What is the easiest way to calculate the earth's athmoshpere's weight?

Asked by: Maria&Bojidar

Answer

You could use the average atmospheric pressure of 14.7 lb/square inch at the earth's surface to estimate the atmosphere's total weight. That pressure means a column of air above every square inch of the Earth's surface weighs 14.7 lbs. Multiplying that by the total number of square inches gives the total weight of air.

Since we're estimating, use 4000 miles for the Earth's radius, and calculate the area of its surface with the formula for the area of a sphere: 4 x x (radius)².

4000 miles x 5280 ft/mile x 12 inches/ft is about 250 million inches for the Earth's radius, so the formula give:

4 x 3.14 x (250,000,000)² or about 8 x 10E17 square inches. Multiplying each of those square inches by 15 pounds gives 1.2 x 10¹⁹ pounds. Dividing by 2000 lbs/ton converts that to 6 x 10¹⁵, or 6,000,000,000,000,000 (that's 6 quadrillion) tons for the total weight of the atmosphere.
Answered by: Paul Walorski, B.A. Physics, Part-time Physics Instructor