GLXP landing sites

Posted in glxp, map, moon, usa on January 24, 2011 by moonmapper

Dr Philip J. Stooke of The University of Western Ontario has compiled a map of planned landing sites of Google Lunar X Prize contestants.

Get it here.

Flying moondust

Posted in ladee, moon on January 20, 2011 by moonmapper

Contrary to what was said in the previous post, our Moon does have an atmosphere… sort of.

When orbiting an airless body, one would expect no light scattering to occur. But when the Apollo astronauts were doing circles above the lunar surface, when approaching the terminator they saw this:

"Twilight rays" as sketched by the Apollo 17 crew. Click to enlarge.

What was that?


Universe Today has a story on this, which quotes a scientist investigating this phenomenon:

“For the first set of experiments, imagine just a piece of surface with dust particles on it, and we shine light on this surface,” he said, “so that half is illuminated, half is not, pretending that there is a terminator region, that the sun is set on one side and is still shining light on the other. When you shine light on the surface with properties that are appropriate, you can emit photo electrons, but you only emit electrons from the lit side, and some of those electrons land on the dark side, — you have a positive charge surplus on the lit and a negative charge pile-up on the night side. Across a couple of millimeters you can easily generate a potential difference of maybe a watt volt, or a handful of watts volts, which translates actually as a small-scale, but incredibly strong electric fields. This could be like a kilowatt kilovolt over a meter. But of course, it only exists over a sharp boundary, and that sharp boundary may be the key to understanding how you get dust moving to begin with.”

(I took liberty of fixing obviously mistaken physical units).

Okay. Since someone has already done the hard part (i.e. calculated electric field near the lunar terminator), we can now apply high school physics, to calculate how fast can dust be ejected from the terminator zone. The result is below (click to enlarge).

Electrostatic acceleration of dust particles on lunar surface (V=1V, s=1mm)

Electrostatic acceleration of dust particles on lunar surface (V=1kV, s=1m)

The analysis assumes that a constant electric field exists across the lunar terminator. The first graph assumes that the acceleration happens  with the potential difference of V=1V along the distance of s=1mm. The second graph assumes a potential difference of V=1000V along the distance of s=1m. In both cases the electric field is 1kV/m (see the quote above), but the result is not the same. Since it’s known that the potential difference between the light and dark side of the Moon is several hundred volts, then probably the second version is closer to the truth.

Dust grains made of different elements are investigated. For each element, two curves are plotted. The bottom one assumes that only a single atom in the grain has been ionized once (i.e. the electric charge of the grain is equal to the elementary charge). The top one assumes that 50% of surface atoms have been ionized once (the illuminated side of the grain becomes ionized).

Please be aware, that this calculation is based on some highly speculative assumptions. The model is highly sensitive to the parameters of electric field near the lunar terminator.

I hope we will know more on this fascinating subject when LADEE flies.


MATLAB/Octave code is below.

function moondust()
A_Au = 197;     rho_Au = 19300;
A_Al = 27;      rho_Al = 2700;
A_Fe = 55.8;    rho_Fe = 7874;
A_Ca = 40;      rho_Ca = 1550;


plot_speed(A_Au, rho_Au, 'y;Au;');
plot_speed(A_Al, rho_Al, 'k;Al;');
plot_speed(A_Fe, rho_Fe, 'b;Fe;');
plot_speed(A_Ca, rho_Ca, 'g;Ca;');

print dust_velocity.png;

function v = dust_velocity(q, m)

% V and s estimates from:

V = 1; % Volts
s = 1e-3; % meters

E = V/s;
a = q/m*E;

t = sqrt(2*s /a);

v = a*t;


function plot_speed(A, rho, style)

amu = 1.66e-27;  % atomic mass unit [kg]
q = 1.6e-19;     % elementary charge [C]
%A = 197;        % atomic mass (Au)
%rho = 19300;    % density (Au) [kg/m^3]
v_esc = 2380;    % escape velocity [m/s]

