Weight of Earth's Atmosphere
Gravity, Force, and Pressure in Fluids & the Power of Physics
Jun 4, 2008
How much does Earth's atmosphere weigh? It seems that answering this question would involve some very difficult experiments or calculations. It turns out that the value of the atmospheric pressure at sea level, combined with an understanding of the physics of weight and pressure, allows us to answer this question relatively easily.
What is Pressure
Pressure is the force divided by the area so that the total force equals the pressure multiplied by the area. Pressure can be measured in newtons per square meter in metric units or in pounds per square inch in English units. Earth's atmospheric pressure is 14.7 pounds per square inch or 1.01 E5 newtons per square meter. (1.01 E5 = 101,000 and 1 newton = 0.225 pounds)
That means that the atmosphere exerts a force of 14.7 pounds on every square inch of Earth's surface or a force of 1.01 E5 newtons on every square meter of surface. To find the total force the atmosphere exerts on a given area multiply this pressure by the area. For example on a surface with an area of 100 square inches, the atmosphere will exert a total force of 1470 pounds (14.7 pounds per square inch X 100 square inches).
What is Weight
The weight of an object on Earth's surface is the gravitational force that Earth exerts on the object. Weight and mass are not the same thing. The weight of an object is its mass multiplied by the acceleration due to gravity, which is 9.8 meters per second squared. Like any force, weight is measured in pounds or newtons. Mass is measured in kilograms.
Calculating the Weight of Earth's Atmosphere
In a fluid, which is either a liquid or a gas, the pressure at some point in the fluid results from the total weight of all the fluid above that point. That is why the pressure increases with depth. For example the atmospheric pressure is lower on a mountaintop than at sea level.
Hence the fact that atmospheric pressure is 14.7 pounds per square inch means that the total weight of atmosphere above 1 square inch of Earth's surface is 14.7 pounds. Similarly the total weight above each square meter of surface is 1.01 E5 newtons. To find the total weight of Earth's atmosphere we need to multiply the atmospheric pressure at sea level by Earth's surface area.
The geometrical formula for the surface area of a sphere is: Area = 4 pi radius squared. Earth's radius is 6.38 E6 meters or 2.51 E8 inches. Applying this formula gives a surface area of 5.12 E14 square meters or 7.94 E17 square inches.
Multiplying Earth's surface area by the atmospheric pressure at sea level gives the total atmospheric force acting on Earth's surface. This total force is the weight of Earth's atmosphere. Doing the math gives the total weight of Earth's atmosphere of 1.2 E19 pounds or 5.2 E19 newtons. Dividing the weight in newtons by the acceleration due to gravity at the Earth's surface gives the mass of Earth's atmosphere, 5.3 E18 kg.
This calculation is a good approximation but it does ignore a few complicating factors that would affect the result a small amount. It is also a nice illustration of the power of physics. One can often calculate seemingly complex things using simple measurements and a basic understanding of physics.
Further Reading
Knight, R.D., Physics for Scientists and Engineers with Modern Physics, Pearson, 2004.
Wilson, J.D., Buffa, A.J., and Lou, B., College Physics 6th ed., Pearson, 2007.
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