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A range of disparate coordinate systems were used for planetary data from different missions stored in PDS, which makes it difficult to search and correlate data from various instruments. Currently, all products in ODE are stored in planetocentric, positive longitude east, 0 to 360 degrees coordinates. Tables 2-4 illustrate the original coordinate system used in the PDS archive. ODE uses a variety of methods to obtain a location for different products. Most of the data coordinates stored in ODE are acquired from the attached or detached PDS labels. ODE also has data coordinates acquired from the Unified Planetary Coordinates (UPC) database. The method used for a particular product can be found under the product results page, metadata tab, at the bottom under ODE notes. NOTE: coordinates are for searching and display only and may vary in precision. Users should explore and understand the data set to determine how to precisely map the product.

 

The UPC project was carried out at the U. S. Geological Survey (USGS) and Jet Propulsion Laboratory (JPL). It provides easy access to planetary data in a set of unified, consistent coordinate systems (Becker et al., 2007), which is also consistent with the MRO and MOLA data.

 

The Planetocentric system has an origin at the center of mass of the body. The planetocentric latitude is the angle between the equatorial plane and a vector connecting the point of interest and the origin of the coordinate system. Latitudes are defined to be positive in the northern hemisphere of the body, where north is in the direction of Earth's angular momentum vector, i.e., pointing toward the hemisphere north of the solar system invariant plane. Planetocentric longitude is measured around the equator of the body from a prime meridian defined and adopted by international agreement. Longitudes increase toward the east making the Planetocentric system right-handed. Radius is the distance from the planetary body’s center of mass to the point of interest.

 

A spheroid usually approximates well to the shape of planets, because the shape of a rotating body in hydrostatic equilibrium is approximately a spheroid. Mapping parameters for different planetary bodies (Mars, Moon, Mercury, and Venus) are listed in Table 1 (Seidelmann et al., 2002; 2005; Davies et al., 1986). The first column gives the mean radius of the body. The standard errors of the mean radii indicate the accuracy of determination of these parameters due to inaccuracies of the observational data. The second and third columns give equatorial and polar radii for 'best-fit' spheroids. An ellipsoid has been adopted for Mars by the IAU with a polar radius of 3376.2 km and an equatorial radius of 3396.19 km. For Moon, Mercury, and Venus, a sphere is used as the reference surface.

 

Table 1. Mapping Parameters (unit: km)

Planet

Mean Radius

Equatorial Radius

Polar Radius

Standard

Mars

3389.5±0.2

3396.19±0.1

AVG 3376.2±0.1

N 3373.19±0.1

S 3379.21±0.1

IAU2000

Moon

1737.4±1

1737.4±1

1737.4±1

IAU2000

Mercury

2439.7±1.0

2439.7±1.0

2439.7±1.0

IAU2000

Venus

6051.8±1.0

6051.8±1.0

6051.8±1.0

IAU2000

Venus

6051

6051

6051

IAU1985

 

Most of the basemaps stored in ODE are provided by USGS. Map projection is based on spheres rather than ellipsoids for these basemaps because of the computational cost and the capabilities of commercial software applications. The adopted projection convention for these basemaps includes Equirectangular (also named Simple Cylindrical) and Polar Stereographic map projections. The global maps are in Equirectangular map projections using the planetocentric coordinate system with east positive longitude. Mars, Mercury and Moon used IAU2000 standard, and Venus used IAU1985 standard. The polar maps are stored in polar stereographic projections.

 

The Equirectangular projection (Snyder, 1987) is typically used at middle and lower latitudes. With this projection, all lines of latitude are parallel to one another, as is also the case with longitude lines. Parallels of latitude and meridians of longitude are straight lines that are perpendicular to one another. This map projection is centered on the equator. The map resolution is constant throughout the image. The Polar Stereographic projection (Snyder, 1987), ideal for maps covering the polar regions, minimizes scale and shape distortion at high latitudes. This projection is centered on the north or south pole. Lines of longitude extend radially from the pole, and parallels of latitude are concentric circles around the center. For Mars, the Polar Stereographic projection is approximated by adopting a spherical geometry with a polar radius of 3376.2 km.

 

More information on how to predefine ArcGIS projection files can be found in the USGS Astrogeology Mapping, Remote-sensing, Cartography, Technology, and Research (MRCTR) GIS Lab website. Projection files can be downloaded from the MRCTR and ODE websites.

