Mapping the Moon

I am fascinated by space exploration. The other day, inspired by the recent anniversary of the Apollo 16 mission, I was watching a short documentary about Moon exploration.

The documentary had an interesting note about the Lunar ReconnaissanceOrbiter, a space probe orbiting the Moon since 2009, and performing different measurement to prepare for future Moon expeditions. One of the six on-board instruments of the orbiter is called Lunar Orbiter Laser Altimeter, or LOLA. It measures the precise height of the lunar surface under the probe by centimeter accuracy, and it is used to build a topographic map of the Moon.

That has turned on my brain and I was carried away. What could be more cool than play around with the real 3D topographical map of the Moon! Then I figured, that NASA is a public institute, they publish practically everything they measure or record during their missions. So maybe, if I dig deep enough, I can find LOLA data out in the Internet wilderness.

And here we go! The orbiter itself has a great and informative website. They provide links not only to interesting images and multimedia, but also to actual real measurements and datasets via NASA's PlanetaryData System archives (sounds mind blowing!).
The actual measured raw data can be downloaded from the Lunar OrbitalData Explorer. For example, a single set of measurements can be imported into R like this:

raw.data<-read .table="" a="" href="http://pds-geosciences.wustl.edu/lro/lro-l-lola-3-rdr-v1/lrolol_1xxx/data/lola_radr/laser1/lro_no_01/lolaradr_092582345.tab">http://pds-geosciences.wustl.edu/lro/lro-l-lola-3-rdr-v1/lrolol_1xxx/data/lola_radr/laser1/lro_no_01/lolaradr_092582345.tab

This is a table file which can be nicely imported into an R data frame. Its structure is explained here.
The main point is that the first two columns contain longitude/latitude coordinates, while column 10 is the distance of the surface measured from the orbiter. It is a simplification, because the measuring laser is not always pointing “down”, but for our purposes that will do. Because after investigating a few of the files (and there are many of them), it is clear that they contain data segmented by collection time, meaning that in a file there are reads from a segment of a single orbit. Since I am more interested in all the measurements from a given lunar location, I was digging further on the website.

Fortunately, they offer also a tool to download all the elevation reads from a location, and it can be selected using simply the coordinates of the desired region: http://ode.rsl.wustl.edu/moon/indextools.aspx

So I have fired up Google Moon and picked up one of my favorite regions: the Posidonius Crater. There are multiple crater rings in this complex, and I have randomly picked up crater “J” and its surrounding and downloaded data between 30 to 32 E; and 33 to 35 N coordinates.

The data is kindly generated as a CSV file, which is very easy to handle with R:

dat.file<- font="" opofull_csv_table.csv="">
my.data<-read .csv="" dat.file="" font="">

The important information is stured in the first three columns of the created data frame: the longitudes, the latitudes, and the “topography”, which can be simply interpreted as elevation compared to a hypothetical “sea level”.
After a brief investigation of this topography data, it can be seen that it is actually “below” that level, so all the elevations are negative:


It is easy to use the plot3d() function to draw a 3D scatterplot of the measured data. I wanted to use a color code which would resemble map colors, with high values as brown and low areas as green. The terrain.colors() function offers a handy solution for that:

zlim<-range font="" my.data="" topography="">
zlen<-zlim font="" zlim="">
colorlut<-terrain .colors="" font="" zlen="">
col<-colorlut font="" my.data="" topography-zlim="">

With the colors prepared, plotting is a matter of providing the proper parameters of plot3d():

       main="Posidonius J crater on Moon",
       sub="Lunar Reconnaissance Orbiter LOLA data")

This is excellent, the passings of orbiter are clearly visible, and with a bit of turning the plot this and that ways, we can clearly see the shape of the terrain. Still, it is not what I wanted as a nice 3D topography. For that, the measurements taken under the orbital passings should e converted to a regular grid format, where the elevation is recorded in a grid like matrix. It is not a trivial task to convert our existing data to grid format as it involves heavy interpolation. It is a computationally expensive calculation, but nothing that a modern computer could not handle. R offers the akima package, which implements the interpolation of H. Akima (http://www.iue.tuwien.ac.at/phd/rottinger/node60.html ).


int.dat <- font="" interp="" my.data="" t_longitude="">

It takes some 10-15 minutes to run the interpolation, but the results are suitable for visualization with the rgl package. First, I wanted to convert the elevation values so that they scale close to 1:10 with the horizontal dimensions of the plot.

elevation<-int .dat="" font="" z="">
elevation<-elevation 1:10="" distortion="" font="" of="" sizes="" vertical="">

Again, the colors are recalculated so the usual topographical colors are scaled to this data:

zlim<-range elevation="" na.rm="TRUE)</font">
zlen<-zlim font="" zlim="">
colorlut<-terrain .colors="" font="" zlen="">
col<-colorlut elevation-zlim="" font="">

And finally, we are ready to see the surface of the Moon!


Incredible! A piece of Moon on my computer screen!

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