Charles T Whitmell (1849-1919) was an Education Inspector by profession and also a member of the Leeds Astronomical Society. Nothing fascinated Whitmell so much as the observation of ‘extreme’ astronomical sights. Many of the published observations of the ‘green flash’ from the setting sun are due to him. He was also an avid observer of the young Moon. His account of a naked-eye observation of a thin lunar crescent in May 1916 makes an interesting comparison with what is thought to be the earliest feasible new moon sighting. As recently as the 1970s (and possibly well beyond) this 1916 observation was widely regarded as a naked eye record.
Whitmell reported that “from Scarborough. in Yorkshire, about 8h p.m. (G.M.T,) on Tuesday, 2nd May 1916, the Moon was observed by Lizzie King and Nellie Collinson, two maids in the service of Mrs. Ackroyd, of 43, Westbourne Grove. I have been in correspondence with this lady, and wish to thank her for convincing evidence most courteously given. On the same evening, about 8h 15m, the crescent was also observed with the naked eye by Mrs. Willimott and her daughter, residing at Heighington in county Durham. Mrs. Willimott has also kindly replied to inquiries. We have thus the evidence of four persons. As might have been expected, atmospheric conditions were perfect …
It seemed to me exceedingly probable that a mistake of a day might have been made with regard to the observations at Scarborough and Heighington. But this was certainly not the case. Among other circumstances which fixed the date as the 2nd May was the occurrence on the same night of a Zeppelin raid over Yorkshire … So far as I am aware, this Moon, 14½ hours old, is the youngest yet observed in England.”
A semi-theoretical limit to the earliest time after New Moon at which the lunar crescent can be observed was established by André Danjon (in an article published in the French magazine l’Astronomie in 1936: ‘Le Croissant Lunaire’, v.50, p.63). He derived a formula for the shortening of the cusps of the lunar cresent as its elongation (i.e. angular distance) from the sun diminished. The shortening effect was so pronounced at about 7 degrees (in geocentric terms – i.e. viewed from the centre of the Earth), that the sunlit crescent disappeared from view altogether.
At the time of the observation by the Scarborough maids (20h 00m UT), the altitude and azimuth of the Sun and Moon (as determined by the web-based almanac calculator of HM Nautical Almanac Office http://astro.ukho.gov.uk/surfbin/first.cgi) were:
Sun 303° 33‘ Az, -3° 51‘ Alt
Moon 302° 29‘ Az, 3° 48‘ Alt
These are topocentric coordinates – i.e. they are the directions of the two celestial bodies as seen from a specific location on the Earth’s surface (namely, Scarborough, 0° 24′ 00″ W, 54° 17′ 00″ N).
With a simple formula we can find the angular separation (A) of any two objects whose position is expressed in such spherical coordinates. If (a1, d1) and (a2, d2) are the two pairs of coordinates, the separation (or elongation), A, is given by:
cos A = sin d1 sin d2 + cos d1 cos d2 cos (a2-a1)
The result here is that A = 7.77 degrees. Recalculated in geocentric coordinates, the separation is approximately 8.45 degrees. In other words, pretty close to the Danjon limit of 7.
The elongation will not always be the same for a given age of Moon, since the orbital paths of the Earth and Moon are elliptical.
With the advent of modern imaging equipment and techniques, the crescent Moon has been photographed at much lesser elongations than the Danjon limit would suggest is possible.
For further information:
The story about Whitmell’s reporting of the 1916 observations and the significance of the Danjon limt can be read in The Astronomical Scrapbook: Skywatchers, Pioneers, and Seekers in Astronomy, by Joseph Ashbrook, Cambridge, 1984.
The Danjon limit of the first visibility of the lunar crescent, by Louay J.Fatoohi, F.Richard Stephenson and Shetha S. Al-Dargazelli (first published in the Observatory magazine) can be downloaded from the ADS website.
Astronomical Algorithms, by Jean Meeus, Willmann-Bell, 1991, pp.105-11 explains how to calculate angular separations.