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.
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.
Three 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 star lineup.
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 lineups
Just how accurate are some of these lineups?
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.
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.
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:
However, we can surpass this with the following five star lineup:
Not to be beaten is the amazing six star lineup:
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.
Some other star lineups from the search
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?
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:
The coordinates of the stars used in all these searches were obtained from the SIMBAD database, operated at CDS, Strasbourg, France.