In August of 2021, I went on a road trip staying at a rural hotel. What I found strange years later was that despite having practically no light pollution, I don't at all remember being fascinated with the supposed extremely beautiful and starry night sky. While I now think that this is because I never really left my room at night, I still had the idea that it could just be because the midyear sky is just that boring... in which case, what is the starriest part of the night sky, then?
Definition
A very literal reading of the question doesn't bring a very useful answer; after all since the universe is isotropic there are about the same number of stars in both hemispheres of whichever axis you choose, in this case being about several hundred sextillion (1023–1024) in each. Limiting the distance doesn't help much either. What we really need is to somehow quantify the "apparent brightness" of a celestial hemisphere, taking into account the apparent luminosity of stars and how a large patch of stars does not feel as bright as a single star of that same brightness (this requirement is not really met at the end, but it works well enough). This led me to devise the "score" of one hemisphere, with the starriest hemisphere being the one with the greatest score.
The score of an entire celestial hemisphere was defined as the sum of the score of each star relative to the hemisphere's center (the axis). I devised four methods to calculate the stellar score, two of which were selected as the others failed gradient ascent and produced strange score graphs where they ended up.
The brightness exponent is necessary to avert an Olber's paradox type scenario, where the additive brightness of the large number of dim stars is greater than the additive brightness of the low number of bright stars, skewing the axis with the greatest score by adding a lot of noise. With a brightness exponent however, the additive exponentiated brightness of dim stars becomes much lower than the additive brightness of bright stars. In the end though, this was not as much of a problem as I was expecting.
Results
To solve this problem, I used the Bright Star Catalogue as a catalog for all stars visible to the naked eye (<6.5m), which numbered 9096 objects. I then wrote a Python program to transform the somewhat awkwardly formatted data into an easily readable C array, and then wrote a C program to solve for the axis with the greatest score, as well as provide a score graph of the surrounding celestial area to check its accuracy. This is all in the folder catalog.
After running the program, these are the results. Each datum indicates the axis right ascension, declination (J2000.0), score and the opposite hemisphere's score.
| Br. exp. | Method I | Method II |
|---|---|---|
| 1 |
RA 118.9° Dec −41.6° 10.69 / −10.69 |
RA 110.2° Dec −35.9° 31.93 / 21.36 |
| 2 |
RA 104.4° Dec −24.0° 18.82 / −18.82 |
RA 100.7° Dec −24.1° 21.32 / 2.53 |
| 3 |
RA 101.8° Dec −20.5° 62.84 / −62.84 |
RA 100.8° Dec −20.8° 64.47 / 1.65 |
As expected, they are close to the two brightest stars in the night sky, Sirius and Canopus, with the brightness exponent 1 coördinates all being within Puppis and the others being in Canis Major. In every case, the brightest star beyond the hemisphere (i.e., 90° of the point) is Arcturus, the 4th brightest star of the night sky.
As for the date and location to get these starriest skies, they occur at midnight on (method I) or a few days after (method II) new years, taking place around latitudes 24° (br. exp. 2) or 21° (br. exp. 3) south. Of course though, the human eye really doesn't care about this unnecessarily precise metric, so any place in the southern hemisphere in December or January should provide skies way starrier than the ones of the northern hemisphere's midyear.
Interestingly, even disregarding the brightness of stars entirely reveals that all visible stars (or the stars in the catalog, at least) are concentrated in this region; the brightness exponent 0 results are RA 94.9° Dec -43.5° 279.86 / -279.86 for method I and RA 114.8° Dec -40.3° 2615.49 / 2345.26 for method II, both coördinates being within Puppis.