NN = logspace(0, 10, 100);  % number of atoms in the grain

vv1 = [];
vv2 = [];

mm = A*amu*NN;
for N=NN
 m = A*amu*N;

 % Worst case: single atom in the grain ionized
 vv1 = [vv1; dust_velocity(q, m) ];

 % Best case: half of grain surface completely ionized
 qx = N^(2/3)/2;
 qx = floor(qx);
 if qx == 0
 v = nan();
 v = dust_velocity(qx*q, m);
 vv2 = [vv2; v ];

% calculate grain size [nm]
grain = (mm/rho).^(1/3) / 1e-9;

if ishold()
loglog(grain, v_esc*ones(1, length(grain)), 'r;escape velocity;');

hold on;
loglog(grain, vv1, style);
loglog(grain, vv2, style(1));

xlabel('grain size [nm]');
ylabel('velocity [m/s]');
title('Electrostatic transport of particles on lunar surface');

Light and darkness

Posted in kaguya, lro, map, moon, shackleton on January 8, 2011 by moonmapper

Readers not interested in cultural musings used as introduction to today’s post, are kindly requested to skip the part written in italic below and proceed directly to the next paragraph.

With the Epiphany behind us, we can say that the period of Christmas festivities is now over. It’s interesting to note that in my part of the world, each year we revert more from using Christian symbolic of, well, Christmas, to pagan Germanic tradition of Yule. (Or, to be more specific, we seem to be doing away with the Christian part of the symbolics, so only the pagan part remains). Now, I am not going to get into the Yule-vs-Christmas discussion, because first, the subject has been widely covered already, and second, this is, after all, a blog about astronomy, and not culture or religion. But I can’t help noting one very ironic twist. Although one can say that Christmas is not a native holiday in my country, so shifting focus back to Yule symbolics is coming back to one’s cultural roots, the joke is that Yule isn’t native here either. Depending on the exact location, actual Slavic holiday celebrated around winter solstice would be Święto Godowe (here’s a Wikipedia article on it, readable although mutilated by Google Translate), Kračún or Koleda. That’s not like these customs were completly lost, though, as some parts of it were simply incorporated into the Christian rituals. But as we are moving away from Christian character of midwinter celebrations, and the major deity nowadays is an overweight, bearded dude in a red coat, affiliated with the Coca-Cola company, there’s a good chance that this part of my cultural legacy will die out completely in my lifetime.  So if you want to know what the world will be missing by the time humans return to the Moon, you can have a look here and here.

Regardless of what particular religious (or commercial) holiday someone celebrates at this point of the year (or spends at work, like me), one must remember that midwinter festivities are in fact astronomical in nature. After the winter solstice, northern hemisphere days become longer and so the world is again moving from darkness into light. And that transition from darkness to light (and back) brings me to the topic of today’s post.

The LRO team has posted a new map of illumination conditions in the lunar South Pole region, and Paul Spudis has given this map an extensive treatment.

Illumination data are very important from the perspective of future surface operations. Since the Moon has no atmosphere, there is no ambient (scattered) light. A given point on the surface is either directly illuminated by Sun (i.e. you can see the Sun if you are there), or it is not. An illuminated region will be hot (+107°C); a dark region will be cold (-153°C). In the equatorial regions (where Apollo landed) the Sun is high above the horizon during the day, so everything is illuminated (and hot); at night, nothing is illuminated (the Sun is below the horizon), so the temperature drops.

Polar regions are different. There, the Sun grazes the horizon all the time. (Since the tilt of the Moon’s axis is minuscule, there is no polar day / polar night effect we have on Earth). So, if you stand on a mountain peak you can see the Sun all the time, going around you. This situation is known as a peak of eternal light. On the other hand, if you dive into a deep crater, you never see the light. Of course, the whole thing is a bit tricky: remember, there is no ambient light. So if you happen to be high up, but a mountain obstructs your view of the horizon, you will be in darkness when the Sun happens to be behind the mountain.

