Introducing the Lego Mars Project

About the Project

One of the finest things about being a nerd is that you are constantly looking for an excuse to learn something new. On occasion, this may take the appearance of a trip down a wikipedia rabbit hole. Or, it might be arguing with someone on reddit, breaking out back of the envelope calculations to prove a point.

The Lego Mars Project is an excuse to learn new things. In particular, new things related to planetary science, materials science, resource estimation, rocketry, and engineering in general. The goal is to illustrate this learning with Lego, while providing linked essays into the engineering and research that went into each decision.

Ultimately, this may end up being an educational resource, not just for myself, but for others - and a back of the envelope design for a planetary settlement on Mars.

About the Author

Troy Unrau is a professional geophysicist, who does R&D on instrumentation used for mineral exploration in the arctic. An accomplished programmer, and general nerd, he went to grad school for planetary science before dropping out to get a real job. Someone forgot to tell him that Lego is for children.

Contents

Introducing the Lego Mars Project

About the Project

About the Author

Contents

A Choice of Scale

Studs

Minifigures

Choosing a Metric

Some Considerations

An Untenable Scale

Taking it Down a Stud - Microfigures

Yet Another Scale

Scale Conclusion

Sunlight, a Primer

Martian Sunlight

Efficiency and Minimum Power

A Beam of Sunlight

Sun Angle Simulator Parameters

The Equator - Sun Angles

The Poles - Sun Angles

The Arctic Circle

Concluding the Solar Angle Simulator

Chemistry: The Atmosphere and the Importance of Water Ice

The Building Blocks of Humanity: The Organic Elements

The Martian Atmosphere Scores 3 out of 4

The Gravity of the Situation - Atmospheric Losses

The Triple Point of Water

Long Term Considerations

Ice Accessibility vs. Insolation

Finding Lower Latitude Ice Deposits

Detecting Ice via High Energy Radiation from Orbit

Using Radar from Orbit

Ice in Craters

Geomorphology and Imaging

Lego Criteria

Choosing a Landing Site

A Closer Look at HiRISE Images

Site Chosen, Now What?

A Choice of Scale

2020-04-12 (edits on 2020-04-13 for typos and mistakes).

Studs

If this project was a real engineering project, the scale would be ‘reality, but in metric’. As the medium of illustration for this project is Lego, a scale must be chosen such that Lego can adequately represent the volumes, surface areas, thicknesses, and so forth as required for useful visualization and ease of building.

The fundamental scales of Lego are as follows: a plate - a mostly flat piece, has a set thickness, or depth. One each plate, there are studs. The studs form a sort of X-Y grid, with the thickness of the plate forming the Z direction.

The thickness of the plate (pink) is one half the distance between two studs. So, while the X-Y scale is uniform, some math is required to maintain the aspect ratio in the Z direction.

Lego nominally has an 8 mm separation between the centre points of the studs. All lego pieces have a 0.1 mm gap around their outer edges in the X-Y direction, and a 0.2 mm gap in the Z direction - a bit of wiggle room. A brick, which are the taller white and red pieces pictured, has a height of 9.6 mm, which is nominally 10 mm with a 0.2 mm bit of play on top and bottom. The white brick is 7.8 mm wide, which is nominally 8 mm with a 0.1 mm gap on either side.

Thus, the ratio between studs and bricks is 5:4. In other words, stack four bricks and you get five studs.

Furthermore, the plate (pink) is one third of a brick, nominally. It is 3.2 mm actual, with less play than the bricks. This creates an awkward ratio: 5:12 - five studs is twelve plates.

Expressing these as decimals, and assuming the stud as the basic unit of measurement, we get: one brick = 1.2 studs; one plate = 0.4 studs. Not great, not terrible.

In this, and all further documents, we will refer to Lego sizes in studs, except where bricks of unusual size occur, in which case we may have to resort to metric.

Minifigures

Lego figurines, useful for showing human scales, require 2x1 studs to stand on, but if you add space for their arms, are approximately 3 studs wide. Realistically, you require a 4x2 stud area on the floor for them to stand upright. Furthermore, they require between 5 and 6 studs of vertical space, depending on their hair and other accessories.

If one were to equate them to average human proportions, one might be inclined to use imperial measurement: one stud is one foot, thus the minifigure is between 5 and 6 feet tall. This isn’t terrible, but a preference for metric in science in engineering requires different units.

Choosing a Metric

In choosing a nice metric scale, we have a few choices.

We could go with one stud = 30 cm, to approximate an imperial foot. This has the advantage of dividing nicely by two when dealing with plates and bricks, in turn making a plate 12 cm tall; a brick, 36 cm. Any number divisible by two grants a similar advantage here. The advantage of being approximately an imperial foot per stud is useful in an educational context as well, should this project ever become popular. The disadvantage is that it is difficult to measure things in metres this way.

