Bright Stars: Angular Distance of 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	number of stars brighter than
-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

number od stars magnitude