Orthographic Projection of Mars (MOLA) in QGIS - Visually correct results, wrong coordinates

Question

I am trying to reproject the coloured shaded relief map of Mars (MOLA). After many tries, I got an orthographic projection of the scene centred on the pole, however, the coordinates are wrong.

I downloaded the MOLA data (.jp2 format) from: https://pdsimage2.wr.usgs.gov/pub/pigpen/mars/mola/Colorshade_global_megt128ppd_merged64ppd/

which got the following projection:

Properties Units: meters Static (relies on a datum which is plate-fixed) Celestial body: Mars Method: Equidistant Cylindrical (Plate Carree) WKT PROJCRS["Mars2000_ECylindrical_clon0",
    BASEGEOGCRS["GCS_Mars_2000_Sphere",
        DATUM["",
            ELLIPSOID["",3396190,0,
                LENGTHUNIT["metre",1,
                    ID["EPSG",9001]]]],
        PRIMEM["Reference_Meridian",0,
            ANGLEUNIT["degree",0.0174532925199433,
                ID["EPSG",9122]]]],
    CONVERSION["Equidistant Cylindrical",
        METHOD["Equidistant Cylindrical",
            ID["EPSG",1028]],
        PARAMETER["Latitude of 1st standard parallel",0,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8823]],
        PARAMETER["Longitude of natural origin",0,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["False easting",0,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",0,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["easting",east,
            ORDER[1],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]],
        AXIS["northing",north,
            ORDER[2],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]]] Proj4
+proj=eqc +lat_ts=0 +lat_0=0 +lon_0=0 +x_0=0 +y_0=0 +R=3396190 +units=m +no_defs +type=crs

if I set QGIS to ESRI:104971 - Mars_2000_(Sphere), which gives accurate coordinates, but in a "flat plane":

Now, I need to display the layer with an orthographic projection. I tried IAU_2015:49965:

Mars (2015) - Sphere / Ocentric / Orthographic, clon = 0
Properties
Units: meters
Static (relies on a datum which is plate-fixed)
Celestial body: Mars
Method: Orthographic
WKT
PROJCRS["Mars (2015) - Sphere / Ocentric / Orthographic, clon = 0",
    BASEGEOGCRS["Mars (2015) - Sphere / Ocentric",
        DATUM["Mars (2015) - Sphere",
            ELLIPSOID["Mars (2015) - Sphere",3396190,0,
                LENGTHUNIT["metre",1]],
            ANCHOR["Viking 1 lander: 47.95137 W"]],
        PRIMEM["Reference Meridian",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["IAU",49900,2015]],
    CONVERSION["Orthographic, clon = 0",
        METHOD["Orthographic",
            ID["EPSG",9840]],
        PARAMETER["Latitude of natural origin",0,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",0,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["False easting",0,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",0,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["(E)",east,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["(N)",north,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    ID["IAU",49965,2015]]
Proj4
+proj=ortho +lat_0=0 +lon_0=0 +x_0=0 +y_0=0 +R=3396190 +units=m +no_defs
Extent
Extent not known

This is visually ok, but the coordinates are completely off:

Following these two pages: https://blog.lidskialf.net/2021/10/20/die-cutter-project-2-a-map-of-barsoom/ and https://github.com/eleanorlutz/mars_geology_atlas_of_space, I tried making a Custom CRS:

Seeting>Custom Projection> Format= Proj String (Legacy - Not Recommended)

+proj=ortho +lat_0=90 +lon_0=-160 +x_0=0 +y_0=0 +a=3396190 +b=3396190 +units=m +no_defs

which was fine to centre the projection over the pole, which is ultimately what I need, but the coordinates are still wrong:

HGow can I reproject the scene as in the picture above, but with the correct coordinates?

Answer 1

Coordinates are not wrong.

Coordinates are expressed in the map reference system. When we want to see in the status bar coordinates in another system, we can use the Capture function of the Lat Lon Tools plugin.

---

You can use predefined CRSes, but you can also create new ones.
For the original image system, use the WKT string that comes in the projection file (the one with the .prj extension).
For the North Pole Orthographic projection, use your proj string. But change the list to WKT before accepting.
For Lat/Lon coordinates use the +proj=latlon +R=3396190 string. Also, change the list to WKT.

The Custom Projections dialog would look like this:

---

Now, load the original JPEG2000 file.
Depending on your QGIS settings, the map may or may not change its coordinate reference system. If it doesn't change itself, you manually change it to the first system created: Mars Equidistant Cylindrical.

The project would look like this:

---

Two notes before continuing:

• EPSG:4326 is an Earth latitude/longitude system. Transformations must be done between same celestial body CRSes.
• The normal use to avoid the warnings is to remove the map on-the-fly reprojection by checking the No CRS (or unknown/non-Earth projection) option for the project (or map, it's the same) CRS. Although the non-Earth projection part is true, we're not going to do it now because the plugin we use reads the coordinates from the map, so we need its on-the-fly reprojection feature.

One more note, look at the output of the Raster Information process:

I assume that the raster was derived from a mesh of nodes, where some nodes had latitude -90° and were used as pixel centers, so some pixels have an invalid extent.
I anticipate that in the next process, which is reprojection, you'll see a few warnings because of this.

---

Now reproject the raster to the Mars North Pole Orthographic CRS. Let me change the spatial resolution to something like 10000 meters because i'm not interested in preserve this billion pixels file, but you can leave that option empty.

The dialog of the Warp (Reproject) process would look like this:

---

Now, install the Lat Lon Tools plugin and configure it to show coordinates in the Mars LatLon CRS for the Capture tool:

---

Last, remove the original layer, change the map CRS to the orthographic one, and check the coordinates shown in the status bar.

My cursor was near latitude 77° North, longitude 21° East: