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Angular Distance of the Nearest Neighbor

The applet is computing the angular separation (degrees) of the nearest neighbor for 200 of the brightest stars (visual magnitudes < 3.0):

The stars are displayed by two frames:
• a right ascension - declination chart,
the angular distance seen at the sky is distorded for high declinations,

• a spherical sky chart of the local horizon.
The number of stars of visual magnitude<3 above horizon (while Sun elevation<-12°) is between 63 and 83.

 number of stars visual magnitude next neighbor mean distance 30 <= 1.73 16.5° 60 <= 2.09 12.4° 120 <= 2.68 8.65° 180 <= 3.02 7.2° 240 <= 3.32 6.6°

Splitting the celestial sphere (size 3602/π square degrees = 41253 square degrees) into equal-sized cells (d*d square degrees each)

and supposing that a star and its nearest neighbor occupy 9 cells (9/2 cells per star), the mean angular distance d of n stars is

distance for number of stars n>240 computed by the formula

Between n=60 and n=240 the mean difference between the observed angular distance (applet) of the nearest neighbor and the value from the formula is 1.7 %.

 number of stars visual magnitude next neighbor mean distance next neighbor mean distance by formula 30 < 1.73 16.50° 17.48° 60 < 2.09 12.43° 12.36° 120 < 2.68 8.65° 8.74° 200 < 3.16 7.11° 6.77° 240 < 3.32 6.46° 6.56° 500 < 4.0 - 4.3° 1000 < 4.6 - 3.0°

 visual magnitude v number of stars brighter than v -1 1 0 4 1 15 2 48 3 171 4 513 5 1602 6 4800 7 14,000 8 42,000 9 121,000 10 340,000

http://en.wikipedia.org/wiki/Apparent_magnitude

 visual magnitude v northern hemisphere number of stars of magnitude v 1 9 2 34 3 96 4 214 5 550 6 1439

Table according to Argelander

The 16 brightest stars visible in the northern hemisphere:

 star constellation visual magnitude Sirius CMa -1.46 Arcturus Boo -0.05 Vega Lyr 0.03 Capella Aur 0.10 Rigel Ori 0.12 Procyon CMi 0.40 Betelgeuse Ori 0.45 Altair Aql 0.76 Aldebaran Tau 0.87 Spica Vir 0.95 Antares Sco 1.06 Pollux Gem 1.16 Fomalhaut PsA 1.17 Deneb Cyg 1.25 Regulus Leo 1.35 Castor Gem 1.59