Popular estimate of the Earth's atmosphere possibly wrong?

AI Thread Summary
The total mass of Earth's atmosphere is frequently cited as approximately 5.1 x 10^18 kilograms. This figure is derived from the atmospheric pressure of 100,000 pascals, equating to 10,000 kilograms-force per square meter, and the Earth's surface area of about 510 billion square meters. A calculation using these values confirms the mass as approximately 5.1 x 10^18 kg. Discrepancies arise when considering different surface area calculations or assumptions about the average radius of the Earth, leading to confusion regarding the mass figure. Ultimately, the correct mass of the atmosphere aligns with the commonly referenced value of 5.1 x 10^18 kg.
Dreksler
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My calculation says 5.1 quadrillion kg yet the frequently mentioned one says 5.1 quintillion kg.
So I just realized that on the internet the number that frequently pops up with regards to the total mass of the Earth's atmosphere is 5,100,000,000,000,000,000 kilograms. For example, the number is mentioned two times on the Wikipedia page for the Earth's atmosphere, there are more examples. Yet per square meter of surface, there is 100,000 pascals of pressure, which is 10,000 kilograms-force per meter square. The Earth's surface area is 510,000,000,000 meters. Multiplying 510,000,000,000 meters with 10,000 kilograms gets you the number of 5,100,000,000,000,000 kilograms and not the number of 5,100,000,000,000,000,000 kilograms, which is the number frequently mentioned. Am I missing something here?
 
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Google says ##5.15 \,\cdot\,10^{18}\text{ kg}.##
 
fresh_42 said:
Google says ##5.15 \,\cdot\,10^{18}\text{ kg}.##
I know, that is what I am questioning.
 
You seem to assume ##10,000 \text{ kg}## per square meter in accordance with the sources I saw. Then
\begin{align*}
4\pi \left(\dfrac{12,730,000\text{ m}}{2}\right)^2\cdot 10,000\text{ kg}\,\text{m}^{-2}=5,091,042,001,329,214,046.932\ldots \text{ kg}=5.1\cdot 10^{18}\text{ kg}
\end{align*}
 
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fresh_42 said:
You seem to assume ##10,000 \text{ kg}## per square meter in accordance with the sources I saw. Then
\begin{align*}
4\pi \left(\dfrac{12,730,000\text{ m}}{2}\right)^2\cdot 10,000\text{ kg}\,\text{m}^{-2}=5,091,042,001,329,214,046.932\ldots \text{ kg}=5.1\cdot 10^{18}\text{ kg}
\end{align*}
Multiplying 510,000,000,000 with 10,000 doesn't get you to the power of 15?
 
Dreksler said:
Multiplying 510,000,000,000 with 10,000 doesn't get you to the power of 15?
Sure, but I used an average radius for the Earth and got 510,000,000,000,000 square meters.
 
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fresh_42 said:
Sure, but I used an average radius for the Earth and got 510,000,000,000,000 square meters.
Okay, I get where I made the mistake now.
 
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