PhilStooke

PhilStooke, 2 days ago to random

Follow some of story of the map here:

http://www.unmannedspaceflight.com/index.php?showtopic=4254&st=0

And for the full size map in all its glory, go here:

https://sbnarchive.psi.edu/pds3/multi_mission/MULTI_SA_MULTI_6_STOOKEMAPS_V3_0/document/00_map_guide.html#eros

And here is a reduced image of my LPSC 2008 poster.

PhilStooke, 3 days ago to random

The images and the shape give us a photomosaic. I also made a shaded relief interpretation of the data, shown here. This was used by USGS as their index image for crater names at:

https://asc-planetarynames-data.s3.us-west-2.amazonaws.com/mathilde_comp.pdf

PhilStooke, 6 days ago to random

Putting all the individual projections together, we get a cylindrical projection map. The extreme elongation makes this very distorted.

PhilStooke, 6 days ago to random

And another - we did this for every image. Then each one was reprojected separately.

PhilStooke, 6 days ago to random

Here is an image of asteroid 243 Ida with a lat-long grid added. The shape model was provided by Peter Thomas. My friend Maxim Nyrtsov was visiting and helped digitize the grid intersections and reproject them to intersections on a rectangular grid to make a photomosaic.

PhilStooke, 7 days ago to random

And leaping ahead, a test map sheet, the only one I made in this format. Next we will look at how we get here.

PhilStooke, 8 days ago to random

This somewhat less attractive set of map sheets makes up the southern side of Gaspra. The globe effect would be better if the maps were divided into more sections (gores) but this works surprisingly well. I have globes like this of Phobos and Deimos plus the northern side of Gaspra. But it really is tricky to do!

I have been involved with this for 40 years but I realize maps like these are rarely seen by others, so I'm putting them out there.

Next: time to move on to Ida.

PhilStooke, 8 days ago to random

An unanticipated bonus from these Gaspra maps is that the map sheets fit together to make a globe. Not exactly perfect but pretty darn good. I join them and print them in the format shown here. Cut them out carefully, leaving a strip of paper on one side of each gap. Then with surgical precision - it's not easy - they can be joined. This set of 7 sheets makes the northern hemisphere of Gaspra, which I have done (as Arne Saknussem might say). Same for Phobos and Deimos on yesterday's link.

PhilStooke, 9 days ago to random

And sheet 2. My Gaspra maps and many others are in NASA's Small Bodies Node of the PDS, here:

https://sbnarchive.psi.edu/pds3/multi_mission/MULTI_SA_MULTI_6_STOOKEMAPS_V3_0/document/00_map_guide.html#gaspra

I only just noticed that some of their links are broken, always to the ones with labelled grids. I think this is because of an update which changes the way some coordinates are defined.

Spoiler alert - that page will lead to lots of maps of other bodies which I will be posting about later. So do not look past Gaspra! I know I can trust you because you are on the Internet.

PhilStooke, 9 days ago to random

For Phobos and Deimos I divided the global maps into 14 map sheets which were each 60 degrees across. I did the same for Gaspra and a few sheets for Mathilde, plus an experimental sheet for Ida, before I moved on to other things. This image shows the global layout of the Gaspra map sheets. On a sphere the six sheets on either side of the equator would be identical in shape, but the elongated shape of Gaspra expands those sheets at either end.

PhilStooke, 10 days ago to random

Second, the photomosaic is projected onto a grid oriented to maximize viewing of the highest resolution imaging in a single map. Here I am exploring different ways to map a body, and we are not finished yet. What about dividing the full map into separate map quadrangles? Can we make a globe of this little world? All will be revealed...

PhilStooke, 11 days ago to random

And a cylindrical map. Don't let people tell you there is one best way to make a map, one 'best' map projection etc. Cartographers want as many tools as possible to select the most useful for any given application. I once had a senior astronomy professor tell me there was no need for map projections any more because we could paste images onto a digital shape model and view it from any direction. Oblivious to the fact maps are needed to make that happen! (and global images are useful).

PhilStooke, 12 days ago to random

Secondly, a shaded relief interpretation can be drawn. This was originally drawn by hand using pencils. It was actually drawn in two separate views of opposite sides of Gaspra in a different projection and then combined here. Now most shaded relief is rendered by software from a digital elevation model but our shape model is much lower resolution than the images. Besides, this is art, not some AI crap. Not great art, I was still learning.

