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Survival of the fittest - follow up #1

A few weeks ago we introduced to you one of the problems that we face during our mission to the moon. How is it possible to keep a rover warm enough in the ice-cold lunar night, so that the damage due to the cold is kept to a minimum? You sent us a number of interesting ideas and we promised to analyze and judge them. Now we are starting a small series, and introduce one of your ideas in each post and evaluate it.

But first, let's review the problem once more and provide some further details. On the moon, our rover is subject to a very wide range of temperatures and types of radiation. The Lunar sourcebook, a very valuable resource for us, lists average values of 107°C (225°F) during the day and -153°C (-243°F) during the night. More precisely, at the equator (e.g. at the Apollo 12 site, ~3°S 23°W) the temperature is 117°C (243°F) during daytime and drops to -170°C (-274°F) at night. Away from the equator (e.g. Apollo 17: ~20°N 30°E) these temperatures change, and the average temperature decreases. There are various reasons for that: For one thing, the incident light from the sun hits the surface at a different angle, and the light from the earth (its „planetary albedo“) also decreases somewhat. And then there are some special cases: For instance, in the polar regions there are areas in craters where the sun never shines, and areas on mountaintops that are constantly exposed to sunlight.

Now, assuming a landing site near the Apollo 12 site, we know the temperature of that area rather precisely. For 14 days there is a lot of sun, and there are cozy 120°C (248°F); and then come 14 days of bitterly cold night at -170°C (-274°F). These temperature differences are not really beneficial to the materials and electronics. Different materials have different thermal expansion coefficients, leading to the buildup of strain in the rover, and potentially causing parts to break. Moreover, not all materials can handle low temperatures well and e.g. become brittle and crumble or lose their structural integrity or melt like a piece of chocolate in the sun above certain temperatures. There are two basic ways to solve this problem: either one only chooses materials that are designed for the lunar temperature range and builds the rover in a way to avoid buildup of strain; or one makes sure that the rover is only subjected to a certain specified, safe, temperature range. Both of these are very difficult or outright impossible to achieve, so that one chooses an optimal combination of both: Good materials in a well-defined temperature range.

Another factor, which makes survival on the moon even more difficult, is its slow rotation and the resulting length of the day. If lunar days only lasted 24 hours, like on earth, the rover couldn't heat up as much during the day and cool down so much during the night. Since it's not exactly feasible to simply accelerate the moon, you have to manage your available energy very well and prepare for 14 earth days (~336 hours), if you want to guarantee a certain temperature for the entire time.

Thus, while you have to keep the rover cool during the day, at night it must be kept warm. Since we already mentioned the former issue already in a previous article, we now concentrate on the latter. But in order to meaningfully consider heat management, it is necessary to know where the energy comes from, how it acts on the rover, and where it is lost.

The moon has almost no atmosphere, which is why many effects that we know from Earth don't exist on the moon in this form. The number of particles per cm³ is very small (~2x105 molecules/cm3 during lunar night and ~104 molecules/cm3 during lunar day on the moon vs. 2x1019 molecules/cm3 on Earth). Because of that there is no heat transfer due to heat conduction. On the one hand, this means that the rover cannot absorb any heat energy from its surroundings; on the other hand it doesn't lose any energy to its surroundings, either.

So, only one possibility remains: Heat transfer through radiation. The closest significant radiation source is the sun. We simply assume the value of the radiated power is equal to those for Earth, since the distance Moon-Earth (0.002794 AU) is insignificant compared to the distance Earth-Sun (1 AU). At the equator, the sun radiates between 1323 W/m2 and 1415 W/m2 onto a flat surface. Aside from that, there is also the lunar albedo (the solar radiation reflected from the lunar surface towards the rover and space), the albedo of Earth (the reflected radiation from the earth towards the moon), and the radiance of the moon and the earth themselves. The radiance and albedo of the earth are not really substantial, but cannot be disregarded entirely.

The only possibility for the rover to lose heat is also by radiation. The radiated power (P) depends on the area of the radiating surface (A), the emissivity of the material (ε) and the temperature of the material (T). P = A * ε * σ * T⁴, where σ is the Stefan-Boltzmann constant. To minimize the radiated energy, all one can do is to make sure that the rover's materials have a small emissivity. This is because the size of the rover can't be changed easily and the temperature of the material is determined by the total incident radiation at the end of the day. For example, non-oxidized aluminum (100°C) has an emissivity of ε = 0.03, while strongly oxidized aluminum (93°C) has an emissivity ε = 0.2. Thus, the choice of materials has a significant influence.

When you have optimized the material of the rover but the energy loss is still too high, there are a number of other strategies that can be used. And in the next blog post we are going to explore them further.

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Image Credits:
  • "Lunar Landing Sites Chart" © by NASA - Public Domain

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