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Astronomical question and answer 295

 

Frank L. Preuss

 

How can I determine the angle between two stars?

 

Here comes a way to determine the angle between two stars. The stars picked are mainly from the constellation of Orion and round it. First we have a table of information about some individual stars. Then comes a table where the angles are calculated.

Stars marked with the same colour are in the same eighth of the celestial sphere.

 

Position, or location, of stars on the celestial sphere
123456789101112131415161718192021
Or- der of bri- ght- ness Name of star Con- stell- ation Coordinates Part of the celestial sphere
Right ascension = RA Declination = Decl. Decl. RA
HH MM SS HH+ MM/60+ SS/3600 15*(HH+ MM/60+ SS/3600) DD MM SS DD+MM/60+SS/3600 up down east N S
ho- urs mi- nu- tes se- conds hours de- grees = cos si- gn de- gre- es mi- nu- tes se- conds de- grees sin cos half eighth
h m s h h*15 = o o ' " o + - 0o- 180o 0o- 90o 90o- 180o
1 Sirius Canis major 6 45 8.91728 6.75248 101.3 -0.19573 - 16 42 58.0171 -16.7 -0.28763 0.95774 down east S
2 Canopus Carina 6 23 57.10990 6.39920 96.0 -0.10432 - 52 41 44.3780 -52.7 -0.79543 0.60605 down east S
6 Capella Auriga 5 16 41 5.27806 79.2 -0.18788 + 45 59 53.0000 46.0 0.71932 0.69468 up east N
7 Rigel Orion 5 15 5.25000 78.8 -0.19509 -8.2 -0.14263 0.98978 down east N
8 Procyon Canis minor 7 39 18 7.65500 114.8 -0.41985 + 5 13 20.0000 5.2 0.09102 0.99585 up east S
11 Betel- geuse Orion 5 55 5.91667 88.8 0.02181 7.4 0.12880 0.99167 up east N
14 Alde- baran Taurus 4 36 4.60000 69.0 0.35837 16.5 0.28402 0.95882 up east N
17 Pollux Gemini 7 45 7.75000 116.3 -0.44229 28.0 0.46947 0.88295 up east S
21 Regulus Leo 10 8 22.311 10.13953 152.1 -0.88371 + 11 58 1.9500 12.0 0.20735 0.97827 up east S
23 Castor Gemini 7 35 7.58333 113.8 -0.40275 31.9 0.52844 0.84897 up east S
26 Bella- trix Orion 5 25 5.41667 81.3 0.15212 6.3 0.10973 0.99396 up east N
27 Elnath Auriga 5 26 5.43333 81.5 0.14781 28.6 0.47869 0.87798 up east N
29 Alnilam Orion 5 36 5.60000 84.0 0.10453 -1.2 0.02094 0.99978 down east N
31 Alnitak Orion 5 41 5.68333 85.3 0.08281 -1.9 -0.03316 0.99945 down east N
37 Wezen Canis major 7 8 7.13333 107.0 -0.29237 -26.4 -0.44464 0.89571 down east S
41 Menka- linan Auriga 6 0 6.00000 90.0 0.00000 44.9 0.70587 0.70834 up east S
44 Alhena Gemini 6 38 6.63333 99.5 -0.16505 16.4 0.28234 0.95931 up east S
47 Mirzam Canis major 6 23 6.38333 95.8 -0.10019 -18.0 -0.30902 0.95106 down east S
48 Alphard Hydra 9 28 9.46667 142.0 -0.78801 -8.7 -0.15126 0.98849 down east S
49 Algieba Leo 10 20 10.33333 155.0 -0.90631 19.8 0.33874 0.94088 up east S
73 Mintaka Orion 5 32 5.53333 83.0 0.12187 0.3 0.00524 0.99999 up east N
Denoba Leo 11 49 4 11.81778 177.3 -0.99886 14 34 19.0000 14.6 0.25160 0.96783 up east S

 

Calculating angles between two stars

Formula for cosine of the angle A:

    cos(A) = sin(Decl.1)sin(Decl.2) + cos(Decl.1)cos(Decl.2)cos(RA.1 - RA.2)

Formula for the angle A:

    A = arccos(A)

 

Calculating angles between two stars
ABCDEFGHIJKLMNO
1 Name of first star se- cond star first and second star first star second star first and second star
2 RA.1 RA.2 RA.1- RA.2 cos (RA.1- RA.2) Decl.1 sin (Decl.1) cos (Decl.1) Decl.2 sin (Decl.2) cos (Decl.2) cos(A) A = arccos (A) A
3 first star second star =COS (RADIANS (E)) =SIN (RADIANS (G)) =COS (RADIANS (G)) =SIN (RADIANS (J)) =COS (RADIANS (J)) =DEGREES (ACOS(M))
4 =C-D =H*K+ I*L*F ∼N
5 o o o o o o o
6 Sirius Canopus 101.3 96.0 5.3 0.99572 -16.7 -0.28763 0.95774 -52.7 -0.79543 0.60605 0.80675 36.22079 36.2
7 Sirius Regulus 101.3 152.1 -50.8 0.63195 -16.7 -0.28763 0.95774 12.0 0.20735 0.97827 0.53245 57.82880 57.8
8 Canopus Regulus 96.0 152.1 -56.1 0.55767 -52.7 -0.79543 0.60605 12.0 0.20735 0.97827 0.16570 80.46222 80.5
9 Capella Aldebaran 79.2 69.0 10.2 0.98429 46.0 0.71932 0.69468 16.5 0.28402 0.95882 0.85991 30.69403 30.7

 

Night sky map

Sternenkarte

 

In answer 281 we had a drawing and got the angle between Capella and Aldebaran and it was 30 degrees. And in the above tabel this angle is calculated and it also resulted in an angel of 30 dgrees. So both methods bring useful results.

The two stars are in the same eighth of the celestial sphere and that is the quarter shown on the above map, that is on the right side, at the top, between 6h and 0h, and between 0o and +60o.

The coordinates of the two stars are
Capella:   5.3h RA and +46.0o Decl. and
Aldebaran: 4.5h RA and +16.5o Decl.

 

 

This is the end of "Astronomical question and answer 295"
To the German version of this chapter: Astronomische Frage und Antwort 295

 

 

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