Accounting for the weight of the air displaced by an aircraft sitting on the runway has me stumped for a minute. But it made a lot more sense if I imagined that the aircraft was a slightly overloaded (or under-inflated) blimp.

If you're keeping track of volume, what about the oxygen from the alumina released into the air (as CO2) at the aluminum smelter?:\

Chu Chu, the oxygen would add to the atmospheric volume, but it's release would also reduce the gravitational mass of the Earth, which would reduce atmospheric pressure.

I don't know what the net effect would be, but since you have raised it, the same would apply to the aircraft which is made from material sourced from the Earth.

That's interesting (though we're getting a little far afield). In general, the gravitational mass of a sphere acts as if it's concentrated at the center of a sphere. And the atmosphere is part of of the Earth's mass. So smelting the alumina should have no effect on the orbit of the Moon, for example.

But it's different if you're looking at the the effect of gravity at a point within a sphere. My recollection is the it's as if only material at your radius or closer to the center counts (so, for example gravity at the center of the Earth would be zero). Trying to figure out the net effect of adding gas to the atmosphere on the amount of gravity affecting all the other gas in the atmosphere is hurting my head.

So I think you're right that the smelting would tend to reduce the net gravity affecting the atmosphere (because it would replace some mass that fully affects the atmosphere with mass that only partially affects it). But the effect would be less than that from simply reducing the mass of the Earth by the mass of oxygen liberated.

Going back a bit... 'Hydrogen and Helium are lost into space'.... I don't think so.... In a vacuum both hydrogen and helium will weigh something, it's only when weighed in air that the buoyancy makes them float.


So I would think they find a gravitational balance, on top of the air layer, much the same as the Ozone layer... We have invented the Hydrogen and Helium layers..! In practice, turbulence and heat energy keeps all the gasses mixed, or else the Nitrogen would separate from the Oxygen.
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Well, you would need to calculate the volume of air now filling the holes in the ground created in mining of the aluminium used to construct the aircraft. LOL

"The average speed of hydrogen molecules and helium atoms is greater than the escape velocity from the Earth, and these light gases were lost and swept away through photoevaporation by the solar wind early in the Hadean Eon due to Earth's weak gravity."
Evolution of the Earth's Atmosphere

The atmosphere has too little helium to be able to extract it commercially. "Helium is one of these very limited resources that once you’ve used it, you can never recycle it,"
The best sources are found trapped in rocks after the natural decay of Uranium and Thorium.
https://www.chemistryworld.com/news/...010122.article

Pretty much wot Goldenrivett said...

It's been a while so I can't remember the joys of the statistical mechanics and probabilities of all of this but as I recall it whilst the average speed of the lighter gases such as Hydrogen and Helium may not be above escape velocity the distribution of velocities of the H/He atoms in the atmosphere means that at any one time some of those will be travelling above escape velocity. If they can exit the atmosphere unhindered by impacting other gas molecules they are indeed lost in space...then at some time later some more H/He atoms end up being at the top of the velocity curve, and they leak away, etc etc.....there will always be a few around in the atmosphere, but they haven't been around long enough to have (by chance) to reach the magic velocity in the right place...when they do, they're gone..It's an ongoing process.

In fact all lighter gases are subject to the same risk, it's just that H and He, being lightweight, have the highest average speeds, and therefore are at most risk of being lost....

Of course school texts should be amended to record the percentage mass of aluminum in the standard atmosphere.

After an excellent landing etc...

Mass of Earth's atmosphere dwarfs mass of aircraft
 

Earth's atmosphere has a total mass of about 5 x 10^18 kg. That so far dwarfs the mass of all aircraft - flying, parked, or long past their days of operation - that the impact on atmospheric pressure is well below anything that could ever be measured.

The big sky theory is alive and well! The only place that falls apart is when we have our aircraft tightly following common prescribed paths and heading to and from a limited number of terrestrial points. Unfortunately for airplane separation that is exactly what we do all day (and night) long every single day. I guess we can't do away with ATC.