Now, assume that you want to build a base. What would be a good spot to do so? The equatorial regions are not a good choice; the 250°C temperature difference between day and night makes engineers nervous. On the other hand, a peak of eternal light would be a nice place. Permanent illumination ensures that the thermal environment would be stable — around -50°C. Also, it provides access to abundant solar energy. (Although in practice you have to erect your solar panels vertically and rotate them following the Sun, which complicates matters a bit).

But wait a moment. We also know that the permanently shadowed regions harbor water and other interesting volatiles. Wouldn’t it be better to set up a base there? Not really, because at ca. -200°C the conditions are not really likable. So what does one need? Well, of course: a well illuminated region near a permanently shadowed region!

Meet the Shackleton crater:

Shackleton crater - illumination and topography.

(for a larger view, click the image or download a full resolution 300dpi PDF with description).

The above map combines the illumination data from LRO (linked above), expressed as shades of gray with the Kaguya laser altimetry data (red isolines) and some annotations. I have drawn isolines only every 250m, to avoid too much clutter inside the crater.

Letters A, B and D mark the areas which are illuminated at least 80% of time. These locations have been identified by Bussey et. al. (see the paper here) by creating a relief model of the terrain and performing a computer simulation of solar illumination; see the paper for details. Also, Paul Spudis’ site contains an iconic image of these interesting locations marked over the Kaguya “Earthset” photography. (The “C” location is too far from Shackleton to be included on my map.)

I must note that a major discrepancy exists between the LRO image and the Bussey paper. The LRO image is 8-bit grayscale image (i.e. values between 0 and 255) with actual pixel values between 2 and 254. So, logically,the value of 254 would correspond to 100% illumination (peak of eternal light) and 2 to 0% illumination (eternal darkness). At the same time, Bussey say that the best illuminated point (D) receives around 86% of illumination on average. Since there is no additional information to resolve this, I have chosen to render the LRO data in 0-100% range anyway.

One can now easily see the attractiveness of the “A” spot for mission planners. The following image, taken from a BBC article about the ill-fated Constellation program, confirms this expectation:

As for getting the volatiles from the crater floor, the matter is a bit tricky. A quick look at my map tells you that the crater floor has the elevation around  -2500m and the “A” spot is at +1500m. This produces a 4000m difference in elevation over a horizontal distance of about 8km. That means an average slope of 26 degrees or 46%. The upside is, we have engineered such systems on Earth already. This is Pilatus railway in Switzerland, world’s steepest cog railway, climbing a track with 38% average and 48% maximum slope.

Pilatus railway, Switzerland. Image credit: JuergenG, Wikimedia

The downside is, building something like that on the Moon is pure madness. It would operate in hard vacuum, low gravity and have to be able to survive 150K temperature difference between the crater bottom and its rim. And there will be no industry around to supply the materials.

I have no idea what will be used to transport the water out of the lunar cold traps, but I am sure that it will require some brilliant engineering.


38 years

Posted in history, moon on December 19, 2010 by moonmapper

38 years ago, on December 19, 1972 at 19:24:59 UTC, the Apollo 17 Command Module America splashed down into Pacific.The first human exploration of a planetary body other than Earth has ended.

The Apollo anniversaries are usually hard for space enthusiasts. It’s hard to acknowledge that in 1972 we have abandoned dreams of space colonization, and instead chosen to remain confined to Earth surface and low Earth orbit. But the aim of this blog is to look forward towards the new perspectives, not back at past glory. Recent discoveries around the poles of the Moon do rekindle hope that one day humans shall return to claim Earth’s Next Continent.

CSM America seen from LM Challenger over the Taurus-Littrow valley prior to descent. NASA frame AS17-147-22466, cropped. Click to enlarge.