 

Table 2. Reference System Used for Mars Data in Different Missions

 

Mission

Instrument

Data_Set_ID

Product_Type

Reference System Used in Archive

MRO

CRISM

MRO-M-CRISM-2-EDR-V1.0

EDR

IAU2000 planetocentric reference system with east longitude (0-360ο) being positive

MRO-M-CRISM-4/6-CDR-V1.0

CDR (contains calibration files used to process EDRs to units of radiance or I/F)

MRO-M-CRISM-6-DDR-V1.0

DDR

MRO-M-CRISM-6-LDR-V1.0

LDR

MRO-M-CRISM-3-RDR-TARGETED-V1.0

TARGETED_RDR (TRDR)

MRO-M-CRISM-5-RDR-MULTISPECTRAL-V1.0

MAP_PROJECTED_MULTISPECTRAL_RDR (MRDR)

MRO-M-CRISM-5-RDR-MPTARGETED-V1.0

MTRDR (not available yet)

CTX

MRO-M-CTX-2-EDR-L0-V1.0

EDR

Image coordinates (Lat, Lon) were computed using NAIF SPICE kernel by MSSS personnel or NAIF

MARCI

MRO-M-MARCI-2-EDR-L0-V1.0

EDR

Using NAIF SPICE kernel

HIRISE

MRO-M-HIRISE-2-EDR-V1.0

EDR

N/A

MRO-M-HIRISE-3-RDR-V1.0

RDR (without the embedded map projection information)

IAU2000 planetocentric

MRO-M-HIRISE-3-RDR-V1.1

RDRV11 (with the embedded map projection information)

MRO-M-HIRISE-5-DTM-V1.0

DTM

MCS

MRO-M-MCS-2-EDR-V1.0

EDR

IAU2000 planetocentric

MRO-M-MCS-4-RDR-V1.0

RDR

Planetocentric spherical coordinates

MRO-M-MCS-5-DDR-V1.0

DDR (TBD)

RSS

MRO-M-RSS-1-MAGR-V1.0

EDR

SPK and CKF files can be converted to a wide range of coordinate frames by the NAIF reader routines. Other data types are not dependent on definition of a coordinate system.

MRO-M-RSS-5-SDP-V1.0

RSDMAP

IAU2000 planetocentric

MRO-M-RSS-5-SDP-V1.0

SHADR

MRO-M-RSS-5-SDP-V1.0

SHBDR

SHARAD

MRO-M-SHARAD-3-EDR-V1.0

EDR

IAU2000 planetocentric reference ellipsoid

MRO-M-SHARAD-4-RDR-V1.0

RDR

Mars Express (MEX)

HRSC

MEX-M-HRSC-3-RDR-V2.0

RDR

Using SPICE kernel

MEX-M-HRSC-5-REFDR-MAPPROJECTED-V2.0

REFDR (map projected image data)

Planetographic spherical coordinates with east longitude being positive (r = 3396.0 km)

MEX-M-HRSC-5-REFDR-DTM-V1.0

REFDR_DTM

Planetocentric spherical coordinates with east longitude being positive (r = 3396.0 km)

SPICAM

MEX-Y/M-SPI-2-IREDR-RAWXCRU/MARS-V1.1

EDR

The SPICAM data products are not projected into any coordinate system

MEX-M-SPI-2-IREDR-RAWXMARS-EXT1-V1.0

EDR

MEX-M-SPI-2-IREDR-RAWXMARS-EXT2-V1.0

EDR

MEX-M-SPI-2-IREDR-RAWXMARS-EXT3-V1.0

EDR

MEX-Y/M-SPI-2-UVEDR-RAWXCRU/MARS-V1.1

EDR

MEX-M-SPI-2-UVEDR-RAWXMARS-EXT1-V1.0

EDR

MEX-M-SPI-2-UVEDR-RAWXMARS-EXT2-V1.0

EDR

MEX-M-SPI-2-UVEDR-RAWXMARS-EXT3-V1.0

EDR

MaRS

MEX-M-MRS-1/2/3-NEV-0001-V1.0

Raw data

N/A

MEX-M-MRS-1/2/3-EXT1-0736-V1.0

RDR

N/A

MEX-M-MRS-1/2/3-EXT2-1334-V1.0

RDR

N/A

MEX-M-MRS-5-OCC-9101-V2.0

Reduced occultation data

Planetocentric coordinates

MARSIS

MEX-M-MARSIS-2-EDR-V1.0

EDR

Planetocentric coordinates

MEX-M-MARSIS-2-EDR-EXT1-V1.0

EDR

Planetocentric coordinates

MEX-M-MARSIS-3-RDR-SS-V1.0

RDR (MEX MARS MARSIS REDUCED DATA RECORD SUBSURFACE V1.0)

