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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 Sphere

Not everyone is familiar with the jargon of the sphere. So be patient while I take us all through this.
 
The stars in the sky, though at varying distances from us, can be imagined to lie on the inside of a large Celestial Sphere. Each star within this sphere can be given a set of Celestial Coordinates consisting of Right Ascension (RA) and Declination (Dec), which are similar to longitude and latitude on the Earth’s surface. RA is measured in hours, minutes and seconds of time, while Dec is measured in degrees, minutes and seconds of arc.

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.

 

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The Celestial Sphere

Star Lineups

Three points A, B, C are in line in a plane if they form an angle of 180 degrees.

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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 star lineup

Example: most astronomers are familiar with the star lineup Fomalhaut-Achernar-Canopus.
If the angle between the three stars was 180 degrees, it would put them on the same Great Circle.

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The Celestial Sphere

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.

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Fomalhaut, Achernar, Canopus

Some fairly well known lineups

Just 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 Search

In 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.
Although keen, I wasn’t really expecting to find much. Maybe just a few lineups.

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.
Mimosa and Gacrux point to Regulus, the angle being 177.9 degrees
Regulus-Spica-Antares form an angle of 177.7 degrees.
Canopus-Wezen (delta CMa)-Procyon are very close to being in line at 179.8 degrees.
 
***** When examining the results, I noticed several of the three star lineups combined to produce four or more in line stars.*****
 
The lineup of four stars Alnitak (zeta Orionis)-Procyon-Regulus-Denebola is rather nice.
Taken three stars at a time, the angle in degrees formed by each set of three stars is:

  • 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 five star lineup:
delta Crucis-Mimosa (beta Crucis)-Girtab (kappa Scorpii)-Kaus Borealis (lambda Sagittarii)-Altair.
There are 10 possible groupings. The angle in degrees formed by each group of stars is:

  • 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 six star lineup:
Betelgeuse-Sirius-Wezen (delta CMa)-kappa Velorum-Acrux-Hadar (beta Cen).
There are 20 possible groupings. The angle varies from 178 to 180 degrees.
The best lineups are for:

  • 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 Southern Cross (Crux) is visible all year round (although very low to the horizon in the early night hours in spring), it can be used to locate some stars and constellations using these lineups.

StarLineupsMap.jpg

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Star Lineups
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-Canopus

Among 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?
 
There were 16 results from the search. Here is a sample of 4 of them:

  • 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-Alphard (alpha Hydra)-Regulus, the weakest combination being Canopus-Alphard-Regulus (175.3 degrees).

  • 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 SIMBAD database, operated at CDS, Strasbourg, France.

Article by Rob Horvat (Robh). Discuss this Article at the IceInSpace Forum

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