$\text{mass}=\frac{\text{pressure}\times\text{surface area}}{\text{g}}.$$ Is this correct? Feb 22 '20 at 0:01
• Thanks. I ended up integrating from $z$ to $\infty$ and realised that $$\int_{z}^{\infty} \rho \ dz$$ was just the mass per unit area of the atmospheric column. Feb 22 '20 at 0:05