Planetocentric coordinates

MEX-M-MARSIS-3-RDR-AIS-V1.0

RDR (MEX MARS MARSIS RDR ACTIVE IONOSPHERE SOUNDING V1.0

Measurements of wave electric fields, which are presented as detected by the sensors and are not rotated into any other coordinate system.

MEX-M-MARSIS-3-RDR-AIS-EXT1-V1.0

RDR

MEX-M-MARSIS-3-RDR-AIS-EXT2-V1.0

RDR

MEX-M-MARSIS-3-RDR-AIS-EXT3-V1.0

RDR

OMEGA

MEX-M-OMEGA-2-EDR-FLIGHT-V1.0

EDR

IAU2000 planetocentric

MEX-M-OMEGA-2-EDR-FLIGHT-EXT1-V1.0

EDR

MEX-M-OMEGA-2-EDR-FLIGHT-EXT2-V1.0

EDR

PFS

MEX-M-PFS-2-EDR-NOMINAL-V1.0

EDR

planetocentric coordinates system

MEX-M-PFS-2-EDR-EXT1-V1.0

EDR

MEX-M-PFS-2-EDR-EXT2-V1.0

EDR

MEX-M-PFS-2-EDR-EXT3-V1.0

EDR

Mars Odyssey

GRS

ODY-M-GRS-2-EDR-V1.0

EDR

IAU2000 planetocentric

ODY-M-GRS-5-AHD-V1.0

AVERAGED_HEND_DATA (AHD)

ODY-M-GRS-5-AND-V1.0

AVERAGED_NEUTRON_DATA (AND)

ODY-M-GRS-5-SGS-V1.0

SUMMED_GAMMA_SPECTRA (SGS)

ODY-M-GRS-4-DHD-V1.0

DERIVED_HEND_DATA (DHD)

ODY-M-GRS-4-DND-V1.0

DERIVED_NEUTRON_DATA (DND)

ODY-M-GRS-4-CGS-V1.0

CORRECTED_GAMMA_SPECTRA (CGS)

ODY-M-GRS-5-ELEMENTS-V1.0

ELEMTS - Element Concentrations

N/A

THEMIS


VIS-EDR; IR-EDR; VIS-RDR; IR-RDR; VIS-ABR; IR-BTR

IAU2000 planetocentric

MARIE

ODY-M-MAR-2-REDR-RAW-DATA-V1.0

REDRs

MARIE's internal coordinate system is defined by the geometry of the detector. The PSDs have their own coordinate system in the sense that each strip (corresponding to a row or a column) is assigned a sequential number from 1 to 24. These values are not referenced to any other coordinate system, as the primary purpose of the PSDs is to calculate the angle at which incident particles traverse the silicon detectors.

ODY-M-MAR-3-RDR-CALIBRATED-DATA-V1.0

RDRs

Radio Science

ODY-M-RSS-1-RAW-V1.0

AGK/ion/ODF/opt/sak/sff/soe/spk/tck/tnf/tro/wea

SPK, TCK, and SAK files can be converted to a wide range of coordinate frames by the NAIF reader routines. Other data types are not dependent on definition of a coordinate system.

Accelerometer

TBD



Mars Global Surveyor (MGS)

MOC-NA / MOC-WA

MGS-M-MOC-NA/WA-2-DSDP-L0-V1.0

NADSDP / WADSDP

IAU1994 planetographic reference system                        (re = 3397.0 km; rp = 3375.0 km)

MGS-M-MOC-NA/WA-2-SDP-L0-V1.0

NASDP / WASDP

MOLA

MGS-M-MOLA-3-PEDR-L1A-V1.0

PEDR

IAU2000 planetocentric (r = 3396.0 km)

MGS-M-MOLA-5-MEGDR-L3-V1.0

MEGDR - Mission Experiment Gridded Data Record

IAU2000 planetocentric (Davies et al., 1994; Duxbury et al., 2001; Seidelmann et al., 2002)

MGS-M-MOLA-5-SHADR-V1.0

SHADR

IAU 1991(Davies et al., 1992), planetocentric, with longitudes measured positive east.

