Archive for the map Category

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.

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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 et.al. 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 et.al. 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.

Related:

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.

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: