The answer theoretically seems simple: just take the number of stars brighter than the sixth magnitude (the limit of visibility to the naked eye) and divide it by two (the number of hemispheres).
Consulting the catalogs it is found that there are about 5,000 stars brighter than the sixth magnitude, so from one hemisphere you could see 2,500.
The answer to this question, however, is much more complex than that. In fact, several other factors must be taken into account, including the place from which we are observing, atmospheric transparency and light pollution.
The numbers found above are primarily related to an observer who sees an unobstructed horizon (such as mountains in the distance).
The number of visible stars then varies slightly depending on the location from which we are observing. In the mountains, for example, the atmospheric transparency will be greater and will allow us to see fainter stars than those seen from sea level.
We must also take into account the direction in which we are looking. In fact, at the zenith it is possible to see stars up to the sixth magnitude, while moving towards the horizon the limit magnitude changes. The light of the stars must in fact pass through a greater atmospheric layer: at twenty degrees of height, for example, it is not possible to see beyond the fifth magnitude.
Finally, we must consider light pollution, which is the most limiting factor of those seen so far: in fact, only the brightest stars are visible from the city center. Light pollution is highly variable from place to place and therefore makes it impossible to give a precise number of stars visible to the naked eye in the sky.
Credit: ESO/B. Tafreshi.
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