## The Suns Corrected Selenographic Colongitude

This next bit is a quite a brain-twister, but you do not need to understand it to image the Moon. However, it may help you understand when a critical illumination will recur, if you get bitten by the lunar imaging bug. The standard reference for finding out the altitude of the Sun above the lunar terrain (and therefore where the night/day terminator falls) is a table of the Sun's selenographic colongitude (SSC). This is a bit of a mouthful but it simply means the height of the Sun (or its longitude) as seen from the lunar surface. When the SSC is 0°, the Moon is around the first quarter phase; at 90°, the Moon is full; at 180°, it is last Quarter; and, at 270°, the phase is new. This might seem like a good way of predicting exactly when the terminator will cross a lunar formation. However, there is a fly in the ointment because of the fact that the Moon's axis of rotation can be tilted with respect to the Sun, too, by plus or minus 1.5°. For high northerly and southerly objects, a correction to the SSC is required to tell you where the terminator will precisely fall. The correction, c (in degrees) can be derived from the formula c = arcsin(tan b x tan i), where c is the correction required, b is the latitude of the formation, and i is the latitude of Sun (N+, S-), otherwise known as the Sun's selenographic latitude. The correction will be + or - depending on whether the Sun and the formation are on the same or opposite sides of the lunar equator respectively. A + correction means that sunrise occurs early and sunset occurs late on the formation, both of which produce shadows that are shorter than the tabulated SSC would indicate; a - correction means just the opposite, of course. Incidentally one degree of longitude = 1.97 hours. A related trap that might conceivably cause problems when trying to see a precise illumination angle is the fact that for formations situated away from the lunar equator, the difference between the corrected SSC and the longitude of the formation is not a measure of the Sun's altitude there; the difference must be multiplied by cos b to obtain the true solar altitude (for low Sun angles). I am indebted to lunar expert Ewen Whitaker for explaining all this to me in a letter some 20 years ago.

Confused? Don't worry! Essentially you just need to bear in mind that, due to librations, you are never quite looking at a lunar formation from the same viewpoint and, due to the Moon's axial tilt with respect to the Sun, the terminator is rarely lying at exactly the same angle across the Moon's face. Will this make any actual difference to your observing, in practice? Well, maybe. If you want to image a lunar feature with a similar play of shadow and light as on a previous occasion, you may be a few hours early or late if you do not correct the SSC. All this is just a great reason to keep imaging the Moon. It never looks exactly the same.

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