Another reasonable choice, assuming that using the minifigures is desirable, is to set three studs equal to one metre. That means that each stud is approximately 33 cm, each plate is approximately 13.3 cm thick, and each brick 40 cm thick. The brick thickness number is convenient, but the other two are not. Furthermore, as this is still close enough to one foot per stud, the approximation for education purposes is still mostly valid.

Some Considerations

Assuming that either of the above scales is chosen, we have some design constraints that immediately present themselves. First - the thinnest material we can represent is 12 or 13 cm thick (approximately 5-6 inches). Assuming that objects are rounded to the nearest plate thickness, this implies that approximately 6-7 cm is the thinnest material we can represent.

As Lego uses the same thickness to represent the smallest round objects (things that can fit in the hands of the minifigures), this also sets our thickness for representing things like pipes, cables, and so forth, without resorting to more interesting methods (like using string).

Furthermore, Lego is excellent at representing squares and squarish objects on the grid, but as soon as round objects need to be represented, a great deal of internal structural elements need to be added. These structural elements take up room inside a structure, reducing usable internal space.

The combined minimum thicknesses and internal structural support may lead to a loss of freedom in interior design elements. This may lead to some cheating with dimensions as represented. The full scope of this problem is yet to be determined in practice.

An Untenable Scale

At the time of this writing, SpaceX is currently designing prototypes for a rocket transportation system intended to ferry people and equipment to Mars on a regular basis. This rocket has a nominal diameter of nine metres (whether that’s exterior diameter, or interior tank diameter is unknown). This spacecraft is known as Starship.

Assuming that Starship ends up being our delivery system, all equipment delivered to Mars must have a maximum diameter less than the cargo bay of Starship. Using the 30 cm stud definition, this makes Starship 30 studs in diameter; using the 33 cm definition, 27 studs in diameter. This is quite large in terms of Lego rockets! Furthermore, Starship is estimated to be 50 m tall, which equates to 167 or 150 studs tall-- 140 or 125 bricks tall. In real terms, building a Starship out of Lego at these scales is prohibitive in terms of numbers of bricks used during construction.

It also implies that any Mars base that is practical at minifigure scale is going to be immense, requiring an investment of thousands of dollars in bricks.

Taking it Down a Stud - Microfigures

One option is to scale everything down by a factor of three and use microfigures. Lego produces microfigures that have a footprint of one stud, and a height of two studs. If a stud were to represent a metre, then these minifigures are approximately two metres tall. Plus the Saturn V rocket set came with microfigures in spacesuits, conveniently.

Using microfigure scale allows for building a Starship that is 9 studs across, and 42 bricks tall. This is an attainable goal without having to spend thousands of dollars on bricks.

Unfortunately, this scale is terrible in terms of the smallest things that can be represented (20 cm), and all of the Lego minifigure accessories (for example, tools) cannot be represented at this scale.

Microfigure scale would be useful for representing the exteriors of buildings, and local colony layouts.

Yet Another Scale

The scale of microfigures is still to large if wanted to represent the colony in the context of geology. Victoria crater, a rather well known and studied crater on Mars - due to being visited by the Mars Exploration Rover Opportunity, is over 750 m in diameter. To represent such a crater in Lego at one metre per stud would require an entire room.

In order to present our colony in the context of its local environment, we will need another scale yet. Thus, proposing a third scale to operate at for regional scale design - one stud equals ten metres. This makes a 75 stud crater if we wish to recreate Victoria crater, with the crater being 5 bricks deep, approximately. The largest Lego base plate is 48x48 studs, thus the above image could be built on four base plates if required.

At this scale, the Starship is one stud around, and 4 bricks high. It’s so easy to build that let’s do it right now.

Take three 1x1 cylinder bricks and a 1x1 conical piece and stack ‘em. We might even have the right colours. I’m totally posting this on r/SpaceXMasterRace for internet karma...

Scale Conclusion

Thus, it is meaningful to build this project on three wholly different scales. The regional scale, at one stud is ten metres; the microfigure scale, one stud is one metre; and the minifigure scale for interior details (cross sections, cutaways) at three studs is one metre. The following table is presented for my own benefit.

Stud X Y Brick Z Plate Z Min Feature Regional 10 m 12 m 4 m 2 m Microfigure 1.0 m 1.2 m 0.4 m 0.2 m Minifigure 33 cm 40 cm 13 cm 7 cm Real 8 mm 10 mm 3.3 mm 1.7 mm

Sunlight, a Primer

2020-04-13

We need to talk about sunlight - since this will be useful to know in advance when choosing the location of our colony. Since we are assuming that solar power will be the primary source of power for our colonists (maybe a dangerous assumption, to be re-evaluated later), we want to maximize the amount of energy we can get from the panels we bring.

