Planetary coordinate reference systems & mapping
Angelo Pio Rossi
Earthgraph GmbH - Bremen (Germany)
EU Horizon 2020 grant #871149

Background: Collins et al. (2013) / NASA / USGS

Reference frames

Source: Hare et al. (2018). See also NASA/JPL/NAIF.

Pointing & imaging

Source: Hare et al. (2018), NASA/JPL/NAIF.

Pointing & errors

Source: Source: Belgacem et al. (2020); Tao et al. (2016). .

### Basic terminology Many definitions, but to keep it short: * **Map projection**: A model of the surface * **CRS**: A model of the surface, and its reference body * **GIS**: A computing / management/ visualisation / analysis system to deal with: * data with a CRS = (digital/ised) geospatial data

Reference surfaces

Source: Knippers, (2009), L. Penasa.

Reference time(scale)

  • Depending on the context/timescale, time might be neglibile
  • In reality, obviously it plays a (big) role
  • Or not: e.g. Earth plates moving (little, ~cm/y ~dm/y)

Map projections

Source: Knippers, (2009).

Map projections

Source: Hare et al. (2018).

Map projection classes

Source: Knippers, (2009).

Map projection properties

Source: NASA/USGS.

Map projection properties

  • Area → Equal Area
  • Distance → Equidistant
  • Angles/Shape → Conformal

Map projection properties

See also: Snyder (1982).

Earth globe

E.g. Vesta

a = 572.6 km
b = 557.2 km
c = 446.4 km

Source: Threjs, based on original at JAXA/Japan Planetarium Association.
Shape model from NASA PDS SBN.

E.g. Vesta

a = 572.6 km
b = 557.2 km
c = 446.4 km

Source: Threjs, based on original at JAXA/Japan Planetarium Association.
Shape model from NASA PDS SBN.

Planetocentric v.s -graphic / -detic

Source: NAIF/JPL.

Planetographic vs. centric

Planetographic vs. centric

CG/67p

Non-uniqueness of latitude, longitude

Source: Threjs, based on original at JAXA/Japan Planetarium Association.
Shape model from ESA/ROSETTA/OSIRIS, Preusker et al. (2017), L. Penasa.

CG/67p

Possible solution: Quack

Source: Grieger (2019).

Ryugu

a= 1004 m
b = 876 m

Source: Threjs, based on original at JAXA/Japan Planetarium Association.
Shape model from NASA PDS SBN.

Bennu

a = 565 m
b = 535 m
c = 508 m

Source: Threjs, based on original at JAXA/Japan Planetarium Association.
Shape model from NASA PDS SBN.

Eros

a= 33 km
b = 13 km

Source: Threjs, based on original at JAXA/Japan Planetarium Association.
Shape model from NASA PDS SBN.

Itokawa

a= 540m
b= 270m
c= 210m

Source: Threjs, based on original at JAXA/Japan Planetarium Association.
Shape model from NASA PDS SBN.

Choice of projections

Orthographic

Source: Fortezzo et al. (2020)., ASU/LROC, D3

Choice of projections

Equidistant Cylindrical

Source: Fortezzo et al. (2020)., ASU/LROC, D3

Choice of projections

Mercator

Source: Fortezzo et al. (2020)., ASU/LROC, D3

Choice of projections

Polar Stereographic

Source: Fortezzo et al. (2020)., ASU/LROC, D3

Deformation & extent

Equidistant Cylindrical

Source: NASA/LRO/LOLA/ASU/USGS.

Deformation & extent

vs. Orthographic

Source: NASA/LRO/LOLA/ASU/USGS.

Deformation & extent

vs. Orthographic

Source: NASA/LRO/LOLA/ASU/USGS.

Deformation & extent

Orthographic extent projected

Source: NASA/LRO/LOLA/ASU/USGS.

Deformation & extent

(the other hemisphere)

Source: NASA/LRO/LOLA/ASU/USGS.

E.g. Ganymede

E.g. Ganymede

Equidistant Cylindrical - Clon 180

Equidistant Cylindrical - Clon 0

Cylindrical Equal Area - Clon 0

Orthographic - Clon 0

Orthographic - Clon 180

Robinson - Clon 0

Choosing projections

Source: NASA/Voyager/Galileo/USGS.

Why quadrangles use a certain projection

Source: NASA/Voyager/Galileo/USGS.

Could it have been like this?

Possibly...

Source: Three-geojson, h3

Ganymede: Quadrangles

Source: USGS/wikipedia.

Venus: Quadrangles

Source: USGS.

Vesta: Quadrangles

Source: Naß and van Gasselt, (2023).

Venus: specific aspects

  • IAU reference body
  • East-positive longitude (0-360), planetocentric latitude
  • In most GIS applications: de facto standard Est+, planetocentric & sphere
  • See also e.g. IAU OGC registry

Jupyter and Saturn system satellites: specific aspects

  • IAU reference body
  • West-positive longitude (0-360), planetographic latitude
  • In most GIS applications: de facto standard Est+, planetocentric & sphere
  • See also e.g. IAU OGC registry, IAU/USGS Gazetteer

Small bodies: specific aspects

  • IAU reference body / shape models
  • Variable complexity
  • In most GIS applications for e.g. Ceres, Vesta, planetocentric & sphere
  • See also PDS SBN CRS

Relevant references

Georgiadou, P.Y., Knippers, R.A., Kraak, M.J., Sun, Y., Weir, M.J.C. and van Westen, C.J. Principles of geographic information systems (Chapter 4.2 on spatial referencing), 2nd edition, ITC Educational Textbook, ITC, Enschede, 2001. Available online.
Hare, T.M., Skinner, J.A., Kirk, R.L. (2018). Cartography Tools. In: Rossi, A., van Gasselt, S. (eds) Planetary Geology, DOI: 10.1007/978-3-319-65179-8_4
Hargitai, H., Wang, J., Stooke, P.J., Karachevtseva, I., Kereszturi, A., Gede, M. (2017). Map Projections in Planetary Cartography. In: Lapaine, M., Usery, E. (eds) Choosing a Map Projection. Lecture Notes in Geoinformation and Cartography, DOI: 10.1007/978-3-319-51835-0_7
Kessler, F. C., & Battersby, S. E. (2019). Working with Map Projections.
Knippers, R., (2009) Geometric aspects of mapping, available online.
NAIF (2022) An Overview of Reference Frames and Coordinate Systems in the SPICE Context available online.
Snyder, J. P. (1987). Map projections--A working manual (Vol. 1395). US Government Printing Office.

See also: https://github.com/europlanet-gmap/winter-school-2024/tree/main/crs