Although not located in the attractive polar regions, the Taurus-Littrow valley visited by Apollo 17 remains a fascinating place. Let’s use the anniversary to explore it:

Space Manufacturing 14

Posted in moon on December 5, 2010 by moonmapper

Space Manufacturing 14: Critical Technologies for Space Settlement, was a conference held by the Space Studies Institute at NASA Ames Conference Center between October 29 and 31, 2010. Many of talks dealt with industrial use of lunar resources.

The materials are now online:

Hat tip to Bob Clark at BAUT.

A map, retro style

Posted in history, map, moon, processing, usa on November 2, 2010 by moonmapper

This is National Geographic map on the Moon, first published in February 1969 issue:

(reduced under fair use. You can see a zoomable version and buy a copy at the NatGeo store).

I have found a fascinating story dealing with the creation of this map, told by the cartographer who was actually working on it: Part 1 and Part 2. The work started back in 1964, before the detailed imagery of the Farside was even available (but after the first images of the Farside returned by Luna 3). As the Lunar Orbiter images were coming in, a special process had to be developed and employed in order to rectify the photographs and put them on a coordinate grid. It worked, although there was one major problem on the Farside:

The gut- killer was that there was nothing I could use to check my work. I had to work across the entire Far Side hoping everything would meet up correctly. Fortunately it did.

I humbly bow before people who were able to accomplish such things.

Contrast this with today, when I can get a gridded and calibrated altimetry dataset from the spacecraft over the Internet in a few minutes; spend one weekend writing processing software and produce a map of interesting area within several minutes — all that without even leaving my home. Or having a formal training in cartography, for that matter. Or, if I’m lazy, fire up VMA or LTVT and be done even quicker. I can even shade the map with titanium concentration in a few clicks, if I feel like it. To quote Phil Plait

We live in the future. Still no flying cars, but we live in the future.

Constellation landing sites

Posted in cxp, lro, moon, usa on October 31, 2010 by moonmapper

The ill-fated Constellation program was supposed to land humans on the Moon by 2020. As a part of this effort, a process of landing site selection has been started, and the Lunar Reconnaisance Orbiter was launched in order to image these sites. Although the program never lived to selecting actual landing sites, a list of 50 targets for LRO imaging, known as Constellation Regions of Interest, has been compiled and given over to the LRO team for detailed imaging.

(CxP regions of interest, click to enlarge. Source.)

It turns out (much to my surprise) that despite the Constellation’s demise, the LRO team has actually acquired the high resolution imagery of the Constellation sites. Even better, they were given coverage at the LROC blog.

Without further ado, the stuff:

The LCROSS brew

Posted in lcross, moon, usa on October 30, 2010 by moonmapper

The LCROSS probe has been featured on this blog before, but now the new goodies have been released, in form of five papers in the Science journal of Oct. 22.

We now know the content of volatiles (and other elements) in the soil at the LCROSS impact site. My visualizations below.

(click the image to get a fullsize view, or  here for an interactive visualization)

(click the image to get a fullsize view, or  here for an interactive visualization)

(click the image to get a fullsize view, or  here for an interactive visualization)

Key to symbols:

  • LTV – Low Temperature Volatiles (<600K)
  • HTV – High Temperature Volatiles
  • CON – early condensate
  • MET – metal
  • SIL – Silicate

Compiled from:

  • Colaprete, “Detection of water in the LCROSS ejecta plume”, Science 330 (2010)
  • Gladstone, “LRO-LAMP Observations of the LCROSS impact plume”, Science 330 (2010)


  1. Gladstone et. al. give H2 content of 1.4% as measured by LRO. This omitted from the dataset, as this hydrogen is most likely already included in the organic compounds detected by LCROSS (as noted by Colaprete
  2. Colaprete et. al. give the H2O content as 5.6+/-2.9% and give the content of other organics as percentage of water mass. To get absolute ppm, I have used the 5.6% figure.
  3. For some molecules, the given value is the upper limit.
  4. Note the difference between Co (cobalt) and CO (carbon monoxide).
  5. The published numbers add up to 34.73% of soil content. The remainder is unaccounted for and has been omitted from the visualizations for clarity.