Martian Sunlight

Mars is somewhat further away from the Sun than the Earth, thus it receives less sunlight in general - about half as much, typically. The amount of sunlight a place received is known as insolation - not to be confused with insulation.

On Earth, the upper atmosphere gets approximately 1386 Watts of solar energy per metre square (W/m²). This varies slightly throughout the year, due to Earth’s orbit being slightly eccentric (not quite a perfect circle), and also with the current state of the solar cycle. For the sake of argument, we’ll assume 1386 W/m² is a constant.

Mars has an average distance from the Sun of 1.524 astronomical units. An astronomical unit is defined as the distance between the Earth and the Sun, on average, so this makes things rather simple for us: Mars is approximately 1.524 times further from the Sun than the Earth. Because it’s moving faster when closer, it actually spends slightly more time further from the Sun, so the time average is closer to 1.530. You can learn many things about the Orbit of Mars on wikipedia.

Now, the amount of sunlight Mars gets falls off using an equation called the inverse square law. This equation looks something like:

Where I is the Intensity of sunlight, and r is the distance from the Sun. The intensity is 43% as much as it is on Earth.

Thus, we conclude that Mars’s upper atmosphere is receiving 1386*.43 or 592 W/m². This is how much light would hit a perfectly aligned solar panel in orbit around Mars, on average.

Efficiency and Minimum Power

Because Mars has an elliptical orbit, at its most distant from the Sun, it is 1.666 AU away. This gives a solar intensity that is only 36% of what you’d get on Earth, or 499 W/m². In any system design, you must assume the worst, so this is the number we’re going to use for a perfectly aligned panel. We’ll round to 500, for convenient numbers.

The wiki article on Solar Cell Efficiency is quite informative. Summarizing: the maximum theoretical solar panel efficiency is somewhere on the order of 68% on Earth - likely slightly lower on Mars as the Sun takes up less of the sky. Nevertheless, one will never achieve the maximum theoretical limit.

Satellites currently being launched from Earth have efficiencies of up to 34%. But these are extremely expensive panels and are not suitable for wide scale deployment.

Commercial solar panels available on Earth have efficiencies that typically range from 17-22%. We will use 20% as a nice round number, and assume that this effects some cost savings versus choosing the most efficient panels.

Thus we now have a solar panel that takes a 500 W/m² with a conversion efficiency of 20%. We have our scenario now where each square metre of properly aligned panels produces 100 W/m².

A Beam of Sunlight

Using our minifigure scale, one square metre is three studs by three studs. Let’s produce a beam of sunlight, for illustration purposes. This beam of sunlight is at least 500 W of power, from which a perfectly aligned solar panel will produce at least 100 W.

Our sunbeam is like a column of sunlight. Here it’s pictured standing straight up, as though the sun were directly overhead. Unfortunately, the sun is rarely directly overhead. On Mars, this can only happen twice per year, at “high noon” between the latitudes of 25°S and 25°N. The rest of the time, it’s hitting any given position on Mars at an angle. Furthermore, the length of the day varies depending on your latitude and the time of year. This can significantly affect the amount of sunlight per m² that Mars can get during any given day.

Now, there’s a lot of trigonometry that one can do to calculate the sunlight at any given location on Mars, and that will be handled in a future post. This project is the Lego Mars Project, so let’s rather build something to physically simulate the different angles of sunlight.

If we vary the angle of our sunbeam, and look at how many studs it blocks, we can estimate the total sunlight just by counting studs! Using a lamp, we mount our sunbeam on an angle, and count the number of studs in shadow. In this case, there are 15 studs in the shadow of a 9 stud sunbeam, so our total amount of sunlight hitting the ground is down by 40%! But, what is the right angle to use...

Sun Angle Simulator Parameters

The first thing we’re going to do is assume that Mars has a circular orbit, rather than it’s slightly eccentric elliptical orbit. This greatly reduces the complexity of the problem, and isn’t so far from accurate as to present a problem.

Next, we need to be aware of the fact that there are two degrees of freedom to this problem: the first being the time of day (Mars spinning on its axis), and the second being the time of year (the Sun’s angle changes with the seasons).

We have two extremely simple test cases to keep in mind: in summer at the North Pole, there should be all day sunlight; in winter, all day darkness. At the equator at equinox, the sun should pass directly overhead.

