Star Lineups
Submitted: Wednesday, 1st April 2009 by Rob Horvat
This article originated from a search I did in 2008 to find if there were other interesting lines of stars such as the well-known Fomalhaut-Achernar-Canopus. The stars in Corvus that point to Spica and those in Aquila that point to Vega are fairly well known but how accurate are they? ## The Celestial SphereNot everyone is familiar with the jargon of the sphere. So be patient while I take us all through this. For example, the star Sirius has coordinates RA, Dec = 06h45m09s, -16d42m58s. A Great Circle is any of the largest circles that can be drawn on this sphere and cuts it into two hemi-spheres. As the Earth is at the centre of the Celestial Sphere, a Great Circle always has the Earth as its centre. Circles passing through both Celestial Poles are RA circles, which are Great Circles. Apart from the Celestial Equator, all Declination circles are Small Circles. A Great Circle can also be formed by tilting any RA Circle about its centre.
## Star LineupsThree points A, B, C are in line in a plane if they form an angle of 180 degrees.
Similarly, three or more stars are considered to be in line in the sky if they are on the same Celestial Great Circle. The spherical angle between the three stars would be 180 degrees. A group of three or more stars that are in line, or close to it, will be referred to as a Example: most astronomers are familiar with the star lineup Fomalhaut-Achernar-Canopus.
Closer inspection reveals that Fomalhaut and Achernar actually lie on a different Great Circle to Achernar and Canopus, the angle between the Great Circles being 177.5 degrees. However, this cannot be discerned visually and they appear to be in line.
## Some fairly well known lineupsJust how accurate are some of these lineups? - Gacrux and Acrux point roughly to Achernar (174.8 degrees). Not too bad.
- Theta Aquilae and Altair point to Vega (178.0 degrees). Pretty good.
- Gamma and delta Corvi point to Spica (177.5 degrees). Same as Fomalhaut-Achernar-Canopus.
## The SearchIn looking for possible lineups, I narrowed my search to 82 selected stars visible to southern observers. There were 21 first magnitude stars, 56 second magnitude and 5 third magnitude stars, one of which was delta Crucis (magnitude 2.8). Next, there was some heavy mathematics and computer programming to do the search. Overall, I restricted the search so that the total span of the three stars was less than 120 degrees of arc. For example, from Fomalhaut to Achernar to Canopus, the total span is 78 degrees of arc. I began by looking for any three stars forming an angle of 175 degrees or better but this produced 1478 results. Ridiculous! Then I tried an angle of 176 degrees or better and got 1173 results. I upped it to 177 degrees or better and got 887 results, then 178 degrees or better with 610 results. To my surprise, there were 297 results with an angle of 179 degrees or better. In fact, there were 18 results with an angle of 180.0, correct to the nearest tenth of a degree! ## What did the search turn up?Acrux and Gacrux point to Porrima (gamma Virginis) at an angle of 178.2 degrees. - Alnitak-Procyon-Regulus 180.0
- Alnitak-Procyon-Denebola 179.1
- Alnitak-Regulus-Denebola 178.2
- Procyon-Regulus-Denebola 178.2
The lineup delta Crucis-Acrux-beta Gruis-Fomalhaut is interesting. The total span of the four stars from delta Cru to Fomalhaut is 90 degrees. The angle in degrees formed by each set of three stars is: - delta Cru-Acrux-beta Gru 179.8
- delta Cru-Acrux-Fomalhaut 179.7
- delta Cru-beta Gru-Fomalhaut 178.6
