Prepared by HM Nautical Almanac Office, Royal Greenwich Observatory, Madingley Road, Cambridge, CB3 0EZ For the Science & Engineering Research Council
A note on the prediction of the dates of first visibility of the new crescent Moon
It is not possible to predict accurately the dates on which the new crescent Moon will first be seen each month since there is no collection of reliable, fully documented, observations that can be used to establish the conditions that must normally be satisfied at the time of first visibility. The simplest basis for prediction is that the Moon should be more than a certain age (measured from the time of astronomical new moon) at the time of sunset at the place concerned. It is, however, better to use the true elongation (i.e. the angular separation) of the moon from the sun at this time, rather than the age.
The new crescent is not normally visible until the sun is below the horizon and so it is desirable to take into account the altitude of the moon during twilight. The chances of seeing the new crescent depend slightly on the distance of the moon from the earth, being greatest when the Moon is closest (i.e. at perigee). The local conditions, especially the height of the observer above sea level and the character of the surrounding surface, are important, and even when the sky is free from cloud they can be considerable variations in the clarity of the atmosphere from day to day.
The visual acuity of the observer is also significant. It must be realized too that there are considerable variations in the astronomical conditions with both longitude and latitude on the Earth so that even if the weather conditions were good everywhere, the dates of the first sightings would differ from place to place. Predictions can, therefore, only be valid for restricted areas.
Read More...
Under ordinary conditions, the first sighting will not occur until the age of the Moon exceeds about 30 hours, but a few reliable reports are known of sightings under very good conditions, when the age has only 20 hours or even less. It is unlikely that the new crescent will be visible unless the elongation exceeds 10 degrees and the altitude of the Moon exceeds 5 degrees when the depression of the sun is 3 degrees. It is interesting to note that the new moon can always be seen 30 days after the previous one and in half the cases it can be seen 29 days after, because the length of the synodic month is 29.53 days.
A different set of criteria based on observations made in the Mediterranean region are given by F. Bruin in Vistas in Astronomy (1980), Vol. 24, pp 325-358 (Pergamon Press). This Office will predict date of the first visibility based on these criteria. The output supplied contains information about the Moon at sunset for four or five evenings from the instant of New Moon. Also, indicated is the first evening on which the new crescent Moon should be visible. Occasionally, under good conditions, the Moon may be visible on the previous evening.
The other data that are given at sunset are the time of sunset in standard time (in hours and minutes), the age of the Moon (in hours and minutes), the elongation (degrees) of the Moon from the Sun, the magnitude of the Moon, the altitude and azimuth of the Moon (degrees), H+S (degrees) which is the sum of the altitude of the Moon plus the solar dip (the altitude of the Sun below the horizon), W (minutes of arc) the width of the lunar crescent, and the bearing which is the difference in azimuths of the Sun and Moon. It is the quantities H+S and W that are used to make the prediction.
Since it is clear that any prediction of the date of first visibility must be uncertain, it is necessary to decide whether to prefer an early prediction that could not be substantiated by direct observation if conditions prove to be good, or a late prediction that could be vitiated by an observation on the previous day. The simple rule that this Office recommends is that the age of the Moon should be about 30 hours at the time of sunset at the place concerned which is of the latter kind, but this rule is not so reliable in middle and high latitudes.
BDY/CYH (1989 October 23)
The Science and engineering Research Council does not accept any responsibility for loss or damage arising from the use of information contained in any of its reports or any communication about its tests or investigations.