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Frank Reed asked:

How many problems do we see in this article about the constellation Grus? 

[hint: how far apart are δ¹ and δ² Gruis? ... but don't stop there!]

Following the link to the article in Frank’s post, Jonathan Nally wrote:

“Grus has some very attractive wide double stars; that is, ones that are far enough apart to be obvious to the unaided eye. Delta1 Gruis (δ1) [ ] and Delta2 Gruis (δ2), for instance, are separated by an easy 16 arcseconds, while Mu1 Gruis (μ1) [ ] and Mu2 Gruis (μ2) are about 19 arcseconds apart ”

There is a problem with this statement: the “unaided eye” is unable to detect a separation of 16 or 19 arcseconds.  This is beyond the resolution limit of the human visual system, even in ideal daytime conditions, and more so after dusk, when a subset of our visual pathways becomes unresponsive. So, to be seen as double stars, either the separation between star pairs has to be larger, or seeing them has to require some type of optical aid.

To figure out what should have been the correct statement, I checked the Southern Skies volume of The Night  Sky Observer’s Guide (Ian Cooper, Jenni Kay, and George Kepple, ed. Willmann-Bell).  These authors give the separation between the δ1 and δ2 Gruis as 17 arc minutes, and that between μ1 and μ2 Gruis as 18 arc minutes. So, Jonathan Nally’s numerical values are in the right range, but his units are wrong by a factor of 60.  An easy mistake to make, but one that a review by him or by his editor should have caught, even for someone unfamiliar with this constellation.

Best, Rafael

P.S. I’m adding the following two introductory paragraphs about the subject of human visual resolution in, in case anyone is interested.

The resolution limit of the human visual system, known as visual acuity, is quantified by the minimal angle of resolution. When viewing two objects, this is the smallest angle subtended by these objects at the eye, at which these visual stimuli may be distinguished as two separate objects, rather than as a single object.  This minimal angle of resolution may be expressed as minutes of arc, but it is traditionally expressed as a fraction: e.g. 20/20, 6/6, or 10/10, in the US, UK, and continental Europe, respectively.  This tradition does not reveal the basic concept of a visual angle underlying acuity very straightforwardly: the fraction is the inverse of the minimal angle of resolution. Therefore, a visual acuity of 20/20, 6/6, or 10/10 is equivalent to minimal angle of resolution of 1 minute of arc, while a very poor visual acuity 20/200, 6/60, or 10/100 means that the minimal angle of resolution is only 10 minutes of arc.

Despite a common misconception, a visual acuity of 20/20, 6/6, or 10/10 is not the definition of “normal” visual acuity. The minimal angle of resolution of most human subjects with normal visual function is smaller than 1 minute of arc or 60 seconds of arc. However, it is only rarely smaller than 1/2 minute of arc or 30 seconds of arc (an exception to this statement is vernier acuity, or other forms of hyperacuity, which aren’t the subject of this discussion).