Riddle: Mathematically solve the value for the mass of Earth's atmosphere in kilograms.
Hint: Pressure has SI units of Pascals which are Newtons per meter squared, the average sea level pressure is 1013.25 millibars, use a gravitational constant of 9.81 meters per second squared, assume earth is a perfect sphere, formula for surface area of earth is 4*PI*r^2
Answer to Riddle: The average sea level pressure is 1013.25 millibars. This is equal to 101,325 Pascals. A Pascal is Force divided by Area with the area being 1 meter squared. Force is mass times acceleration with the acceleration being supplied by gravity. If we can solve for Force we can then determine the mass of the atmosphere.
Pressure = Force / Area
Pressure = 101,325 Pascals
Area = Area of Earth
The earth is a near sphere. A sphere has an area of 4*PI*radius^2. Earth has a radius of 6,371 km = 6,371,000 meters. Area of Earth = 4*PI*6,371,000^2 meters^2 = 5.1 * 10^14 m^2
Force = Pressure * Area
Force = (101,325 Pascals * 5.1 * 10^14 m^2) = 5.17 * 10^19 Newtons
Force = mass * gravity
mass = Force / gravity
mass = 5.17 * 10^19 Newtons / 9.8 ms^-2 = 5.27 * 10^18 kilograms