Lunar Grid Reference System Rasters and Shapefiles

USGS is assessing the feasibility of map projections and grid systems for lunar surface operations. We propose developing a new Lunar Transverse Mercator (LTM), the Lunar Polar Stereographic (LPS), and the Lunar Grid Reference Systems (LGRS). We have also designed additional grids designed to NASA requirements for astronaut navigation, referred to as LGRS in Artemis Condensed Coordinates (ACC), but this is not released here.
LTM, LPS, and LGRS are similar in design and use to the Universal Transverse Mercator (UTM), Universal Polar Stereographic (LPS), and Military Grid Reference System (MGRS), but adhere to NASA requirements. LGRS ACC format is similar in design and structure to historic Army Mapping Service Apollo orthotopophoto charts for navigation.
The Lunar Transverse Mercator (LTM) projection system is a globalized set of lunar map projections that divides the Moon into zones to provide a uniform coordinate system for accurate spatial representation. It uses a transverse Mercator projection, which maps the Moon into 45 transverse Mercator strips, each 8°, longitude, wide. These transverse Mercator strips are subdivided at the lunar equator for a total of 90 zones. Forty-five in the northern hemisphere and forty-five in the south. LTM specifies a topocentric, rectangular, coordinate system (easting and northing coordinates) for spatial referencing. This projection is commonly used in GIS and surveying for its ability to represent large areas with high positional accuracy while maintaining consistent scale.
The Lunar Polar Stereographic (LPS) projection system contains projection specifications for the Moon’s polar regions. It uses a polar stereographic projection, which maps the polar regions onto an azimuthal plane. The LPS system contains 2 zones, each zone is located at the northern and southern poles and is referred to as the LPS northern or LPS southern zone. LPS, like is equatorial counterpart LTM, specifies a topocentric, rectangular, coordinate system (easting and northing coordinates) for spatial referencing. This projection is commonly used in GIS and surveying for its ability to represent large polar areas with high positional accuracy, while maintaining consistent scale across the map region. 
LGRS is a globalized grid system for lunar navigation supported by the LTM and LPS projections. LGRS provides an alphanumeric grid coordinate structure for both the LTM and LPS systems. This labeling structure is utilized in a similar manner to MGRS. LGRS defines a global area grid based on latitude and longitude and a  25×25 km grid based on LTM and LPS coordinate values. Two implementations of LGRS are used as polar areas require a LPS projection and equatorial areas a transverse Mercator. We describe the difference in the techniques and methods report associated with this data release. Request McClernan et. al. (in-press) for more information.
ACC is a method of simplifying LGRS coordinates and is similar in use to the Army Mapping Service Apollo orthotopophoto charts for navigation. These data will be released at a later date.
Two versions of the shape files are provided in this data release, PCRS and Display only. See LTM_LPS_LGRS_Shapefiles.zip file. PCRS are limited to a single zone and are projected in either LTM or LPS with topocentric coordinates formatted in Eastings and Northings. Display only shapefiles are formatted in lunar planetocentric latitude and longitude, a Mercator or Equirectangular projection is best for these grids. A description of each grid is provided below:
Equatorial (Display Only) Grids: 
	Lunar Transverse Mercator (LTM) Grids:
		LTM zone borders for each LTM zone
		Merged LTM zone borders 
	Lunar Polar Stereographic (LPS) Grids:
		North LPS zone border
		South LPS zone border
	Lunar Grid Reference System (LGRS) Grids:
		Global Areas for North and South LPS zones
		Merged Global Areas (8°×8° and 8°×10° extended area) for all LTM zones
		Merged 25km grid for all LTM zones
PCRS Shapefiles:`
	Lunar Transverse Mercator (LTM) Grids:
		LTM zone borders for each LTM zone
	Lunar Polar Stereographic (LPS) Grids:
		North LPS zone border
		South LPS zone border
	Lunar Grid Reference System (LGRS) Grids:
		Global Areas for North and South LPS zones
		25km Gird for North and South LPS zones
		Global Areas (8°×8° and 8°×10° extended area) for each LTM zone 
		25km grid for each LTM zone 
The rasters in this data release detail the linear distortions associated with the LTM and LPS system projections. For these products, we utilize the same definitions of distortion as the U.S. State Plane Coordinate System.
Scale Factor, k - The scale factor is a ratio that communicates the difference in distances when measured on a map and the distance reported on the reference surface. Symbolically this is the ratio between the maps grid distance and distance on the lunar reference sphere. This value can be precisely calculated and is provided in their defining publication. See Snyder (1987) for derivation of the LPS scale factor. This scale factor is unitless and typically increases from the central scale factor k_0, a projection-defining parameter. For each LPS projection. Request McClernan et. al., (in-press) for more information.