We have two slightly less simple test cases to keep in mind for our limits: at 25°S and 25°N, the sun should be able to pass overhead at the winter solstice and summer solstice, respectively. And at 65°S and 65°N, you should have at least one day of all day sunlight and all day darkness.

Assuming our physical analogue can handle all four of these test cases as expected, we will have done pretty well.

So our Lego angle determination device requires two axes. Let’s block out the simplest form first, and then see what pieces we have available to build it.

The Equator - Sun Angles

Assume left is South, and right is North.

From left to right, you have, Winter solstice, Spring/Fall equinox, Summer solstice.

As a day goes by, the brown axis turns. The gold bar is the direction of the Sun. The grey plate is the horizon, or the ground. In the morning (top), the gold bars point at different spots on the horizon, but at the horizon nonetheless. By high noon (middle), the gold bars are pointing upwards, except only the centre one is pointing straight up. In winter and summer, the Sun is never directly overhead at the equator. At the end of the day (bottom), the gold bars are once again pointing at the horizon, but in the opposite direction.

The black piece is conveniently holding the brown bar horizontal in this example. The angle of the brown bar is what we must vary to get other locations on the planet.

It should be clear that you only get direct overhead sunlight twice per year, at noon on spring/fall equinoxes. And during winter/summer, noon is never worse than 25° away from overhead (65° from the horizon). The equator would be the best place to put a colony to harvest solar power.

The Poles - Sun Angles

To get this simulation to the poles, we must change the angle of the brown bar. This is conveniently done by swapping out the black pieces for the white pieces, which simply change the angle.

Once again, the direction of the Sun changes as the brown bar rotates. Polar summer is on the left, polar spring/fall equinox in the middle, and polar winter on the right.

It should be immediately apparent that rotating the brown bar in polar summer results in 24 hour sunlight, as the gold bar never points downwards. The centre example has the gold bar pointing directly at the horizon at equinox, and then you settle into cold dark winter, waiting half a year for the angle to change back up over the horizon.

It should be clear that the sun is never above 25° above the horizon at any time of year - and half the year, it is simply below the horizon completely. This would not be a good place to harvest solar power.

The Arctic Circle

In order to simulate the other latitudes, not the simple cases of the poles or the equator, we must be able to vary the angle of the brown bar. That angle needs to be able to vary 90° to reach both extremes. Fortunately, Lego has just such a piece.

Here we demonstrate the arctic circle (65°N) - three seasons, at three different times of day. On the left is summer solstice, the middle is spring/fall equinox, and the right is winter solstice. It is clear that at the arctic circle in summer, the gold rod never points below the horizon. Whereas, it spends exactly half the day above the horizon at the spring/fall equinox. And, at winter solstice, you get a moment on the horizon at high noon.

Concluding the Solar Angle Simulator

Success! We can simulate sunlight angles. And we can choose our latitude, time of year, and time of day. From this, we can tell that being nearer the equator is always better, from a sunlight perspective.

A note on math: this whole operation can be done with trigonometry. It is non-trivial to work out those equations, but it might be easier if you build your own simulator with Lego prior. These simulations work just as well for the Earth as they do for Mars, however, the angles are slightly different -- 23.5° rather than 25°. You can use it to predict where the sun will rise and set at your house. It won’t be perfect, because we assumed circular orbits, but it’ll be close!

I will keep one of these angle simulators aside, as a useful tool in other parts of this project.

Chemistry: The Atmosphere and the Importance of Water Ice

2020-04-14

All models are wrong, but some are useful. -- George Box, 1978

Before we can get into a serious discussion into choosing the location where we will put our colony, we need to take a diversion into chemistry and primary resources.

There are four elements which are the primary elements that make up all organic matter: carbon, oxygen, hydrogen, and nitrogen. These four form the basis for our entire biosphere on Earth. We will talk about them generally, first, and then in the context of Mars.

The Building Blocks of Humanity: The Organic Elements

A human male, a bit on the larger side, might weigh 100 kg (220 lbs) on Earth. I’m choosing 100 kg because it’s a nice round number for doing math, and we’re using metric. The human body has a lot of elements in it - see the wiki article for the full list. Summarizing, a 100 kg human is made up of 65 kg of oxygen, 18.5 kg of carbon, 9.5 kg of hydrogen, 3.2 kg of nitrogen, and some mineral stuff (calcium, phosphorus, potassium, sulphur, sodium, chlorine, magnesium). These elements are also important for just about any organic material we use or consume, and are found with varying ratios.

Another example, 100 kg of wood has: 50 kg carbon, 42 kg oxygen, 6 kg hydrogen, 1 kg nitrogen, and some mineral stuff (calcium, potassium, sodium, magnesium, iron, and manganese). These can be illustrated in Lego to stress the importance of these elements. Human body (left), wood (right). Each square is 100 studs in size, with the (approximate) composition recreated in the coloured blocks.

