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Angular distance between stars

The formula for calculating the angular distance d between two objects is

cos d = cos δ1 cos δ2 cos (α2 − α1) + sin δ1 sin δ2

where α1 and α2 are the right ascensions and δ1 and δ2 are the declinations of the objects.

Below are angular distances in degrees. J2015.5 means that the distances are for the middle of the year 2015. The distances change slowly due to the stars' proper motions (motion in space relative to the Solar System). They are independent of the precession. Precession is the phenomenon of Earth's axis of rotation tracing out the surface of a cone during 25 800 years.

The distance from Castor to Pollux is, to the nearest minute of arc, 4°30′. To the nearest second of arc, it is 4°30′18″.

The Winter Triangle is nearly an equilateral triangle. Moreover, the Summer Triangle is nearly an isosceles triangle, and the Great Square of Pegasus is not exactly a sqaure. The table shows how long the sides of the shapes actually are, and thus how much the shapes differ from the approximate geometric shapes.

Angular distances J2015.5

Winter Triangle  
Betelgeuse–Sirius 27.1
Sirius–Procyon 25.7
Procyon–Betelgeuse 26.0
Orion & Taurus  
Bellatrix–Aldebaran 15.8
Aldebaran–Alcyone 13.7
Betelgeuse–Rigel 18.6
Gemini & Canis Minor  
Procyon–Pollux 22.8
Castor–Pollux 4.5
Leo  
Regulus–Denebola 24.6
Ursa Major (Big Dipper) & Ursa Minor  
Dubhe–Polaris 28.7
Merak–Alkaid 25.6
Dubhe-Alkaid 25.7
Dubhe–Merak 5.4
Merak-Phad 7.9
Phad-Megrez 4.5
Megrez-Dubhe 10.2
Megrez-Alioth 5.4
Alioth-Mizar 4.4
Mizar-Alkaid 6.7
Mizar-Alcor 0.197
Mizar-Alcor = 0°11.8′
Ursa Major, Boötes & Virgo  
Alkaid–Arcturus 30.7
Arcturus–Spica 32.8
Summer Triangle  
Vega–Altair 34.2
Altair–Deneb 38.0
Deneb–Vega 23.8
Great Square of Pegasus  
Markab–Scheat 12.9
Scheat–Alpheratz 14.2
Alpheratz–Algenib 14.0
Algenib–Markab 16.5