Climbing Mount Malapert

Posted in kaguya, map, moon on October 9, 2010 by moonmapper

On Earth, we have mountains so we can climb them. Why should we act differently once we are on the Moon? Why not get yourself a copy of The Rough Guide to Solar System Mountaineering or Higher then Everest: an adventurer’s guide to the solar system and go conquering the lunar Alps? Or, choose one of the hiking trips proposed by a German magazine: to Mare Tranquillitatis, Tycho, or the South Pole traverse?

This is our target:

(click the image above or here to get the full resolution PDF).

The Malapert Mountain, or Mount Malapert, or Malapert Alpha. A mountain ridge, rising over 5 kilometers above the surrounding terrain, located in the South Polar region of the Moon. Illuminated by Sun 89% of the time (almost a peak of eternal light), and neighboring some permanently shadowed craters (potentially harboring ice), it is an often proposed site for future mining operations, industrial operations, or a moon base. But, the potential usefulness of this site should not distract us from its main feature: it is a mountain, and we climb every one of them, just because they’re there.

So, how would you plan your trip? Would you set up a base at the bottom of Malapert, and start your 7.3km climb from there, with the Earth shining behind your back?

BELOW: View back from Kaguya/SELENE flying toward the South Pole. The Earth sets behind the Malapert Mountain.

Or, would you try a tougher route, and start from the bottom of Haworth, resulting in 8.4km climb, without the visibility of your home planet until you reach the top? Or maybe, set out from the plateau between Haworth and Shoemaker, starting almost 2km higher (at -1500m)? Or, would you rather make it easier for yourself and go for the valley NE of Haworth, with +500m elevation, and attack the ridge with the least steep, Western slope?


A map in five easy steps

Posted in map, moon, processing on October 3, 2010 by moonmapper


Astronomy is one of few fields of scientific endeavor where amateurs can make valuable contributions. Published astronomy data are a real treasure trove, and thanks to the wonders of computers and the Internet, you can go looking for treasures yourself. You can find a new class of astronomical object, or a lost Russian rover, or an alien base… oh, wait.

This post describes my current work flow of producing lunar maps from Kaguya LALT (Laser ALTimeter) dataset. I use GNU Octave, which is a free clone of MATLAB, but this page references original MATLAB documentation simply because it is better. The referenced functions work the same in both, the only difference being that MATLAB produces prettier plots.

Step 1. Obtaining the dataset.

For making height maps, we need an altimetry dataset. (Similarly, e.g. in order to draw a map of thorium concentrations, we need a dataset containing Th levels). Altimetry datasets are also referred to as DEMs (Digital Elevation Models). Basically, there are two kinds of datasets: time series data and gridded data. Time series data contain measured values (in our case, altitude) versus time. In order to obtain useful information (where exactly on the Moon a particular measurement was made), these have to be combined with data about the spacecraft location versus time. Gridded data are derived from time series data, and contain measurement results versus location. (Since a particular area can be measured multiple times, i.e. once per orbit, while other areas can be skipped, the gridded datasets are usually averaged and interpolated appropriately). Here we will work with gridded data.

NASA datasets are can usually be obtained through the Planetary Data System (PDS). For information on how to obtain Kaguya data, see this page.

Step 2. Loading the dataset.

An altimetry dataset can be represented either as an image (.IMG file) or a table (.TAB) file. A table contains (longitude, latitude, altitude) triplets, such as these in the Kaguya South Polar datataset:

12.453125 -80.00390625  1.907
12.484375 -80.00390625  1.895
12.515625 -80.00390625  1.894
12.546875 -80.00390625  1.894
12.578125 -80.00390625  1.907

(I currently work with tabbed data, because it can be loaded into Octave directly after the header is stripped).

In case when data is represented as an image, altitude is represented by a pixel value (color/brightness), while latitude/longitude information is encoded in pixel coordinates. In other words, such image, when opened using an image processing software, will represent an altitude map. Unfortunately, there is no single convention (map projection, pixel values) on how such image datasets are encoded. Fortunately, the people at UMSF have most of these worked out already. In principle, the image can be converted into the table like the one above and used in the following steps.