You’ll notice that I’m using a colouring scheme here. There is a somewhat standard colour code for chemistry called CPK colouring - based on the colours used in ball and stick models. We are choosing a number of colours so we can represent them in Lego.

The important takeaway is that the four primary elements make up most of the organic world. And we will need these in large quantities on Mars to sustain a human population.

The Martian Atmosphere Scores 3 out of 4

The first important thing to note is that Mars has an atmosphere. It’s thin, but it exists. This is both a blessing and a curse. Let’s talk about the good things first.

The composition of the Martian atmosphere is mostly carbon dioxide - 95%, with 3% nitrogen and 2% argon to round it out. There are some trace elements, but they aren’t important. Carbon dioxide by mass is 27% carbon, and the rest oxygen, so we can create a nice Lego diagram for the martian atmosphere too! 26% carbon, 69% oxygen, 3% nitrogen, 2% argon. We’ll use clear blocks to represent argon, since it’s inert. Let’s update our figure. Humans (left), wood (centre), atmosphere (right).

It is immediately apparent that the atmosphere of Mars provides most of the stuff that we need to live - all we need to do is suck it in with a big fan and do some work to it. Add some mineral stuff from the soil and you’re good to go. But there’s a major problem - there’s no hydrogen!

The Gravity of the Situation - Atmospheric Losses

Mars has 38% as much gravity as earth does. This means our 100 kg (220 lb) human can walk around feeling like they’ve lost some weight - and in fact, they will only weigh 38 kg (83 lbs) on Mars. This doesn’t mean that they literally shed 62 kg of material, but rather, there’s simply less force from gravity pulling them towards the planet. This is really useful for doing certain kinds of activities on Mars, such as building things out of iron or brick, as a human can lift a lot more on Mars without problems. But, it does present a problem when talking about the atmosphere. Here we divert into a bit of science.

Temperature is a concept that everyone is familiar with on a daily basis. Nobody really thinks about what temperature really is. But, under the hood, a gas is made up of a bunch of molecules - and they bump into each other all the time. The amount of energy these molecules have as they bump into each other is the temperature. If they’re moving faster, they bump into each other with more kinetic energy. Not all molecules will have exactly the same amount of kinetic energy - some will have more, and some less, but we call the average temperature.

In a really dense atmosphere, like Earth’s, there are a really really ridiculously high number of molecules in a cubic metre of air. On the order of 1025 to use scientific notation. That’s 10,000,000,000,000,000,000,000,000 molecules of air per cubic metre. On Mars, because the air is much thinner, there’s only 1023 molecules -- lop two zeros off the end. There’s so many molecules and they’re all banging into one another.

But what happens when you get close to the edge of space and the density of the air starts to drop. Well, this is where it gets interesting. Turns out the small light molecules like to move faster than the big heavy molecules. Imagine a group of people all standing around a pool table, and everyone randomly moves a pool ball. But, somewhere on the table is a tennis ball - much lighter. It goes flying. Some of the momentum of one of the randomly moving pool balls got transferred into the tennis ball.

Now, depending on how strong the gravity is on a planet, it is easier to escape that planet’s gravity. On Earth, something needs to be moving 11.2 km/s in order to escape the planet forever. On Mars, this is only 4.3 km/s. If you managed to get a tennis ball to move 5 km/s, it would escape Mars forever, but on Earth, it would fall back down to the surface (eventually).

Imagine the molecules of gas at the very top of the atmosphere all running into each other - the light ones get going faster, and can escape easier. On Mars, they can escape much easier.

This process is called Jeans Escape, or thermal escape. Borrowing a graph from wikipedia:

On Earth, we can hold onto every gas except the two lightest gases: hydrogen gas and helium. More importantly, we can hold onto water, ammonia, and methane - but most importantly water. Water is about 6% hydrogen and 94% oxygen. So our gravity preserves hydrogen in the form of water. And we have lots of it.

Mars, on the other hand, cannot hold onto water, ammonia, methane. These are the three common chemicals that store hydrogen in the solar system, aside from hydrogen gas, which only the gas giants can retain. This dooms Mars to lose water if water gets into the atmosphere. And it means we have trouble finding hydrogen on Mars. But we need hydrogen, right?

The Triple Point of Water

The most common form of water on Earth is in liquid form. But it can also exist as a gas (steam), or a solid (ice). The fact that water can exist as a liquid on Earth is rather remarkable. It is a side effect of our distance from the Sun keeping our temperature just right, and the fact that Earth has a nice thick atmosphere with lots of pressure, at least relative to Mars. The following graph was lifted from the wiki article on the triple point of water, but I’ve modified it to add Earth and Mars. This is a cartoon sketch - locations and values are approximate..