MGS-M-MOLA-3-PRDR-L1A-V1.0

PRDR

IAU2000 planetocentric

Note

CRISM: Compact Reconnaissance Imaging Spectrometers for Mars
CTX: Context Camera
GRS: Gamma Ray Spectrometer
HiRISE: High Resolution Imaging Science Experiment
HRSC: High Resolution Stereo Camera
MARCI: Mars Color Imager
MARIE: Martian Radiation Environment Experiment
MARSIS: Mars Advanced Radar for Subsurface and Ionosphere Sounding
MCS: Mars Climate Sounder
MOC: Mars Orbiter Camera
MOLA: Mars Orbiter Laser Altimeter
MRO: Mars Reconnaissance Orbiter
MaRS: Mars Express Orbiter Radio Science
OMEGA: Observatoire Mineralogie, Eau, Glaces, Activite
PFS: Planetary Fourier Spectrometer
RSS: Radio Science Subsystem
SHARAD: Shallow Radar
SPICAM: Spectroscopy for the Investigation of Characteristics of the Atmosphere of Mars
THEMIS: The Thermal Emission Imaging System

 

Table 3. Reference System Used for Moon Data in Different Missions

Mission

Instrument

Data_Set_ID

Product_Type

Reference System Used in Archive

 

Clementine

HIRES

CLEM1-L-H-5-DIM-HIRES-V1.0

MDIM

Planetographic spherical coordinates with r = 1737.4 km      

HIRES/LWIR/NIR/UVVIS/A-STAR/B-STAR

CLEM1-L/E/Y-A/B/U/H/L/N-2-EDR-V1.0

EDR

Planetocentric

UVVIS

CLEM1-L-U-5-DIM-BASEMAP-V1.0

MDIM 5-Band Mosaic

Planetographic spherical coordinates with r = 1737.4 km

CLEM1-L-U-5-DIM-UVVIS-V1.0

MDIM Global Basemap Mosaic

LIDAR

CLEM1-L-LIDAR-3-TOPO-V1.0

TOPO Raw Data

N/A

CLEM1-L-LIDAR-5-TOPO-V1.0

TOPO

Planetocentric (Williams et al., 1993; Dickey et al., 1994)

RSS

CLEM1-L-RSS-1-BSR-V1.0

Raw Data Record

SPK ephemeris files and CK attitude files are produced for the J2000 inertial reference frame. SPICE reader routines may be used to convert these to other coordinate systems. Other data types are not dependent on definition of a coordinate system.

CLEM1-L-RSS-5-BSR-V1.0

RDR

Planetocentric system with positive east longitude (r = 1737.4 km)

CLEM1-L-RSS-5-GRAVITY-V1.0

GRAVITY

Planetocentric (Davies et al., 1992)

LWIR

CLEM1-L-LWIR-3-RDR-V1.0

RDR

Planetocentric

Lunar Prospector (LP)

{GRS, NS, APS, MAG, ER}

LP-L-ENG/GRS/NS/APS/MAG/ER-1-MDR-V1.0

MDR

Selenocentric/selenographic

GRS

LP-L-GRS-3-RDR-V1.0

RDR

N/A

NS

LP-L-NS-3-RDR-V1.0

RDR

N/A

RSS

LP-L-RSS-5-GRAVITY-V1.0

GRAVITY

Planetocentric system with positive east longitude (r = 1738.0 km) (Newhall and Williams, 1997)

LP-L-RSS-5-LOS-V1.0

LOS

Planetocentric system (Newhall and Williams, 1997)

MAG

LP-L-MAG-4-SUMM-LUNARCRDS-5SEC-V1.0

Magnetic field data from LP MAG

in two different coordinate systems: selenocentric solar ecliptic (SSE) and body-fixed selenographic (SEL)

LP-L-MAG-4-LUNAR-FIELD-TS-V1.0

LP MAG Level 2 Data (CODMAC Level 4): Lunar Magnetic Field Time Series V1.0  

in two coordinate systems: selenographic (SG) coordinates; and east, north, and radial (ENR) coordinates

