The Danjon limit is dead Version of 26. Oktober 2008
Martin Elsässer

The Danjon limit

The work of Danjon focussed on the apparent shortening of the crescent at small elongations. Danjon extrapolated the (purely visual, no imaging) crescent-observations available to him and the perceived length of these crescents to the elongation of 7°, at which the crescent-length would apparently approach zero and thus any crescent should become invisible. Danjon tried to explain this crescent shortening effect by a shadowing effect of lunar features.

Danjon proven incorrect

Visual and fotografic observations in recent years have gone beyond the "Danjon limit". The moon has been recently imaged at an elongation of 4.7°. Older, space-based imaging has even gone as low as 2°. This clearly shows, that the theory of "shadowing effects" behind the supposed "Danjon-limit" is incorrect, or at least that the extrapolated value of 7° is not a hard limit. As the "Danjon limit" has been "broken" repeatedly by different means and as the theory behind it is incorrect we should probably stop using the term altogether.

Extreme "limits" are of little practical relevance

The Danjon "limit" is of little importance for 99.9% of all visual crescent observations, as the conditions required to detect a crescent at such elongations are very rare for any given location. Most locations on this planet will probably never allow to see the crescent at such elongations. The existing visibility rules take these real-world conditions into account and show probabilities of crescent visibility and state the observing-techniques required, such as naked-eye, binoculars or telescope.
Still, under favourable conditions (perfect weather at a high-altitude site, little air polution) with proper preparation and equipment ever smaller crescents should be detectable, well below the "limit", though this will become more and more difficult and thus very rare.

Contrast is all important

Sighting/imaging the crescent is extremely sensitive to contrast, which depends on the crescent/horizon geometry, sky-conditions, magnification, eye/instrument characteristics and other aspects.
How to image extreme crescents

A recent work by professor A. H. Sultan investigates the moonsighting issue in terms of contrast in detail. He predicts, that under near-perfect conditions with optimized equipment, the crescent could actually be seen visually at some conjunctions, when the elongation is near 5°. We know that the moon can be imaged at these elongations, as was proven in 2007, with optimized equipment for the task.

Whether imaging is acceptable for some religious uses of crescent-sighting is not relevant to the scientific discussion of crescent visibility. Imaging can show the crescent at elongations which are probably impossible to reach with the human eye, because optimized camera systems can resolve low contrast detail beyond the limits of the human eye..

Crescent visibility curves

The visibility curves and numerous visiblity rules capture the wide range of practical experience available and derive at predictions of crescent-visibility. Some of these predicted probabilities will be higher than others, simply because the data used will be slightly different, or because the probability deemed "acceptable" will be slightly different.

There is no hard limit of crescent visiblity at 7° or 6.5°. It is all a matter of contrast. With increasing effort (climbing higher mountains with bigger optics, better training and preparation) ever smaller crescents might be possible. (Just because it has not been done yet does not mean it is impossible. Climbing Mt. Everest was also considered impossible for a long time.)

Of course, for the layman, which does not climb a mountain, does not have an optimized telescope and has not prepared/trained for the task, the practical limit will be where the well established visibility curves predict it to be. But these are only probabilities of visibility. There is no hard limit, and definitely not the "Danjon limit".

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