This page contains simplified approximate formulas for calculating the optical libration in longitude and latitude, the selenographic coordinates of the sub-solar point and the position axes of the Moon's polar axis and bright limb. The results of calculations based on these formulas should agree to within 0.1 degree with more accurate ephemerides. Corrections for your position on the Earth (topocentric corrections) are included for the libration figures, and you can download a Microsoft Excel spreadsheet implementation of the formulas.
The Moon 'turns the same face to the Earth', so that its rotation about its axis is equal in period to the time for one orbit around the Earth. The Moon has an elliptical orbit about the Earth, so the Moon speeds up near perigee and slows down near apogee in accordance with Kepler's laws. The Moon's speed of rotation about its axis remains essentially constant from month to month as a consequence of the conservation of angular momentum. The Moon's orbit is tilted to the ecliptic plane and to the Earth's equator. As a consequence of these facts, the Moon appears to 'nod' from side to side and up and down during a lunar month, and it is possible to observe about 59% of the Moon's surface over a period of time, although we can only see 50% at any one instant.
The Moon has one hemisphere illuminated by the Sun at any given instant. As the Moon orbits the Earth, the part of that illuminated hemisphere we can see changes. We refer to the part of the Moon's disc visible to us as the bright limb. The 'sub-solar point' is a point on the Moon where the Sun is overhead, ie the 'pole' of the illuminated hemisphere. By working out the selenographic coordinates of this point, we can calculate the appearance of the bright limb of the moon for any given time.
Oliver Montenbruck and Thomas Pfleger,
Astronomy on the Personal
Computer
Springer
1994, 3rd edition
ISBN 3-540-63521-1
[ Root ]