Scale Error, (k-1) - Scale-Error, is simply the scale factor differenced from 1. Is a unitless positive or negative value from 0 that is used to express the scale factor’s impact on position values on a map. Distance on the reference surface are expended when (k-1) is positive and contracted when (k-1) is negative. 
Height Factor, h_F - The Height Factor is used to correct for the difference in distance caused between the lunar surface curvature expressed at different elevations. It is expressed as a ratio between the radius of the lunar reference sphere and elevations measured from the center of the reference sphere. For this work, we utilized a radial distance of 1,737,400 m as recommended by the IAU working group of Rotational Elements (Archinal et. al., 2008). For this calculation, height factor values were derived from a LOLA DEM 118 m v1, Digital Elevation Model (LOLA Science Team, 2021).
Combined Factor, C_F – The combined factor is utilized to “Scale-To-Ground” and is used to adjust the distance expressed on the map surface and convert to the position on the actual ground surface. This value is the product of the map scale factor and the height factor, ensuring the positioning measurements can be correctly placed on a map and on the ground. The combined factor is similar to linear distortion in that it is evaluated at the ground, but, as discussed in the next section, differs numerically. Often C_F is scrutinized for map projection optimization.
Linear distortion, δ - In keeping with the design definitions of SPCS2022 (Dennis 2023), we refer to scale error when discussing the lunar reference sphere and linear distortion, δ, when discussing the topographic surface. Linear distortion is calculated using C_F simply by subtracting 1. Distances are expended on the topographic surface when δ is positive and compressed when δ is negative.
The relevant files associated with the expressed LTM distortion are as follows.
        		The scale factor for the 90 LTM projections:
                			LUNAR_LTM_GLOBAL_PLOT_HEMISPHERES_distortion_K_grid_scale_factor.tif
        		Height Factor for the LTM portion of the Moon:
               			 LUNAR_LTM_GLOBAL_PLOT_HEMISPHERES_distortion_EF_elevation_factor.tif
        		Combined Factor in LTM portion of the Moon
                			LUNAR_LTM_GLOBAL_PLOT_HEMISPHERES_distortion_CF_combined_factor.tif
The relevant files associated with the expressed LPS distortion are as follows.
	Lunar North Pole
		The scale factor for the northern LPS zone: 
			LUNAR_LGRS_NP_PLOT_LPS_K_grid_scale_factor.tif
		Height Factor for the north pole of the Moon:
			LUNAR_LGRS_NP_PLOT_LPS_EF_elevation_factor.tif
		Combined Factor for northern LPS zone:
			LUNAR_LGRS_NP_PLOT_LPS_CF_combined_factor.tif
	Lunar South Pole
		Scale factor for the northern LPS zone: 
			LUNAR_LGRS_SP_PLOT_LPS_K_grid_scale_factor.tif
		Height Factor for the south pole of the Moon:
			LUNAR_LGRS_SP_PLOT_LPS_EF_elevation_factor.tif
		Combined Factor for northern LPS zone:
			LUNAR_LGRS_SP_PLOT_LPS_CF_combined_factor.tif
For GIS utilization of grid shapefiles projected in Lunar Latitude and Longitude, referred to as “Display Only”, please utilize a registered lunar geographic coordinate system (GCS) such as IAU_2015:30100 or ESRI:104903.
LTM, LPS, and LGRS PCRS shapefiles utilize either a custom transverse Mercator or polar Stereographic projection. For PCRS grids the LTM and LPS projections are recommended for all LTM, LPS, and LGRS grid sizes. See McClernan et. al. (in-press) for such projections. 
Raster data was calculated using planetocentric latitude and longitude. A LTM and LPS projection or a registered lunar GCS may be utilized to display this data.
Note: All data, shapefiles and rasters, require a specific projection and datum. The projection is recommended as LTM and LPS or, when needed, IAU_2015:30100 or ESRI:104903. The datum utilized must be the Jet Propulsion Laboratory (JPL) Development Ephemeris (DE) 421 in the Mean Earth (ME) Principal Axis Orientation as recommended by the International Astronomy Union (IAU) (Archinal et. al., 2008). 


Tags: acc, artemis, artemis-condensed-coordinates, farming, geodesy, lgrs, lps, ltm, lunar, lunar-grid-reference-system, lunar-polar-stereographic-system, lunar-transverse-mercator-system, mgrs, military-grid-reference-system, moon, nasa, universal-polar-stereographic-system, universal-transverse-mercator-system, ups, usgs, usgs-667b1061d34e6151c9d6bcc7, utm
Organization: Department of the Interior