How much does the Earth's atmosphere weigh?

Question

Assuming the weight at the surface of the sphere=1atm and decreases by some factor the further away from the sphere the atmosphere is.

Answer 1

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.

Answer 2

The mathmatical approach to solving this would be as follows:

We estimate/assume a few things,

-The Earth is a perfect sphere and thus has a surfact area equal to 4(pi)r^2

-At every location on the surface of the Earth, the atmpspheric pressure is 1 atmpshere (~= 101300 Pa).

-The gravitational acceleration experienced by the entire atmosphere is a constant 9.81 m/s^2

In reality, we know these things are not totally true, but they are reasoble eastimations considering the scale of the total amount of atmosphere we will "weigh".

The radius of the Earth is about 6,378.1 kilometers, and thus the Earth has a surface area of about 5.112 E14 m^2.

Since pressure equals a force applied over an area (F/A), then we can calculate the total force applied by the atmosphere assuming a constant pressure of 1 atm over the surface of the Earth.

From this we calculate the weight of the atmosphere to be 5.18 E19 Newtons.

To then find the mass of the atmosphere, we must realize the weighr is a force caused by gravity,

weight = mass * gravitational acceleration

so the mass of the atmosphere would be the weight divided by 9.81 m/s^2, thus the atmosphere has a mass of about 5.28 E18 kg.

Answer 3

close to a hundred billion tons but its spread out over a large area so its light on our body.