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Miscel-

laneous

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



next neighbor
                        separation

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

cell
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

formula mean angular
                        distance

mean angular separation
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


number od stars 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




Last modified: 2023, Oct 05