As NASA ramps up preparations for Project Artemis to return astronauts to the moon, one of the many technical challenges it faces is providing an ultra-precise lunar map to use when astronauts are exploring the moon. Even small but unexpected surface obstructions could spell disaster for a landing spacecraft or a rover driving across the lunar surface.

When Apollo astronauts went to the moon more than 50 years ago, their landing sites were carefully chosen for relative blandness. Bland was safer! But Artemis astronauts intend to visit the most interesting sites on the moon, not just bland ones.

A Better Lunar Map

Over the decades since Apollo, scientists have imaged the moon's surface features in enormous detail, so the Artemis lunar map team has far better information to work from than their predecessors had in the 1960s. As Space.com reports, the photographic imagery that is used to construct a lunar map has very high precision indeed, with one pixel covering less than one square meter of the surface. Thus, scientists can establish the latitude and longitude of a lunar feature to within a meter — accurate enough to support safe landing and driving on the lunar surface.

But the laser altimetry that is used to establish the elevation of the lunar surface is far less precise, accurate only within about 100 meters. This is nowhere near good enough.

There are existing methods for measuring shadows on the lunar surface to determine more precise elevation "fixes" for topographical mapping, but these are typically cumbersome. Not only are they computationally intensive, putting heavy demands on computers, they also require a great deal of estimating and fiddling that only highly trained people can do, but they must do so very carefully — and slowly.

For the lunar map team, this was a severe bottleneck, but help was on the way.

The Cliffs of Stevns Klint

As the Artemis lunar map team wrestled with this challenge, a geophysics graduate student at the University of Copenhagen's Niels Bohr Institute also ran into a problem. Former grad student Iris Fernandes (per the University of Copenhagen, she has since earned her PhD) wanted to use photographic images of Stevns Klint — a dramatic and geologically important limestone cliff on an island in Denmark — to analyze surface patterns on the face of the cliff.

Her problem, as Science Daily reports, was that the algorithm she was using to study the patterns was thrown off by complex interplay of sunlight and shading in the photographs. As Fernandes explains, "It created a bias in the model. We needed to find ways to remove the shades, in order to remove the bias."

To mathematically cancel out the shading, Fernandes needed a test environment with varied rock forms, a lack of patterned colors, and where sunlight and shadow were the dominant features. Like many geophysicists, Fernandes was interested in the planets, and she was aware of a place that met her requirements well: the moon.

Shades of Gray

We may sing about the light of the silvery moon, but the lunar surface is almost entirely gray, with few small-scale patterns other than those produced by sunlight and shadow. This made it a perfect place for studying those shading patterns — and finding a way to cancel them out.

As it happens, the human eye and the vision centers of the brain, shaped by millions of years of evolution, are extremely good at processing the shadings of light and shadow. As a result, even a good pair of binoculars can vividly display the shadows cast by lunar mountain ranges.

Because this effect is most visible near the lunar terminator (the lines of dawn and dusk lie) where the sun is very low in the lunar sky and shadows correspondingly long, one effect is to make lunar mountains appear much more jagged in a telescope than they actually are. This capability of the human eye was crucial to the established methods for determining elevation from light and shadow. But the need for extensive human input and judgment was exactly what made these methods so cumbersome.

Adding to the intrinsic complexity of these established methods was the wide range of variation in the quality of lunar imagery and laser altimetry data, which Fernandes had to deal with, similar to the Artemis lunar map team.

Eyes on the Prize

Faced with all this complexity, Fernandes and her PhD advisor, geophysicist Klaus Mosegaard, focused tightly on the underlying mathematics. They zeroed in on "inverse theory" — the mathematical process of getting from a result to the inputs that would produce that result — as well as the Sylvester Equation. As Fernandes explains in Science Daily, they set to work "basically, to see if this equation could solve the problem."

"And it did," she adds. "You could say that we â€¦ found the mathematical key to a door that had remained closed for many years."

The new mathematical method that Fernandes pioneered greatly reduces the amount of computation (and pre-computation "fiddling") required and takes out the guesswork. The variations in the quality of source data are automatically incorporated as inputs, producing not only a more precise output (such as a lunar map) but also one with a clearly specified precision level. Fernandes notes, "This method is fast, it is precise and it doesn't have to rely on any assumptions."

Science: The Surprise Machine

As Science Daily notes, scientific curiosity can lead you to surprising places. Fernandes and Mosegaard set out with the initial goal of canceling out the patterns of sunlight and shading on the cliffs of Stevns Klint, effectively eliminating light shading in order to reveal other patterns in the cliff rocks. They were not at all concerned with the challenges of elevation measurement and the limitations of laser altimetry, since the cliffs are right here on Planet Earth and can be surveyed as precisely as needed.

For NASA, in contrast, the patterns of sunlight and shading on the moon's surface are the whole ballgame — the key to providing a topographical map with sufficient precision for human astronauts exploring the moon. And the same techniques can be applied to Mars, asteroids, outer-planet moons and other bodies with solid surfaces awaiting exploration.

Meanwhile, Fernandes also sees other possible implications, such as using shading patterns to look for small, round stones on Mars as a sign that they might once have been exposed to water.

Science as a human activity is, in no small part, the art of finding surprises and putting them to surprising use.

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