LP-L-MAG-5-LUNAR-FIELD-BINS-V1.0

LP MAG Level 3 Data (CODMAC Level 5): Lunar Magnetic Field Bins V1.0

Measurements in east, north, and radial (ENR) coordinates

LP-L-MAG-5-SURFACE-FIELD-MAP-V1.0

LP MAG Level 4 Data (CODMAC Level 5): Surface Magnetic Field Maps V1.0

Selenographic with mean lunar radius (1738 km)

ER

LP-L-ER-4-SUMM-OMNIDIRELEFLUX-V1.0

low resolution data from LP ER

N/A

LP-L-ER-3-RDR-HIGHRESFLUX-V1.0

high resolution data from LP ER

N/A

LP-L-ER-3-RDR-3DELEFLUX-80SEC-V1.0

3-D spectrum data from LP ER

in ''despun spacecraft'' (SCD) coordinates, closely related to GSE coordinates. (http://starbrite.jpl.nasa.gov/pds/viewProfile.jsp?dsid=LP-L-ER-3-RDR-3DELEFLUX-80SEC-V1.0)

LP-L-ER-4-ELECTRON-DATA-V1.0

LP ER Level 2 Data (CODMAC Level 4)

N/A

LRO

All LRO data products including LROC, LOLA, LAMP GDR, LEND, DIVINER and Mini-RF use a common Lunar Coordinate System unless being specified in the SIS document. See LRO Project and LGCWG White Paper. The planetocentric coordinates were used, which are compatible with the one used within the PDS for Clementine data.

Exceptions: No coordinate system applicable for data sets: Diviner EDR/PRP, LEND EDR/RDR, LAMP EDR/RDR, Mini-RF CDR, LOLA EDR/SHA, and LROC SDRPHO. See product SIS documents.

ISRO’s Chandrayaan-1

Mini-RF and M3 use the planetocentric coordinate system, which is the same as the LRO instrument.

 

Note

CRaTER: Cosmic Ray Telescope for the Effects of Radiation
DIVINER: Diviner Lunar Radiometer Experiment
HIRES: High Resolution Camera
LAMP: Lyman-Alpha Mapping Project
LEND: Lunar Exploration Neutron Detector
LGCWG: Lunar Geodesy and Cartography Working Group
LIDAR: Laser Image Detection and Ranging
LOLA: Lunar Orbiter Laser Altimeter
LROC: Lunar Reconnaissance Orbiter Camera
LWIR: Long Wavelength Infrared
M3: Moon Mineralogy Mapper
Mini-RF: Miniaturized Radio Frequency
Mini-SAR: Miniature Synthetic Aperture Radar, also called Forerunner
NIR: Near-Infrared
UVVIS: Ultraviolet/Visible

 

Table 4. Reference System Used for Mercury Data in Different Missions

Mission

Reference System Used in Archive

MESSENGER (Mercury Surface, Space Environment, Geochemistry and Ranging)

There are two general coordinate systems in use for the MESSENGER project:

• The celestial reference system used for target and spacecraft position and velocity vectors and camera pointing.

• The planetary coordinate system for geometry vectors and target location.

The celestial coordinate system is J2000 (Mean of Earth equator and equinox of J2000). The planetary coordinate system is planetocentric system with east longitude being positive.

 

Table 5. Reference System Used for Venus Data in Different Missions

Mission

Reference System Used in Archive

MESSENGER at Venus

There are two general coordinate systems in use for the MESSENGER project:

• The celestial reference system used for target and spacecraft position and velocity vectors and camera pointing.

• The planetary coordinate system for geometry vectors and target location.

The celestial coordinate system is J2000 (Mean of Earth equator and equinox of J2000). The planetary coordinate system is planetocentric system with east longitude being positive.

Magellan Mission

The ALTIMETRIC AND RADIOMETRIC Global products shall adopt the J2000 coordinate system for all inertial values, i.e. those that define the motion of the spacecraft relative to celestial objects. Locations on the Venus surface shall be expressed in a Venus body-fixed reference frame (Davies et al., 1992B).

Note:  The global basemaps of Venus used IAU1985 standard.

