Colongitude

(glossary entry)

Description

```The colongitude of the Sun (also known as the Sun's Selenographic Colongitude) is a traditional way of specifying the approximate location of the terminator on the Moon. It is defined as 90° minus longitude of subsolar point.
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• The colongitude is an expression of how the Sun is shining on the Moon. It does not depend on where the observer is located or from what direction the Moon is being observed. It changes constantly with time; but at a particular instant it is same for all observers.
• Numerically, the colongitude is equal to the longitude at which the "morning terminator" (the theoretical line of sunrise on the Moon) crosses the Moon's equator measured west from the Moon's central meridian (the line of zero longitude) on a scale of 0 to 360°. The "evening terminator" (the line of sunset) crosses the equator 180° away from this. The colongitude is near 0 at First Quarter, near 90° at Full Moon, near 180° at Last Quarter and near 270° at New Moon (see the definition of lunar Phases for why the correspondence is only approximate). It might seem better to define the colongitude as 180° minus longitude of subsolar point. That would give a quantity that starts at zero at New Moon and increases to 360° over the course of the longitude; but the current definition is the one we have to live with, possibly because of the way the prefix "co-" is used in trigonometry (a "cosine" is equal to the "sine" of 90° minus the angle). Thinking of colongitude as the "longitude of the morning terminator" helps one remember that it must be zero near First Quarter rather than near New Moon.
• On average, the colongitude advances by 360° in one synodic month (the period between successive passages in front of the Sun, about 29.5306 days), giving a rate of change of +12.191° per day or +0.5079° per hour. Since colongitude is independent of the observing position, this rate is actually more closely related to the Moon's relatively constant rate of spin in space plus its annual revolution around the Sun, rather than to its appearance from Earth, so the rate of change of colongitude is more constant than the length of the synodic month (which varies by about +/-1%), but the actual hourly rate still varies from the average by as much as about +/-0.3%.
• As an expression of the Sun's position relative to the lunar surface features, colongitude is only half of a two part picture: the other half is the Sun's latitude north or south of the Moon's equator, which varies in an annual cycle over a range of about +/-1.6°.
• When the Moon is stated as having been observed at a particular colongitude, one can be sure that the terminator is crossing the equator at a known point; but if the Sun is north of the equator the morning terminator will be twisted in a counter-clockwise direction, and if it is south of the equator the morning terminator will be twisted in a clockwise direction. The evening terminator is twisted in the opposite direction. This twisting of the terminator can cause features north and south of the equator (that might otherwise be observed when the Moon is seen at the same colongitude in another lunation) to be thrown in or out of sunlight.
• The Sun's latitude north or south of the Moon's equator is listed as the "solar inclination" in the popular Virtual Moon Atlas.
• For regions north or south of the Moon's equator, predictions of repeat illumination based on colongitude alone (without taking into account the Sun's changing latitude) are not particularly accurate. They can easily be off by several hours. Yet the lighting does approximately repeat every lunation; so it is much better to base such predictions on when the sun returns to the same elevation above the horizon (also known as the "sun angle"), and approximately the same azimuth (overhead clock direction measured from north), as seen from the point of interest.
• An alternative, but rarely (if ever) used, way of stating the lighting condition required to see a feature in a particular way is to give the longitude at which the (theoretical) terminator crosses a parallel of latitude drawn through the feature of interest. In other words, one might say the central peaks of Copernicus first become visible when the morning terminator at 10° N is between 22.9° and 23.3° W. This would be similar to stating the colongitude , but the values are corrected to the specific latitude of interest, thus negating the effect of changing solar latitudes.
• Colongitude data (like all other data) presented on the web should not be taken at face value. Instances of incorrect or inaccurate calculation are fairly frequent. Only the universal time is required to determine the colongitude, so any critical instance the value stated should be verified by re-computing the colongitude from the time that is hopefully provided with the observation. The JPL Horizons system provides a relative simple way of making a definitive calculation. On request, that system will return the selenographic longitude and latitude of the Sun for any desired time. As indicated by its definition, the colongitude is obtained by subtracting the Sun's selenographic longitude from 90°.