Table of angular distances

  Acher­nar Acrux Adara Alde­baran Alioth Alnair Alni­lam Altair Ant­ares Arc­turus Bella­trix Betel­geuse Can­opus Ca­pella De­neb El­nath Fo­mal­haut Ga­crux Hadar Mia­placi­dus Mi­mosa Pol­lux Pro­cyon Regu­lus Rigel Rigil Ken­taur­us Shaula Siri­us Spica Vega  
Achernar 0.0 58.9 60.8 82.5 173.9 32.8 73.1 95.7 88.9 141.3 78.4 82.9 39.4 112.8 119.5 98.3 39.1 64.9 62.3 44.5 62.7 114.3 94.6 119.9 64.3 61.3 73.5 68.9 111.6 129.6 Achernar
Acrux 58.9 0.0 60.8 117.1 119.2 66.6 94.6 107.3 53.5 85.0 102.6 100.2 45.1 137.4 144.1 122.0 85.6 6.0 11.8 19.8 4.2 106.5 86.6 79.7 90.6 15.6 51.6 73.0 53.0 125.1 Acrux
Adara 60.8 60.8 0.0 57.1 113.1 92.9 34.0 156.5 114.0 115.6 41.9 39.5 24.6 78.5 154.0 61.7 98.3 62.4 72.6 45.0 63.9 58.1 35.6 61.4 32.1 76.0 111.0 12.6 90.3 169.2 Adara
Aldebaran 82.5 117.1 57.1 0.0 93.9 106.7 23.1 125.5 170.0 130.4 15.8 21.4 73.0 30.7 97.0 16.8 93.5 119.3 128.3 98.6 120.6 45.0 46.3 80.1 26.5 131.0 155.8 46.0 133.5 117.9 Aldebaran
Alioth 173.9 119.2 113.1 93.9 0.0 153.1 101.8 90.4 94.2 39.8 96.8 92.0 134.7 64.2 65.7 77.7 146.6 113.2 117.1 131.8 115.7 60.1 79.3 54.4 110.6 118.6 110.3 105.0 67.4 56.5 Alioth
Alnair 32.8 66.6 92.9 106.7 153.1 0.0 103.9 63.6 67.6 123.0 107.7 113.5 69.5 131.7 94.2 123.4 19.8 71.8 62.5 62.9 68.5 146.4 127.4 145.0 95.1 59.2 50.3 101.7 107.2 97.8 Alnair
Alnilam 73.1 94.6 34.0 23.1 101.8 103.9 0.0 145.6 148.0 127.7 8.0 9.8 52.4 47.4 120.1 29.9 97.8 96.4 106.2 77.2 97.9 42.6 31.4 68.8 8.8 109.3 141.7 23.0 116.4 139.9 Alnilam
Altair 95.7 107.3 156.5 125.5 90.4 63.6 145.6 0.0 60.3 81.3 140.6 146.9 132.8 115.2 38.0 128.8 59.2 108.2 96.1 117.7 105.6 143.1 165.6 140.0 141.4 91.9 56.1 162.2 97.9 34.2 Altair
Antares 88.9 53.5 114.0 170.0 94.2 67.6 148.0 60.3 0.0 56.0 155.9 152.1 97.0 158.3 91.7 167.2 82.9 51.7 42.0 71.6 50.2 136.7 130.0 99.9 143.7 39.1 17.3 125.7 45.9 71.7 Antares
Arcturus 141.3 85.0 115.6 130.4 39.8 123.0 127.7 81.3 56.0 0.0 126.8 119.8 122.0 103.0 80.9 113.7 134.1 79.4 79.6 103.1 80.9 87.5 96.8 59.7 135.3 80.2 73.1 116.3 32.8 59.1 Arcturus
Bellatrix 78.4 102.6 41.9 15.8 96.8 107.7 8.0 140.6 155.9 126.8 0.0 7.5 60.4 39.7 112.3 22.3 99.1 104.3 114.2 85.2 105.8 39.6 33.4 70.0 14.8 117.4 149.2 30.4 120.6 131.9 Bellatrix
Betelgeuse 82.9 100.2 39.5 21.4 92.0 113.5 9.8 146.9 152.1 119.8 7.5 0.0 60.4 39.5 115.5 22.3 106.1 101.1 111.9 84.1 103.0 33.2 26.0 62.4 18.6 115.5 149.9 27.1 113.4 132.8 Betelgeuse
Canopus 39.4 45.1 24.6 73.0 134.7 69.5 52.4 132.8 97.0 122.0 60.4 60.4 0.0 99.7 156.5 82.3 78.5 48.9 55.6 25.6 49.1 82.7 60.1 80.5 46.7 58.0 89.5 36.2 90.2 165.9 Canopus
Capella 112.8 137.4 78.5 30.7 64.2 131.7 47.4 115.2 158.3 103.0 39.7 39.5 99.7 0.0 78.2 17.5 113.9 136.4 148.7 123.4 139.2 34.2 51.1 69.6 54.2 152.9 170.6 65.8 120.1 93.3 Capella
Deneb 119.5 144.1 154.0 97.0 65.7 94.2 120.1 38.0 91.7 80.9 112.3 115.5 156.5 78.2 0.0 93.8 81.1 143.4 132.4 155.2 141.5 105.6 127.6 119.5 122.2 128.6 92.6 142.5 111.3 23.8 Deneb
