Librations, Phases, Colongitude and the Sun’s position
Every 29,5 earth days, the Moon evolves through its cycle of new moon, first quarter, full moon and last quarter. Thereby the terminator, the line between lunar day and night, moves with about 15 kilometers per hour over its surface. For a lunar observer it is important to know the terminator’s position to prepare observations beforehand and for the interpretation of observations in general.
The phase coefficient, varying between 0,00 and 1,00 gives the proportion of the Moon that appears to be sunlit as seen from Earth. This, however, gives only an approximation of the terminator’s position since the orientation of the Moon with respect to the Earth and Sun is not considered. More useful is the solar colongitude. It is defined as the lunar longitude of the sunrise terminator, measured westward along the equator, ranging between 0° to 360°, from the apparent mean center of the Moon’s disk. The colongitude at first quarter is then 0°, 90° at full moon, 180° at last quarter and 270° at new moon.
Visualisation of libration in longitude and latitude and the libration angle. In the figure at right, longitudinal and latitudinal libration are positive bringing the norheastern limb in a favoured view.
Although the Moon always keeps its same side towards the Earth, it actually wobbles both east-west and north-south to our line of sight. The east-west oscillation is called libration in longitude and is due mainly to the eccentricity of the lunar orbit. If more of the eastern side of the Moon can be seen, the libration is longitude is positive, otherwise it is negative. This can be as much as ±7,95°. The north-south oscillation is called libration in latitude and is caused by the inclination of its equator to its orbital plain and the inclination of the Moon’s orbital plain to the Earth’s orbital plain. If more of the northern side of the Moon can be seen, the libration in latitude is positive, otherwise it is negative. This can be as much as ±6,85°. Librations make it thus possible to lure ‘around de corner’ and to see 59% of the Moon’s surface. Features at the lunar disk’s limb regions, also called the libration zones, are visible under different conditions because of the librations. Librations also influence the position of the terminator. It is thus important to know the libration in longitude and latitude and the colongitude for a certain observation or to prepare observations. Terminator position and librations make it for instance possible to see the mighty Orientale impact basin at certain times.
Librations can be calculated for an observer positioned in the center of the Earth, being the geocentric librations. Obviously, an observer is positioned somewhere on the Earth’s surface altering the libration in longitude and latitude as seen by him or her slightly. Librations for an observer’s position are called the topocentric librations. Given a certain date, one position on the moon’s limb is favoured because of the librations. This position is indicated by what is here called the (topocentric/geocentric) libration angle. It is the angle from the north of the lunar disk, clockwise towards the favoured position.
Mare Crisium and Mare Marginis are excellent markers to visualise the effects of librations. The left picture was taken on 23 March 2002. The Mare Crisium region is tilted about 8° away from the observer showing only a small fraction of bright highland between the mare and the limb. Mare Marginis is then not visible. On 04 May 2002 (right picture) librations favoured this region, now showing Mare Marginis on the limb (arrow).
An example of libration, phase and colongitude for July 2004. This is very handy in the preparation of observations of the libration zones. For instance it can be seen that around the 20th July, the south-west limb region is favoured making observation of the Orientale basin possible. However, the Moon is not co-operative since the phase and colongitude diagram show it is then only a few days after new moon. Notice also the effect of Earth’s daily rotation on the topocentric librations.
For all observations in this book the topocentric libration in longitude and latitude, topocentric libration angle, phase and colongitude are indicated.
To compare different observations it is sometimes also interesting to know, besides the aforementioned parameters, the position of the sun relative to the observed structure. Therefore the sunheight and the azimuth of the sun can be calculated. This is illustrated for the crater Copernicus in the following figures.
Azimuth and height of the Sun above crater Copernicus during July 2004. The third figure shows the longitude of the morning and evening terminator and the longitude of the position were the sun is at its zenith. These figures can help to prepare observations. Note that due to Copernicus’ position close to the equator, Sun rises quickly to relatively large heights.
This figure can be quite handy to compare different observations of a formation. Here crater Copernicus (20°W and 9.7°N) is used as an example. The date is 06/07/2004 at 2200 UT. Libration conditions (topocentric) are indicated in red. The red lines give with their relative lengths the topocentric libration in longitude (here 7,95°) and latitude (here 6,43°). Both are positive, otherwise the lines are indicated on the opposite side. Since it is mostly the result of the two that is of interest, the red asterix depicts the position of maximum librations (relative to the north, top of figure) and the value with which this side is inclined to the observer. The blue asterix denotes the height of the Sun. Its position shows it azimuth. So here the sunheight is 55,1 ° and the sun would be visible almost in the west for an observer fortunate enough to be in Copernicus.