# Shape and dimensions of the Moon's reference surface for selenographic latitude/longitude?

For Earth, the reference surface for "GPS" latitude, longitude, and altitude is the WGS84 ellipsoid, with equatorial and polar radii $a, b$ of 6378.1370 and 6356.7523 kilometers, respectively. Altitudes are calculated as the distance from a point to this reference surface along a line normal to the surface, not along a line from the geocenter. Math is given in this answer.

Does the Moon's selenographic coordinate system have a reference surface? Is it a sphere or an ellipsoid or something else? What are it's dimensions?

I've looked in Wikipedia, and in

but these are not helpful and the Moon's "selenography" has been evolving as lunar exploration and metrology has increased over time.

Question: What are the dimensions and shape of the Moon's reference surface for selenographic latitude/longitude?

below: exaggerated illustration of Earth's ellipsoid, from here.

I don't think there's precisely one selenographic coordinate system, but section 2.3 of the Lunar Constants and Models Document (JPL D-32296) seems to recommend spheres.

2.3 Moon Shape Parameters

The general shape of the Moon is very nearly a perfect sphere, excluding local topography variations. In fact, the magnitude of the local topography variations are much larger than the overall flattening of the lunar poles or any ellipticity of the lunar equator. Based upon the data presented in Reference 7, the magnitude of the lunar flattening relative to the equatorial radius is about 2 km. This memo, however, recommends representing the verall shape of the Moon for any mission design and navigation analyses as a perfect sphere

It goes on:

$R_{Moon-Equator}$ = 1737.4 km (Radius of Moon equator from IAU/IAG)

$R_{Moon-Pole}$ = 1737.4 km (Radius of Moon pole from IAU/IAG)

$f_{Moon}$ = 0.0 (Moon flattening factor, derived from IAU/IAG values)

Terrain elevations in section 2.6.1 are referenced to the same sphere; altitude for many applications could be taken with reference to those elevations.

• Thanks! That's now 13 years old, and even predates the launch of the Lunar Reconnaissance Orbiter. Presumably LRO data is available in a well defined, coordinate system. If LRO data has latitude and longitude, then whatever surface is used for that might be a good answer. – uhoh May 21 '18 at 9:22
• :/ this answer "might be a good answer..." The LRO data pds-geosciences.wustl.edu/missions/lro/default.htm isn't really monolithic, and understanding it isn't something I want to spend a lot of time on, though the LOLA experiment's height data uses an offset of 1737400. pds-geosciences.wustl.edu/missions/lro/lola_faq.htm – Erin Anne May 21 '18 at 16:05
• It may in fact be the best answer, I'll keep looking around as well. So far I found the bottom of this page links to a 2008 LRO document [A Standardized Lunar Coordinate System for the Lunar Reconnaissance Orbiter and Lunar Datasets ](lunar.gsfc.nasa.gov/library/LunCoordWhitePaper-10-08.pdf) but which still says "The existing lunar reference frames that define the coordinates of surface features are expected to undergo improvement, some significantly, during the LRO mission..." – uhoh May 21 '18 at 16:35
• "...as a result of the measurements and observations LRO is expected to acquire." – uhoh May 21 '18 at 16:36