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

- cos
*d*= cos δ_{1}cos δ_{2}cos (α_{2}− α_{1}) + sin δ_{1}sin δ_{2}

where α_{1} and
α_{2} are the
right ascensions and
δ_{1} and δ_{2} 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.

- Alkaid, Alcaid and Benetnasch are three different names of the same star.
- Phad, Phekda and Phecda are three different names of the same star.
- The distance between Mizar and Alcor is also given in degrees and arc minutes. For example, 0°11.8′ means 0 degrees and 11.8 arc minutes. One arc minute is 1/60 degree.

## 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 |

## Sources

- We have created the formula in accordance with directions from I.
Todhunter:
*Spherical Trigonometry For the Use of Colleges and Schools. With numerous examples.*(1886), page 35, Article 65 + page 47, Article 82 - Calculated with coordinates from
*The Astronomical Almanac Online*, the list "2015 Bright Stars in PDF and ASCII format"

## In other languages

- Vinkelafstand mellem stjerner (Danish)
- Vinkelavstand mellom stjerner (Norwegian)