# What are the "Moon L, B, C" angles shown in this solar eclipse simulation?

The NASA Goddard video Tracing the 2017 Solar Eclipse is a visualization of the calculated shape of the umbra during the upcoming August 2017 total solar eclipse, as it moves across North America.

The simulation takes into account the actual measured 3D shape of the Moon from the LRO's laser altimeter, the shape of the Earth is from SRTM (radar map from the space shuttle), and the locations of the Sun, Earth and Moon from the JPL Development Ephemeris.

Question: What are the "Moon L, B, C" angles shown in this solar eclipse simulation?

note: If you haven't seen the video, it's worth watching! The realistic shape of the umbra gives plenty to think about, as discussed in the question The Moon's shadow could not possibly look like this — could it? and the (likely to be) excellent answer(s) there.

• Two comment-less close votes for off-topic?
– uhoh
May 20, 2018 at 14:25

These 3 numbers describe changes in the orientation of the Moon as seen from Earth, expressed in terms of the selenographic longitude and latitude of the observed center (also known as the Sub-Earth point).

L and B description from Source 1:

The librations in longitude and latitude are frequently abbreviated by the letters "l" and "b" although this convention is by no means universal. "L" and "B" were probably originally abbreviations for the German words "länge" (longitude) and "breite" (latitude). On diagrams, and in mathematical discussions they are sometimes replaced by the Greek letters lambda and beta, although again, this is not a universal convention.

The magnitudes of the librations are traditionally stated as +/- numbers (rather than N-S/E-W). As indicated in the definition, these are the selenographic coordinates of the Moon's apparent center. In longitude ("l"), positive values are in the Mare Crisium direction. In latitude ("b"), they are in the Mare Frigoris direction. Hence a "+" value for "l" means the Mare Crisium limb is tipped into view. A "+" value for "b" means the Mare Frigoris limb is tipped into view. The convention that longitudes towards Mare Crisium are positive is a very old one, so no change in the way librations are stated or understood was required when the IAU reversed the meaning of "east" and "west" on the Moon.

C description from Source 2

...the position-angle C of the moon's axis, i.e. of that lunar meridian which bisects the apparent disk and so appears as a straight line.

A picture from Source 3 showing the 3 variables (and much else). I'm dubious about the C variable but the text clearly states "In Figure 3 the position angle C ′ of the axis is shown on the selenocentric sphere. "

Source 1

Source 2

Source 3

• This is of course an excellent answer, thank you very much!! I've asked a follow-up; Dimensions and shape of the Moon's reference surface for selenographic latitude/longitude?
– uhoh
May 21, 2018 at 0:21
• For some reason I can't access aa.usno.navy.mil and so while I see that the url for "Source 3" contains Tayloretal2011.pdf I can't find out what that reference is because neither a title nor some document ID number is present. I want to refer to this document in this question. This falls under the general scenario described in Are meaningless link titles like “Source” sub-optimal, leaving the answer unrepairable if a link rots/breaks?
– uhoh
Mar 28, 2020 at 4:22
• If the link doesn't work for someone then they can not find out what this source even is, how to cite it, or how to find a different way to access the document if they would like to read it. If you can access Source3, would you be able to tell me what it is? Thanks!
– uhoh
Mar 28, 2020 at 4:22
• Mar 28, 2020 at 4:40
• Okay I can see that one, thanks!
– uhoh
Mar 28, 2020 at 4:41

According to the book "Measure of the Moon" page 169 the angles l,b,c stand for "geocentric libration of the Moon (longitude, latitude and position angle)"

The Geocentric Libration of the Moon describes how the Moon appears to pitch, yaw and roll over time.

The L and B values are selenographic longitude and latitude of the apparent disk centre and the position angle is the angle of the Moon's north pole relative to celestial north

• @uhoh, you asked what they were, not for a definition. Regardless, given the name, google was able to explain the rest.
– user20636
May 20, 2018 at 6:43
• I only fixed a couple of spelling errors... @JCRM I think supplied the video. May 20, 2018 at 14:31
• @JCRM so I've asked a follow-up; Dimensions and shape of the Moon's reference surface for selenographic latitude/longitude?
– uhoh
May 21, 2018 at 0:22