The important thing to note is that Mars is both cold and has low pressure. As a result, water cannot exist as a liquid on the surface of Mars. The plot points for Mars and Earth will move left or right depending on the temperature. For Mars, this means moving between ice and vapour, while on Earth this usually means moving between ice and liquid water.

So, on Mars, on a warm day, ice will melt. This is a bad thing, as water vapour in the atmosphere leaves Mars forever! Fortunately, it does so quite slowly, and there’s quite a bit of frozen water still on Mars at the ice caps. Here’s an image of the north polar ice cap on Mars. It is about 1000 km across and averages 2 km thick, which is 6% hydrogen. That’s a lot of hydrogen!

So, we found our hydrogen! Problem solved, right?

Long Term Considerations

If it is reasonable and possible to mine ice and extract hydrogen, a Martian colony needs to be aware that there is a limited supply on Mars. Depending on how careful one is with recycling it, this hydrogen could sustain a human colony on Mars for a very long time. However, if this hydrogen is turned into rocket fuel, and blasted off into space, over a long period of time, the total amount of hydrogen available on Mars will decrease. Furthermore, releasing the hydrogen into the atmosphere as hydrogen gas, water vapour, ammonia, or methane will slowly lead to a loss of hydrogen to space. It is important that long term planning of a colony consider hydrogen as both a short term limited resource, but also a long term limited resource.

Carbon and nitrogen may see similar shortages as well, once it has all been sucked out of the atmosphere. Oxygen may as well be considered infinite, since you can get it from rocks too.

A short term requirement for producing rocket fuel on Mars will use some combination of carbon, hydrogen, and oxygen. Some of that will necessarily be lost to space. In the long term, Mars should build alternative means to launch into space - elevators, railguns, trampolines, etc. to preserve its limited organic elements.

Ice Accessibility vs. Insolation

The available ice on Mars is generally near the poles. And, from our previous discussion on insolation, we decided that we wanted to be as close to the equator as possible to maximize solar power. But we need the hydrogen, so we need to be as close to the poles as possible. Thus it is useful to try to find large ice deposits near the equator. This is a major academic task at various research organizations.

Finding Lower Latitude Ice Deposits

2020-04-20

We’ve previously discussed the two major criteria for choosing a landing site, in terms of primary resources: energy from sunlight, and hydrogen via water ice. And these two criteria are at odds with each other. Thus, we need to search for large quantities of ice at lower latitudes. Fortunately, we have all sorts of instruments in orbit around Mars with a variety of instruments. In this chapter, we eschew Lego for the day and talk about finding ice.

Detecting Ice via High Energy Radiation from Orbit

The first useful tools are photos. It finds the obvious things, like ice caps. But, Mars has regular dust storms which cover most of the planet’s ice in a layer of debris. This is both a blessing and a curse: it makes ice harder to find, but it also protects the ice from sunlight, keeping it frozen in place for periods that could very well be billions of years.

There are a number of coarse mapping tools that can create broad scale maps. One such tool is the Gamma Ray Spectrometer on the Mars Odyssey spacecraft. Ice is not radioactive, so it doesn’t naturally emit gamma rays, thus we need to come at this problem sideways - we rely on secondary reactions from cosmic ray strikes. Borrowing a figure from JPL:

The Odyssey spacecraft has instrumentation to detect both gamma rays, and neutrons. Because hydrogen is such a tiny atom - it is essentially just a proton and an electron - a neutron striking it causes a specific amount of energy to be transferred into the system, which, when returning back to a normal state, causes radiation to be emitted.

Cosmic rays can penetrate fairly far into materials. But, the lower energy secondary radiation cannot penetrate as well. Thus, using this as a source of information on the location of hydrogen (water ice) is limited in its usefulness to the top metre or so of the soil. Any location on Mars where the temperature stays below the freezing point all year should retain ice in the top metre of soil, but near the equator, that ice should have sublimated into the atmosphere.

And, in fact, we can produce really coarse maps of water ice expected to be in the martian soil. The following image is from NASA/JPL/Los Alamos National Laboratory, created with the Odyssey Neutron Spectrometer.

The resolution of this map leaves something to be desired - the background crater outlines are fine, but the colours overlain are big blobs. This is because there is no way to focus neutrons on the spacecraft, so it’s based on flying around in orbit and noticing how the neutron counts change. Very coarse, but useful. It shows, for example, that the darling landing locations of science fiction, the Mariner Valley, is probably not great. This doesn’t preclude water ice in the Valley, as it may exist and simply be too coarse of a resultion to determine this, but certainly the region the Valley is in is quite dry.