Altitude values are expressed with respect to a reference ellipsoid. In case of Moon, this is a sphere with the radius of 1737.4km. The latitude and longitude coordinates are expressed in a terrestrial convention: in degrees, positive values to north and east. For more information, see A Standardized Lunar Coordinate System for the Lunar Reconnaissance Orbiter.

Step 3. Projecting.

As most of us know, planetary bodies are spherical, while maps are flat. In order to render a 3D planetary surface into a 2D map, we must perform a projection. As stated above, our dataset is expressed in terms of latitude (λ) and longitude (Φ), i.e. (λ, Φ, z) triplets, where z is the altitude. First, we select a center point of the map (λ0, Φ1). Then we calculate the (x,y) coordinates on the projection (map) plane for each (λ, Φ) (latitude, longitude) pair in the dataset, producing (x, y, z) triplets. The particular equations for calculating (x, y) values from (λ, Φ) pairs depend on a chosen projection. For details, as well as a comprehensive discussion of advantages and disadvantages of different projection systems, see:  Snyder, P. Map Projections – a Working Manual. Or, get an accelerated course in orthographic projection at Wikipedia.

Step 4. Resampling.

We now have the (x,y,z) coordinates of the terrain surface. Here comes a tricky part, as we encounter two problems.

The first problem: we have too much data. For example, if we are mapping a 100km x 100km area, and the dataset it sampled at 10m resolution, that means we have 10’000×10’000 = 100’000’000 points. However, when drawing a map of a 100km x 100km area, we may find that 500m resolution would be more then satisfactory (that works out to 200 points along each axis of the map, which is generally enough to get a good understanding of the shape of the terrain). We solve that by randomly extracting 40’000 points from the dataset and throwing out the rest. (Yes, there are better methods to do this, but this one is the fastest and works surprisingly well.)

The second problem: plotting tools usually require z(x,y) values, with the (x,y) arguments describing points of a rectangular grid. (Such grid is constructed by using the meshgrid function). However, our (x,y,z) triplets do not form a rectangular (x,y) grid — they form a latitude/longitude grid which, in general, is no longer rectangular once projected on a plane. If you look at a (terrestrial) map, the lat/long lines are usually not straight, but curved; since our z values are expressed in terms of latitude and longitude, this poses a problem. (We have actually made the problem worse during the previous step, by sampling the data randomly). We solve this by using the griddata function. This function takes our projected (x,y,z) data and the grid coordinates (xi,yi) returned by meshgrid, and returns (xi,yi,zi) triplets (matrices, actually; see the meshgrid documentation if you really want to know), containing interpolated altitude values (zi) in the map grid points (xi,yi).

Step 5. Plotting.

Finis coronat opus. We pass (xi, yi, zi) to the plotting functions. Isolines can be ploted using contour function, or contourf if you want coloring. Alternatively, we can plot a 3D view by using surf. Add labels for named terrain features, descriptions, and you now have a map.

Caveat emptor

As you can see, drawing a map yourself is hardly rocket science. But we must remember that our maps will contain errors. There are several sources of error in the plotted data, which we must be aware of:

  1. Measurement errors (artifacts)
  2. Measurement resolution (horizontal and vertical)
  3. Missing data and interpolations used during production of the gridded dataset
  4. Projection errors (deformations)
  5. Errors introduced during downsampling the dataset
  6. Errors introduced during final re-griding and interpolation

The bottom line is that with this method, one can make a pretty good map relatively quickly, however making an authoritative map would require more advanced processing and strict error analysis. So if you want to use these maps to familiarize yourself with the lunar features, they are fine. If you want to use them to plan lunar observations, they should be fine as well. If you want to write a realistic sci-fi story, they should be fine as well. If you plan to use them for guiding a spacecraft — that would not be a good idea.