- Acrux-beta Gru-Fomalhaut 178.5
However, we can surpass this with the following - delta Cru-Mimosa-kappa Sco 179.3
- delta Cru-Mimosa-Kaus Borealis 179.8
- delta Cru-Mimosa-Altair 180.0
- delta Cru-kappa Sco-Kaus Borealis 178.7
- delta Cru-kappa Sco-Altair 179.3
- delta Cru-Kaus Borealis-Altair 179.7
- Mimosa-kappa Sco-Kaus Borealis 178.7
- Mimosa-kappa Sco-Altair 179.2
- Mimosa-Kaus Borealis-Altair 179.6
- kappa Sco-Kaus Borealis-Altair 179.3
Not to be beaten is the amazing - Betelgeuse-Sirius-Wezen 179.9
- Betelgeuse-Sirius-Acrux 180.0
- Betelgeuse-Sirius-Hadar 179.8
- Betelgeuse-Wezen-Acrux 180.0
- Betelgeuse-Wezen-Hadar 179.7
- Sirius-Wezen-Acrux 180.0
- Sirius-Wezen-Hadar 179.7
- kappa Velorum-Acrux-Hadar 179.9
Altair-gamma Gruis-beta Gruis form an angle of 178.9 degrees. In fact, theta Aquilae can be added to this group. Gamma and beta Gruis point to Achernar at an angle of 175.5 degrees. If you remember, theta Aquilae and Altair point to Vega. Combined, though not as accurate, this produces another six star lineup! The above star lineups are illustrated in the following diagram. Constellations and distances are not to scale. Stars and constellations have been arranged to illustrate the lineups on one page. As the
## Some other star lineups from the search- Alpheratz (alpha And)-Aldebaran-Betelgeuse 178.2
- Achernar-Sirius-Procyon 178.1
- Aldebaran-Alnilam (epsilon Ori)-Wezen (delta CMa) 180.0
- Aldebaran-Canopus-Rigil Kent (alpha Cen) 178.6
- Rigel-Alnilam (epsilon Ori)-Castor 179.8
- Rigel-Procyon-Arcturus 179.9
- Capella-Denebola-Spica 179.6
- Betelgeuse-Alhena (gamma Gem)-Pollux 180.0
- Wezen (delta CMa)-Alphard (alpha Hya)-Denebola 179.5
- delta Crucis-Acrux-Fomalhaut 179.7
- Hadar (beta Cen)-Antares-Vega 179.7
- Vega-Altair-Alnair (alpha Gru) 179.4
## More to do with Fomalhaut-Achernar-CanopusAmong the 21 first magnitude stars, the only lineup better than 176 degrees is Fomalhaut-Achernar-Canopus at 177.5 degrees. The next best lineup is Canopus-Rigil Kent-Antares at 175.5 degrees. There are no others that form an angle better than 174 degrees. Fomalhaut-Achernar-Canopus is not only remarkable because the stars are first magnitude but they are also equally spaced (taken to the nearest degree). Fomalhaut-Achernar are 39 degrees apart and Achernar-Canopus are 39 degrees apart. Are there any other stars from the 82 chosen that are equally spaced? - Achernar-Naos (zeta Pup)-Regulus (177.8 degrees).
Equally spaced with Achernar-Naos and Naos-Regulus each 60 degrees apart. - Betelgeuse-Wezen (delta CMa)-kappa Velorum (179.0 degrees).
Equally spaced with Betelgeuse-Wezen and Wezen-kappa Vel each 38 degrees apart. - Kappa Velorum-delta Crucis-alpha Lupi (178.3 degrees).
Equally spaced with kappa Vel-delta Cru and delta Cru-alpha Lup each 24 degrees apart. - Hadar-Antares-Rasalhague (alpha Oph) (178.2 degrees).
Equally spaced with Hadar-Antares and Antares-Rasalhague each 42 degrees apart.
However, for each of these results, at least one of the stars is second magnitude. Finally, the familiar lineup Fomalhaut-Achernar-Canopus can be extended to: - Fomalhaut-Achernar-Canopus 177.5
- Fomalhaut-Achernar-Alphard 179.7
- Fomalhaut-Achernar-Regulus 179.1
- Fomalhaut-Canopus-Alphard 178.3
- Fomalhaut-Canopus-Regulus 179.8
- Fomalhaut-Alphard-Regulus 177.7
- Achernar-Canopus-Alphard 176.7
- Achernar-Canopus-Regulus 178.5
- Achernar-Alphard-Regulus 177.4
- Canopus-Alphard-Regulus 175.3
The coordinates of the stars used in all these searches were obtained from the Article by Rob Horvat (Robh). Discuss this Article at the IceInSpace Forum. |