on the speed bar below the main menu.Help on libration graphs is found here. You can get to it quickly by clicking on on the speed bar below the main menu.
Libration is the apparent side to side rocking and up and down nodding of the Moon. There are two components: the more obvious "optical" and the very subtle "physical" libration.
Optical libration can be readily visible to the naked eye - use Mare Crisium, Oceanus Procellarum, and Mare Frigoris as your reference points. The white dot, visible only at low power, shows which limb of the Moon is rocked towards us.
Here are two images, about 10 days apart:
You can watch a movie of a lunar month, showing both the libration as well as the changing distance.
It is “apparent” because this is not a true wobbling of the Moon’s axis, but due to our different viewing perspectives from Earth, as the Moon travels in its orbit.
Want a quick way to get an appreciation of how visible this effect is? Click on “Animate” and hit the forward animate button. It's also interesting to choose a full Moon date and animate at one lunar month intervals.
The Moon’s orbit is tilted 6.7 degrees to the ecliptic. An observer then has the opportunity of looking “down” on the lunar north pole when the Moon is below the ecliptic and half an orbit later to look “up” at the lunar south pole from “underneath” when the Moon is above the ecliptic. These are north and south librations.
North libration South libration
The Moon’s orbit is also elliptical. If it were perfectly circular, the Moon would rotate 1/4 around its axis while traveling 1/4 of the way around its orbit (in order to keep the same face towards us). When the Moon is closer to us, it travels faster. This means that it can travel 1/4 of its orbit before having rotated 1/4 around its axis. The result is that we can see “around the edge”. A week or so later, we can see “around the other edge”. Note how close or far Mare Crisium can be from the limb.
We can add still more to our perspective view: An observer standing at 45 degrees latitude is “standing higher in space” than a fellow observer at the equator. This added height enables the northern observer to see farther past the lunar north pole. Likewise someone south of the equator can see more past the lunar south pole. This is called TOPOCENTRIC libration, and can exceed 1 degree. Values of libration published in handbooks are geared for all of the world, and so are calculated as if the observer was in the center of the Earth, hence GEOCENTRIC.
There is also a factor called “diurnal” libration. This is caused by the daily rotation of the Earth. Imagine looking at the full Moon at midnight; you are looking straight on. But by dawn, the Earth has rotated you over to one side, enabling you to see a little more past one edge. This factor is included in topocentric values.
Depending on the time of observation and your latitude, your topocentric perspective can add to the geocentric libration or subtract from it. For example if the south pole is exposed, and you live in the northern hemisphere, you will see the Moon librated a bit less from the south.
Together these factors mean we can see some 10 degrees of lunar latitude and longitude more than the face on view, or 59% of the lunar surface.
There are two ways of presenting the numerical libration of the Moon. One simply lists the values of the North (positive)/South(negative) component and the East/West component in degrees of lunar latitude and longitude. The more common way is to give PA (position angle) and amount (in lunar degrees). A libration of 5 degrees in PA 1 means we are seeing more of the north area. A libration of 5 degrees in PA 270 means we are seeing more of the “right” limb of the Moon, the side with Mare Crisium (as seen from the northern hemisphere).
The monthly libration pattern slowly changes over the course of the months (Lite users can only go back and forth.1 month). Check it out with the graphing facility available under the Utilities menu. More detailed explanations can be found below.
One important fact to know: the limb that is librated towards us may not be in sunshine. If you want to plan ahead for the time when a certain feature is best librated, use the libration graph. A future release of LunarCal will search for dates that satisfy your criteria.
Different libration values only reflect a different perspective that the Earth has towards the Moon. It does not change the depth of shadows or the longitude of sunset/sunrise on the Moon (colongitude of the Sun).
In the following example, the colongitude is the same (sunrise at a crater), but the libration is different (as well the phase).
Physical libration is the true wobble in the lunar axis and is never larger than 0.04 degrees. It is calculated and displayed under the Output menu --> Display Data.
If there are particular values of libration you are looking for, you can enter them in a search utility, found on the spped button bar below the menu: 
If you prefer looking at a table of days and values, you can do this through the utility menu.