But, halfway around the planet from Olympus Mons, there’s a lot of blue.

There’s been a lot of work on sharpening this data, in order to refine locations, and match them up with geology and soils interpreted from photos. Here’s one such example near the equator, in the blue area. The white areas outlined are known as the Medusae Fossae Formation, and is considered a candidate for ice bearing soil:

This would really be ideal if it bears up - all the sunlight in the world, and 10% water ice in the soil. However, estimates for the density of the material indicate that this is a thin layer of captured water in the near surface, and that the bulk of the material is likely dry, young, volcanic ash. It looks great on the radiation maps, because they are most sensitive to the near surface.

Using Radar from Orbit

Anecdotal story - the truth of which may or may not resemble reality, as it has been told and retold too many times, but: During WW2, when planes were first developing the use of radar altimeters, they used to fly over Greenland to get planes from North America to England. It was too far to fly on a single tank, and the great circle route was shorter if you flew over the ice. But planes kept on crashing into the ice, because their altimeter was getting reflections from the bottom of the ice rather than the top. So, while they thought they were 3 km above the surface, they were 3 km above the base of a 3 km thick ice sheet. The story remained an anecdote for a long time, until the development of modern ground penetrating radar equipment in the 1970s, incidentally as part of the Apollo program.

There are two excellent ground penetrating radar units currently in orbit around Mars, the MARSIS and SHARAD instruments. Radar and ice go together like hand in glove. We use it on Earth to measure ice thicknesses on lakes, map the bottoms of glaciers, etc. Ice is incredibly transparent to radar, and an excellent use case.

On Mars, the first radar results yielded information on the thicknesses of the ice caps. This was the design goal of the orbital radar systems. Here’s an example of an image creating a cross section of the Martian North Pole taken with the SHARAD instrument (NASA/JPL-Caltech/ASI/UT):

At the time of launch, these results were expected to be the best that the instrument can do. And they’re very impressive, seeing internal structures and layering within the ice cap. There have been a number of secondary results that are interesting as well, such as determining how much the weight of the ice cap is causing the Martian crust to bend, and thus drawing conclusions about interior properties. But those are outside our scope. We just want to find ice.

Ice in Craters

An unexpected result is the discovery of ice cap like radar responses from certain craters. One of the most prominent results is from Korelev crater. Image cropped from Brothers and Holt, 2016:

Now, Korolev crater is quite large, at 80 km across. If the interpreted thickness of this crater bottom ice deposit is accurate, we’re looking at 500 to 1000 m of ice almost anywhere in the crater. This is excellent. Unfortunately, Korolev crater is at 72°N, which is terrible for solar panels. But, the result proved how useful orbital GPR was in terms of being able to identify major, thick ice deposits.

Geomorphology and Imaging

The final form of water detection useful from the orbit of Mars is good old fashioned imaging. While it’s hard to find and image ice when it’s covered by debris, it’s possible to interpret where ice is from the textures of the images. The HiRISE instrument has probably been the most useful in this context, allowing extremely high resolution images where textural analysis has been possible. However, due to the incredibly high resolution of these images (25 cm pixels is not unusual), and the amount of data required to send back to Earth, we do not have global coverage at this resolution. So, lower resolution images are used to find areas of interest, then HiRISE gets pointed for a close up of something interesting. This method has been used to determine the locations of hundreds of features which are probably ice, including many glaciers, craters with ice floors, and valley floors that appear to have ice.

The end result is, we have been mapping glaciers all over the place, and some are in useful places! Map from Brough, Hubbard, Hubbard, 2019.

The craters in the study above were mostly identified between 30° and 60° latitude. At 30° latitude, our noon solar angle varies from 5° from zenith to 45° from zenith, and would be the equivalent of using solar in Northern India, North Africa, or Texas. This is fantastic!

Ideally, we use this map to find a tiny crater with ice, for our initial colony and landing, to keep the scope reasonable, but that has a large volume of ice in proximity.

Lego Criteria

In order to build a crater at a scale of 1 stud = 10 m and fit it onto a 96x96 stud table, we need to limit our crater selection to craters that are less than, say, 900m across. Furthermore, we want a crater that has HiRISE imagery in stereo (for topography) and a known ice quantity. This Lego related restriction is somewhat arbitrary, and a real colony wouldn’t have a size restriction. Nylosirtus Mensae looks promising. Much research required.

