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

Notes:

  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 et.al.).
  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.
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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?

Related:

A map in five easy steps

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

Introduction

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.

LCROSS impact site

Posted in kaguya, lcross, map, moon, usa on October 3, 2010 by moonmapper

On October 9th, 2009 the LCROSS spacecraft has been intentionally crashed inside the Cabeus crater in an attempt to verify presence of water ice. The mission proved successful and water molecules have been observed in the impact ejecta.

The mission actually involved two impacts. The first one, by a spent Centaur upper stage used to boost LCROSS to the Moon; the second one by the LCROSS shepherding spacecraft (SSC) itself, four minutes later. The SSC followed the Centaur on its way to annihilation, flying through the plume raised by the rocket’s impact and analyzing its composition. The concept has been neatly explained in this video:

This is the topography of the impact site (my render from Kaguya LALT data, click to get the high resolution PDF).

For comparison, below is a map of the impact site made available by NASA (from this PowerPoint presentation).

A NASA map of the impact site, from the LRO LOLA altimeter

Luna Resurs

Posted in chandrayaan-2, india, kaguya, luna-resurs, map, moon, russia on October 2, 2010 by moonmapper

Luna Resurs is a currently developed joint Russian-Indian mission to the Moon, targeting southern polar regions. The mission will carry an Indian rover, Chandrayaan-2. The aim of the mission is to investigate presence of volatiles on the Moon, in particular, water ice in permanently shadowed craters. The launch, planned for 2013, will likely coincide with the mission of a Chinese rover, Chang’e-3. This has provided grounds for claims that we are observing a new space race between India and China.

In 2010, a paper by E.N. Slyuta et.al. titled Proposed Landing Sites for Russian Luna-Resurs Mission to the Moon has been presented during the 41st Lunar and Planetary Science Conference. The paper lists two landing sites: 87.2°S, 68°E (primary) and 88.5°S, 297°E (backup). Although the paper includes maps showing the landing site locations in the South Polar region, it does not give detailed landing site topography.

Using the published Kaguya LALT dataset, I have rendered maps showing the landing sites, available here in PDF format.

Slyuta et.al. describe the primary landing site as located

between craters Shoemaker (D = 63 km) and Faustini (D = 45 km) (Fig. 1). The landing site is at a relatively flat plain with the hundred meters altitude range. The illumination rate of the landing site is high enough and reaches 40-50 % (Fig. 2), including both summer and winter periods. Following the topography the illumination rate at the northern and southern parts of the ellipse decreases to 30 % and less [19]. The closest permanently shaded areas are in craters Shoemaker and Faustini (Fig. 2) as well as in small craters near the northern border of the ellipse. Permanently shaded areas in craters Shoemaker and Faustini are the largest cold traps at the South Pole.

The secondary landing site

is located at the western rim of crater de Gerlach (D = 31 km) (Fig. 1). Deep crater of 15 km in diameter, which is a double cold trap, is located in a southeast part of crater de Gerlach. The crater rim within the landing ellipse is a flat-top height dominating over surrounding area by ~2 km. The illumination rate of the landing site is high, and even during the winter period does not fall below 70-75 %. […] Permanently shaded areas are in small craters near the eastern border of the landing ellipse and in crater de Gerlach. The mentioned 15- km crater is a double cold trap. And small craters inside it will be the threefold cold traps. The equilibrium temperature in the latters can reach 30-40 K [4]. The landing site No2 is in a zone of the maximum hydrogen concentration of 145 ppm in the South Pole [20]. The basic objects of research are permanently shaded areas in small craters near the east border of the landing ellipse and in a double trap in crater de Gerlach.

Thus, the envisioned mission profile appears to be landing in a well-illuminated, highland area and using a rover to drive to the potential cold traps for in situ inspection. As you can see from the map, in case of a primary site, the interesting areas are likely the -3200m depression inside Faustini and the -4100m depression inside Shoemaker. That is respectively ca. 12 km and ca. 25 km from the center of the landing ellipse. For a 15kg rover, that is really going to be a challenging job!

See also:

Hello world!

Posted in moon, Uncategorized on October 2, 2010 by moonmapper

This site will be dedicated to the current and future exploration of our nearest Solar System neighbor – the Moon.

Of course the explorers will need maps, so the maps will be of our primary interest here.