The effect of Lunar Libration (how the Moon tilts left/right and up/down) and changing phase over the course of a month

We all know that the moon always presents the same face to observers since it takes as long to turn once on its axis as it does to complete one orbit of the Earth.

This is because the Moon in tidally locked to our planet. A crude analogy is swinging a bucket on a piece of string around your head - the bucket's opening always points to your head.

The Moon's orbit is elliptical rather than circular, so it speeds up near perigee (closest to Earth) and slows down near apogee (farthest from Earth) 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.

As on Earth, the position of features on the Moon are measured in Latitude and Longitude (called Selenographic Latitude and Longitude).

The lunar equator lies at 0 degrees latitude and the Prime Meridian (at 0 degrees longitude), runs from the north to south pole along the vertical running down the centre of the Moon's disk.

The Moon's orbit is also tilted to the ecliptic plane and to the Earth's equator by about 5 degrees.

As a consequence of these factors, 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 term given to this 'nodding' is "Libration". There are in fact three types of libration involved in the moon's motions.

Libration in latitude is due to the Moon's axis being slightly inclined relative to the Earth's. Each of the lunar poles will appear to be alternately tipped slightly toward and away from the Earth-based observer over a roughly four week cycle.

Diurnal libration is due to the observer being up to four thousand miles to one side of the Earth-Moon axis on the surface of the Earth - a significant proportion of the centre-to-centre distance. The difference in perspective between the rising and setting of the Moon appears as a slight turning of the Moon first to the west and then to the east.

Diurnal Libration

Libration of longitude is an effect of the Moon's varying rate of travel along its slightly elliptical orbit. Its rotation on its own axis is more regular, the difference appearing again as a slight east-west oscillation.

Libration of Longitude of the MoonThis image shows how the Moon can swing left and right slightly over time and how this Libration of longitude results in lunar features appearing to move slightly

Although the Moon always presents the same face towards the Earth, due to its rotation and revolution being locked to the same period, the combined effect of these different librations allows us over time to see some 59% of its surface.

LunarPhase Pro is my astronomy software tool that displays numerical Libration information in its Libration window. The information is presented in two formats - as distinct North-South and East-West rotations in degrees (e.g.: N-S: 3° 15' 04"; E-W -1° 38' 18") and as an overall figure in a specific direction (e.g.: 4° 2' 41" in PA 275° 07' 21" [PA stands for Position Angle]).

LunarPhase Pro Main Screen

Here's a closeup of the Lunar Libration information provided by the software:

Lunar Libration information as provided by LunarPhase Pro

...and a closeup of the Current Phase Window that marks the position of greatest libration with a yellow dot:

LunarPhase Pro's Current Phase Window

The software also creates a more detailed Lunar Libration Diagram which shows how the Moon librates over the course of a month. Two tracks can be shown. One (in blue) shows lunar libration in relation to the centre of the Earth (Geocentric Libration).

The other track (in orange) shows libration as seen from the user's location (Topocentric Libration). This is a more intricate diagram as it takes the user's position on the planet into account rather than assuming they're at the centre of the Earth.

Lunar Libration for August 2015

The orange tracks are unique to each observer's location on the planet.

The dots in the diagram represent each day of the month with every 5th day being marked by a larger dot.

The way to read this diagram is to pick the date you're interested in and measure left/right to the vertical axis to see how many degrees the Moon has rotated North/South.

A positive value (e.g. +2.5 degrees for August 6th) shows that the Moon's north pole is better placed for observing.

A negative value indicates that the south pole is better placed. The higher the number of degrees, the more the Moon is tilted towards you and the better your chance of seeing features at the extreme edges of the Moon.

Measure to the horizontal line to see how far the Moon librates in latitude; e.g. for August 6th, it's +5.5 degrees, so the Moon's Eastern limb is better placed for viewing.

At very favourable librations, the Moon can rotate by as much as 8 degrees in latitude or longitude, bringing features that are normally on the limb into better view (as was the case with Mare Orientale on November 17th, 2003).

If these diagrams seem a bit too technical, then just remember that they give you a clue as to when to point your binoculars or telescope at the Moon to see limb features that are normally very difficult to see due to the foreshortening you get when you see them edge-on.


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Filed under: Observing The Moon