Choosing a Landing Site

2020-04-22

After obtaining a copy of the database associated with the aforementioned Brough, Hubbard, Hubbard, 2019 paper, we discovered that there were GIS Shapefiles included, complete with all sorts of juicy metadata. Using Google Earth Pro (free download), you can change from Earth to Mars. Then, drag and drop the shapefile into Google Earth Pro to get locations for mapped glaciers. You can click on a glacier to see what its details are, including estimates for volume of ice. Here’s a randomly selected glacier in Nilosirtus Mensae.

Now, not all of these glaciers have high resolution HiRISE imagery available, or a high resolution digital topography model, and Google Earth’s built in selection of HiRISE imagery is not up to date. So, to figure out which one we should choose, we need to go to the HiRISE website and take a look at the area.

Here’s the same area, approximately, as shown on the HiRISE DTM Mapping tool.

There are only three features on the HiRISE DTM map in this area that have high resolution DTMs. We could seek out HiRISE stereo pairs and produce our own DTMs, but that’s a rabbit hole that might take weeks to emerge from. Thus, for now, we look at these three and pick one. This unnamed glacier exists in both datasets, giving us some estimate for total volume of water ice available at our chosen location, plus a bunch of nearby glaciers should we need to expand beyond our initial site.

Let’s look at it in a few other datasets, to compare. Here’s the same Google Earth view as above, except with the CTX (wide angle context) imagery.

If we overlay the HiRISE bounding boxes, we can see that this was an imaging target of some scientist at some point, and that the two overlapping HiRISE images were taken together to produce the DTM. “Possible Glacier on Mesa Wall in Protonilus Mensae”. There’s also a bunch of HiRISE imaging nearby, but they are only single images, not pairs, so no DTMs are available.

Let’s look at the DTM to see if there is a flat spot suitable for landing and building.

There’s a difference in elevation, from the floor of the valley (south edge of image) to top of the plateau of about 1.5 km. This image comes with a convenient 500 m scale bar, and we were looking for a square that is 960 m by 960 m to build on our four Lego base plates. Using the very precise method of Microsoft Paint, we draw a box to choose our colony location.

Well, after all that work, we didn’t select a crater. But, we have ice, estimated to be well over a cubic km worth (hurrah!), we’re at 42.2 N latitude, which is okay for solar power angles. We’ve got a relatively flat spot to land rockets on dead centre -- or even further south if necessary, or one day on top of the plateau. There’s likely to be glacial moraine related gravel available, for burying things in. And, we have a south facing slope we can burrow into if we decide that tunnels are good -- and the walls weren’t created by an impact, so they likely aren’t fractured all to hell. The glacier forms a much less steep incline, should we desire a way to drive to the top of the plateau for whatever reason. And we have other glaciers nearby if satellite colonies make sense.

A Closer Look at HiRISE Images

There’s a wonderful writeup on this location attached to the high resolution HiRISE image. Let’s look at the highest resolution image and see what it looks like - oh, it’s over 700 MB in the best quality format (JPEG2000). We will need to use their HiView tool to look at this image.

In the bottom right, south of the glacier, you can see something called polygonal terrain, which indicates ice in the soil. The slope coming down from the mountain looks like it’s talus -- debris that’s fallen down the slope -- but there’s some small craters in it indicating it hasn’t moved in a long while (geologically speaking). Let’s zoom into a few spots. First, the ridges on the glacier. Full colour images are available there, so let’s use the colour version.

The scale of the original image is 25 cm per pixel, so the red line is 30 m across. In Lego terms, this means that this trough is three studs across. This is a scale we can work with.

Note that you can see a bolder on the surface, which is very small, likely on the scale of about a metre. It is casting a shadow.

We don’t have colour at the centre of our colony location, but the black and white image has excellent resolution. Let’s look at the toe of the hill and see what it looks like.

The 200 pixel scale is 50 m across, or 5 Lego studs. Some of the dunes at the bottom could actually be represented in Lego. That could be fun. There’s some debris coming down the slope, but it doesn’t look very large. This raises the curious question: what kind of rock(s) are coming down that wall?

Finally, let’s look at the polygonal terrain in the southeast corner of our Lego build site.

The scale bar is 600 pixels across, or 150 m. This is 15 studs. If we wanted to, we could represent them in great detail. These features are likely created through ground ice wedging. It will be interesting to look at these in the DTM and determine just how much vertical variation they produce.

Site Chosen, Now What?

The next steps will be to build this site in Lego. This will be a non-trivial task involving thousands of pieces and many many hours of time. To pull this off properly, we will first need to take our DTM, import it into something like GIS software, and create contour maps from it. Each contour should be one plate in thickness, or 4 metres vertical thickness. We take that contour map and start building upwards, one contour at a time. The creation of this contour map will warrant another chapter.