 

Related documents:

1.Becker, K.J., L.R. Gaddis1, L.A. Soderblom, J.A. Anderson, J.M. Barrett, T.L. Becker, T.M. Hare, S.C. Sides, D.L. Soltesz, A. Stanboli, R.M. Sucharski, T.L. Sucharski, and K.N. Winfree (2007), The Unified Planetary Coordinates Database, 38th Lunar and Planetary Sciences Conference, March 12 - 16, 2007. League City, Texas. (abstract) [Url: http://www.lpi.usra.edu/meetings/lpsc2007/pdf/2022.pdf].
2.Davies, M.E., V.K. Abalakin, M. Bursa, T. Lederle, and J. H. Lieske (1986), Report of the IAU/IAG/COSPAR working group on cartographic coordinates and rotational elements of the planets and satellites - 1985, Celestial Mechanics (ISSN 0008-8714), Vol. 39, pp. 103-113.
3.Davies, M.E., V.K. Abalakin, A. Brahic, M. Bursa, B.H. Chovitz, J.H. Lieske, P.K. Seidelmann, A.T. Sinclair, and Y.S. Tjuflin (1992A), Report of the IAU/IAG/COSPAR working group on Cartographic Coordinates and Rotational Elements of the Planets and Satellites: 1991, Celestial Mechanics and Dynamical Astronomy, Vol. 53, pp. 377-397.
4.Davies, M.E., et al., (1992B), The rotation period, direction of the North Pole, andgeodetic control network of Venus, J. Geophys. Res., 97 (E8), pp. 13141-13151.
5.Davies, M.E., V.K. Abalakin, M. Bursa, J.H. Lieske, B. Morando, D. Morrison, P.K. Seidelman, A.T. Sinclair, B. Yallop, and Y.S. Tjuflin (1994), Report of the IAU/IAG/COSPAR Working Group on Cartographic Coordinates and Rotational Elements of the Planets and Satellites, Celestial Mechanics and Dynamical Astronomy, Vol. 63, pp. 127-148.
6.Dickey, J., J.E. Faller, X.X. Newhall, R.L. Ricklefs, J.G. Ries, P.J. Shellus, C. Veillet, A.L. Whipple, J.R. Wiant, J.G. Williams, and C.F. Yoder (1994), Lunar Laser Ranging: A Continuing Legacy of the Apollo Program, Science, 265, pp. 482-490.
7.Duxbury, T.C., R. Kirk, and B.A. Archinal (2001), Mars Geodesy/Cartography Working Group recommendations on Mars cartographic constants and coordinate systems, International Society for Photogrammetry and Remote Sensing, WG IV/9: Extraterrestrial Mapping Workshop "Planetary Mapping 2001", USGS, Flagstaff, Arizona.
8.Hare, T.M. (2008), ArcMap 8.x and 9.x Planetary Projection Tutorial 14 [Url: http://webgis.wr.usgs.gov/pigwad/tutorials/planetarygis/arcmap_projections.htm].
9.LRO Project (2008), A Standardized Lunar Coordinate System for the Lunar Reconnaissance Orbiter and Lunar Datasets, LRO Project and LGCWG White Paper, version 5 of October 1 [Url: http://lunar.gsfc.nasa.gov/library/LunCoordWhitePaper-10-08.pdf].
10.Newhall, X.X., and J.G. Williams (1997), Estimation of the Lunar Physical Librations, Celestial Mechanics and Dynamical Astronomy, 66, pp. 21-30.
11.Planetary Science Data Dictionary Document, JPL D-7116, Rev. E, August 28, 2002.
12.Seidelmann, P.K. (Chair), V.K. Abalakin, M. Bursa, M.E. Davies, C. De Bergh, J.H. Lieske, J. Oberst, J.L. Simon, E.M Standish, P. Stooke, and P.C. Thomas (2002), Report of the IAU/IAG Working Group on Cartographic Coordinates and Rotation Elements of the Planets and Satellites: 2000, Celestial Mechanics and Dynamical Astronomy, 82, pp. 83-110.
13.Seidelmann, P.K. (Chair), B.A. Archinal (Vice-Chair), M.F. A'Hearn, D.P. Cruikshank, J.L. Hilton, H.U. Keller, J. Oberst, J.L. Simon, P. Stooke, D.J. Tholen, and P.C. Thomas (2005), Report Of The IAU/IAG Working Group On Cartographic Coordinates And Rotational Elements: 2003, Celestial Mechanics and Dynamical Astronomy, 91, pp. 203-215.
14.Snyder, J.P. (1987), Map Projections, U.S. Geological Survey Professional Paper 1395.
15.Williams, J. G., X.X. Newhall, and E.M. Standish (1993), Users of Ephemerides of the Earth-Moon System, JPL Internal Memorandum, December 18.