The Denition of Dark, Grey and Bright Time at ING

The algorithm used to partition telescope time at ING into dark, grey and bright categories, which is based on the moonless fraction of each night, is shown to be an inconsistent measure of sky surface brightness because it ignores the eect of the daily change in longitude of the Sun on the illuminated fraction, k, of the Moon. This is manifested by frequently-occurring large dierences in k on, for example, rst and last bright nights within a lunation. In 15 % of all rst/last bright nights in the same lunation, k 0:25, and k can be as high as 0:35. This corresponds to dierences in the sky surface brightness of V sky 1 magnitude/arcsec 2 with the Moon in the sky for the same fraction of the night. An improved partitioning scheme, in terms of the lunar illuminated fraction acting as a proxy for the sky brightness component from scattered moonlight, and quantied in terms of its impact on observing eÆciency, is derived: Dark: 0:00 k < 0:25; Grey: 0:25 k < 0:65; Bright: 0:65 k 1:00 This scheme has a smaller range than the legacy method in the number of nights in each category over long base-lines, and averaged over a Saros cycle yields the same number of dark nights, four more grey nights and four fewer bright nights per semester. The range in V sky at low airmass, corresponding to high galactic- and ecliptic latitudes at solar minimum, and at an angular separation from the Moon of 90 Æ, is 21:2 21:9 magnitudes/arcse