I have had several discussions where people have said that the atmosphere is so enormous that man could not affect it. When you look up at the sky and think about the size of the Earth, it is not difficult to see why they think this. I began to wonder what volume it would take up if it was a liquid such as water – will it be as big as an ocean, a sea or a lake.

Air is a gas and is easily compressed – a fact that is obvious if you climb a high mountain or fly in a plane – the air becomes a lot ‘thinner’ i.e. less dense. Another indication is that the atmosphere is not that big is that we live beneath it. We have the weight of the entire atmosphere above pressing down on us – something we call atmospheric pressure.

So this is my quick ‘back of the envelope’ calculation on the mass of the atmosphere, which was done with the help of my friend Ethan.

The way we have done this is to take the average atmospheric pressure at sea level (101325 Pa). One Pa (Pascal) is a unit of pressure equal to 1 Newton per meter squared (N/m²). This is acting on the entire surface of the Earth (radius, 6371Km = 6.371 x 10⁶m). The surface area of a sphere is 4?r² which gives an area of 5.1 x 10¹⁴m². If we multiply this area by the pressure (force per unit area) we get the force of the atmosphere on the Earth which turns out to be 5.17×10¹⁹N.

We now use Newtons law F=ma – force equals mass times acceleration, which means that mass is force divided by acceleration m=F/a. The acceleration due to the Earth’s gravitational field is 9.81m/s. This gives a mass for the atmosphere of 5.26 x 10¹⁸Kg. Looking on Wikipedia, we find that they give 5.1480 × 10¹⁸Kg. So our figure is not that much out². However, looking at the recent literature¹ we noticed that they give a mean surface pressure (98305 Pa) which is much lower than the one we used (101325 Pa). If we use this in our calculations we get a mass of 5.11 x 10¹⁸Kg which is much closer to the figure quoted on Wikipedia.

Since density is mass per unit volume (?=m/V) then volume is mass divided by density (V =m/?. The density of water is 1g/cm³ or 1 x 10³ Kg/m³. This gives the volume of 5.15 x 10¹⁵m³ or 5,150,000Km³. This is a bit bigger than the Mediterranean³ (4,390,000Km³) but much smaller than major seas and oceans – e.g. the Atlantic is 310,410,900Km³

Could man have a significant effect on the Mediterranean by pollution – we already have.

¹ The Mass of the Atmosphere: A Constraint on Global Analyses K. E. Trenberth and L.S. Smith, Journal of Climate, March 2005 (http://acd.ucar.edu/~lsmith/massERA40JC.pdf)

² There are several inaccuracies with our ‘back of the envelope’ calculation. For instance it would be necessary to take into account the variation in the height above land since the air is much denser near sea level, the Earth is not totally spherical and the gravitational force decreases with height.

³ Volumes of the World’s Oceans from ETOPO1, NOAA (http://www.ngdc.noaa.gov/mgg/global/etopo1_ocean_volumes.html)