# LRO LOLA Spherical Harmonic Data Records (SHA)

### SHA – Spherical Harmonic Data Records

**Instrument:** Lunar Orbiter Laser Altimeter

**PDS Data Set ID:** LRO-L-LOLA-5-SHADR-V1.0

For more information about LOLA RDR and derived products, see the RDR Product SIS.

For more information about all LOLA products, see the LOLA Archive Volume SIS.

The Lunar Orbiter Laser Altimeter (LOLA) Spherical Harmonic Data Records (SHA) data products are produced through the transformation of digital elevation models into spherical harmonic expansions of the lunar shape. The SHADR is a set of spherical harmonic coefficients describing the lunar shape, selenopotential reference surface, albedo, and static gravitational potential.

The PA subdirectory contains a shape map and spherical harmonic model of the Moon using the dynamically defined Principal Axis coordinate system for consistency with other lunar gravity spherical harmonic models, including that acquired by the Gravity Recovery and Interior Laboratory (GRAIL) mission.

The SHADR data products consist of ASCII tables, preceded by PDS labels. The form of these tables are that of Comma-Separated Values. The tables closely resemble that of the Lunar Prospector gravity archives. Spherical harmonic shape and bidirectional reflectance models complete the SHADR dataset. The gravity potential coefficients are customarily normalized so that the spherical harmonic functions each have unit mean variance on a sphere, in accordance with geophysical practice, and are further normalized to a reference equatorial radius of 1,738,000 meters. This choice of radius is for compatibility with legacy datasets, and with observation equations – “normal equations” – used in orbital and potential analysis that, for compact storage, are summed with respect to a particular radius. The derived potential coefficients may be transformed to any other choice of reference radius.

The LOLA SHADR Principal Axis product is named LRO_LTM01_PA_1080_SHA.TAB, with its corresponding label file.

### LOLA SHADR products have the following file names:

LRO_LTMvv_nnn_SHA.TAB (with detached PDS label)

where:

vv = 2-digit version

nnn = maximum degree and order

There are two products which are earlier versions of the most recent 720 maximum degree and order product: LRO_LTM02_SHA.TAB, with its corresponding label file, and LRO_LTM03_SHA.TAB, with its corresponding label file.

### In ODE, SHADR products have the following product IDs (in order of appearance above):

LRO_LTM01_PA

LRO_LTMVV_NNN

LRO_LTM02

LRO_LTM03