Elnath 98.3 122.0 61.7 16.8 77.7 123.4 29.9 128.8 167.2 113.7 22.3 22.3 82.3 17.5 93.8 0.0 109.4 122.4 133.8 106.4 124.6 30.5 39.2 67.3 36.9 137.5 171.4 49.2 121.3 110.6 Elnath
Fomalhaut 39.1 85.6 98.3 93.5 146.6 19.8 97.8 59.2 82.9 134.1 99.1 106.1 78.5 113.9 81.1 109.4 0.0 91.0 82.3 78.9 87.8 138.1 127.3 159.0 89.6 79.0 66.0 103.5 125.9 91.4 Fomalhaut
Gacrux 64.9 6.0 62.4 119.3 113.2 71.8 96.4 108.2 51.7 79.4 104.3 101.1 48.9 136.4 143.4 122.4 91.0 0.0 12.4 24.5 3.4 104.0 85.3 75.1 93.2 16.8 52.1 74.1 47.1 122.5 Gacrux
Hadar 62.3 11.8 72.6 128.3 117.1 62.5 106.2 96.1 42.0 79.6 114.2 111.9 55.6 148.7 132.4 133.8 82.3 12.4 0.0 30.0 9.5 116.3 97.6 86.0 101.9 4.4 40.1 84.8 49.7 113.7 Hadar
Miaplacidus 44.5 19.8 45.0 98.6 131.8 62.9 77.2 117.7 71.6 103.1 85.2 84.1 25.6 123.4 155.2 106.4 78.9 24.5 30.0 0.0 24.0 99.0 76.6 82.2 72.1 32.5 66.0 57.7 70.4 142.9 Miaplacidus
Mimosa 62.7 4.2 63.9 120.6 115.7 68.5 97.9 105.6 50.2 80.9 105.8 103.0 49.1 139.2 141.5 124.6 87.8 3.4 9.5 24.0 0.0 107.1 88.1 78.5 94.3 13.8 49.6 75.9 49.0 121.5 Mimosa
Pollux 114.3 106.5 58.1 45.0 60.1 146.4 42.6 143.1 136.7 87.5 39.6 33.2 82.7 34.2 105.6 30.5 138.1 104.0 116.3 99.0 107.1 0.0 22.8 37.0 51.4 120.7 151.0 47.1 90.9 111.3 Pollux
Procyon 94.6 86.6 35.6 46.3 79.3 127.4 31.4 165.6 130.0 96.8 33.4 26.0 60.1 51.1 127.6 39.2 127.3 85.3 97.6 76.6 88.1 22.8 0.0 37.4 38.5 101.9 137.1 25.7 87.6 133.7 Procyon
Regulus 119.9 79.7 61.4 80.1 54.4 145.0 68.8 140.0 99.9 59.7 70.0 62.4 80.5 69.6 119.5 67.3 159.0 75.1 86.0 82.2 78.5 37.0 37.4 0.0 75.8 90.0 114.1 57.8 54.1 109.3 Regulus
Rigel 64.3 90.6 32.1 26.5 110.6 95.1 8.8 141.4 143.7 135.3 14.8 18.6 46.7 54.2 122.2 36.9 89.6 93.2 101.9 72.1 94.3 51.4 38.5 75.8 0.0 104.6 134.5 23.7 119.8 144.2 Rigel
Rigil Kentaurus 61.3 15.6 76.0 131.0 118.6 59.2 109.3 91.9 39.1 80.2 117.4 115.5 58.0 152.9 128.6 137.5 79.0 16.8 4.4 32.5 13.8 120.7 101.9 90.0 104.6 0.0 36.0 88.4 51.5 110.7 Rigil Kentaurus
Shaula 73.5 51.6 111.0 155.8 110.3 50.3 141.7 56.1 17.3 73.1 149.2 149.9 89.5 170.6 92.6 171.4 66.0 52.1 40.1 66.0 49.6 151.0 137.1 114.1 134.5 36.0 0.0 123.6 61.1 77.3 Shaula
Sirius 68.9 73.0 12.6 46.0 105.0 101.7 23.0 162.2 125.7 116.3 30.4 27.1 36.2 65.8 142.5 49.2 103.5 74.1 84.8 57.7 75.9 47.1 25.7 57.8 23.7 88.4 123.6 0.0 96.2 157.9 Sirius
Spica 111.6 53.0 90.3 133.5 67.4 107.2 116.4 97.9 45.9 32.8 120.6 113.4 90.2 120.1 111.3 121.3 125.9 47.1 49.7 70.4 49.0 90.9 87.6 54.1 119.8 51.5 61.1 96.2 0.0 87.8 Spica
Vega 129.6 125.1 169.2 117.9 56.5 97.8 139.9 34.2 71.7 59.1 131.9 132.8 165.9 93.3 23.8 110.6 91.4 122.5 113.7 142.9 121.5 111.3 133.7 109.3 144.2 110.7 77.3 157.9 87.8 0.0 Vega
  Acher­nar Acrux Adara Alde­baran Alioth Alnair Alni­lam Altair Ant­ares Arc­turus Bella­trix Betel­geuse Can­opus Ca­pella De­neb El­nath Fo­mal­haut Ga­crux Hadar Mia­placi­dus Mi­mosa Pol­lux Pro­cyon Regu­lus Rigel Rigil Ken­taur­us Shaula Siri­us Spica Vega  

Sources

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