PhilStooke, 12 days ago to random

Michael is right, of course, that Gaspra is not tumbling, but there are things in complex rotation states. Often it's not really tumbling (which to me implies chaotic motion), it is a very slow rotation combined with rapid precession. A worse problem is an object like Mathilde which rotates so slowly that images don't reveal the rotation state.

Michael's comment about the axis is good, but I would define that as north on that body. Mathilde - just an arbitrary choice. We'll see it soon.

PhilStooke, 13 days ago to random

Peter Thomas gave me the shape model and I adapted it to my software to generate latitude-longitude grids (or graticules) corresponding to each image. The grids can be laid over the images to locate features for mapping. Here is a full set of grids. Read more here:

Stooke, P.J., 1996. The surface of asteroid 951 Gaspra. Earth, Moon, and Planets, 75, pp.53-75.

And also:

Stooke, P.J., 1996. Linear features on asteroid 951 Gaspra. Earth, Moon, and Planets, 74, pp.131-149.

PhilStooke, 1 month ago to random

And here is Deimos. There was a poor shaded relief map but it was not very useful so I made a global photomosaic of Deimos using all available images.

I am travelling for the next 3 weeks and will not be working on this during that time. I will come back to this on about May 6th and we will start looking at maps of some other worlds. 5/n

PhilStooke, 1 month ago to random

So here are the eventual maps of Phobos and Deimos. For Phobos, the shape was from Peter Thomas. The drawing is shaded relief made by the US Geological Survey, provided by Ray Batson. But they had used a preliminary shape with poor accuracy so I re-mapped the relief to fit a global photomosaic made by Thomas and colleagues including Damon Simonelli. 4/n

PhilStooke, 1 month ago to random

Here are four grids for Deimos as an example. The shape model was provided by Peter Thomas. Orthographic is like a view from a great distance, foreshortened at the edges. The equal area and conformal ('true shape') versions open up that foreshortening. The actual properties of equal area and true shape are not preserved but are approximated. Finally I began using the convex hull of the shape to reduce distortion at the edges. 3/n

PhilStooke, 1 month ago to random

I added the ability to change the radial scaling, so I could change from orthographic to Lambert's equivalent, to equidistant, to stereographic. Then I changed the radius component so it was a variable, not a constant. The global shape was read out of a 2-D array addressed by latitude and longitude and holding the radius at each point. The starting point was a triaxial ellipsoid. Enter values for its long, short and intermediate axes and the array is populated with radii. 2/n

PhilStooke, 1 month ago to random

Two next steps are apparent from the last few posts. The map projection has to be made mathematical and a digital shape model must be be made to feed into the projection. This was my PhD work. I wanted to show the shape of the body so I chose azimuthal projections - they map a sphere in two circular maps for opposite hemispheres. I wrote code to draw azimuthal projection grids of a sphere and view them from any direction. For a sphere, the radius is constant but on other shapes it varies. 1/n

PhilStooke, 1 month ago to random

And the accompanying Deimos map. Here the failure of the shape concept is apparent in hindsight. The bulge at 180 degrees longitude (facing away from Mars) should point out at about 15 south, not 45 south as I imagined it.

PhilStooke, 1 month ago to random

Here is the resulting Phobos map. My shaded relief drawing (pencil on mylar) has improved! Gilmartin suggested I submit the maps and a short report to the National Geographic Society's Award in Cartography competition, and I won it. 2/2

PhilStooke, 1 month ago to random

So back to Deimos. There was no shape model in the modern sense. I looked at all available images to get a sense of the shape - large flat or gently curved facets separated by more sharply curving ridges, and a large south polar depression. I used that to make this sketch map. Still crude but it illustrates my concept. I made this in 1981 as a first year undergrad student at Simon Fraser University, before switching to the University of Victoria.

PhilStooke, 1 month ago to random

How will this approach work for Deimos? Here are some Viking images of Deimos to show that it poses a different problem. It's not just elongated. Can a map show this sort of shape?

PhilStooke, 1 month ago to random

I wanted to see the Viking details from Thomas's map on Turner's projection, so I made this rather crude map. To distinguish it a bit from Turner's work I made an equatorial version rather than Turner's polar projection, but it still shows the elongation of Phobos. Crude, but Patrick Moore liked it enough to put it in his Yearbook of Astronomy for 1983. The big crater is now called Stickney and many grooves are mapped.