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At night, I look at the planes in the sky and count them. I can normally spot between 2-5 planes, never more.

As the visible sky is always a constant area and there are security distances and aerial ways, is it possible to use a formula/approximation to determine the maximum number of visible planes in the sky?

Assume horizon to horizon visibility.

EDIT - Note to all those who spent some time for me

I didn't imagine this question would be such broad... this was just a though I had last night in my garden.

So, I have no idea how to be more precise... I learned some things of your comments, I am now reading some articles to learn what all that means (new words, moreover in English), and I will enrich the question some further day.

Thanks to all !

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    $\begingroup$ This actually depends a lot on which airspace you are looking at, since separation minima vary with a number of factors (procedural/surveillance airspace, controlled/uncontrolled airspace, PSR/SSR equipment, precision of surveillance equipment, wake turbulence minima, RVSM/VSM, ... the list goes on). Try specifying the exact area, and if possible please specify how large an area you are able to visually observe. Even with these details, an answer would be purely theoretical (and probably much larger than you might think) $\endgroup$ – J. Hougaard Sep 26 '16 at 14:42
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    $\begingroup$ The airspace around London is one of the busiest airspaces in the world, but there is still physically room for many, many more planes. Feel free to start counting for yourself: flightradar24.com/51.64,-0.22/8 $\endgroup$ – J. Hougaard Sep 26 '16 at 14:48
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    $\begingroup$ With usually dozens of available Flight Levels (outside mountainous terrain), you can have far more than 5 planes right above you - let alone in the visible sky. There are 3 main dimensions of separation: vertical (flight levels), lateral and longitudinal. But with planes flying in different directions at different speeds, the separation limits do not practically convert to a maximum plane density. $\endgroup$ – MSalters Sep 26 '16 at 14:50
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    $\begingroup$ When pilots fly in formation, well... $\endgroup$ – kevin Sep 26 '16 at 15:51
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    $\begingroup$ To approximate the maximum amount of aircraft flying overhead (barring special flights), you have to take the volume of the sky that you can see and divide that by the minimum separation distances between aircraft. $\endgroup$ – SMS von der Tann Sep 26 '16 at 16:05