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Compared to Martian nights, Lunar nights are long and cold. This has posed a lot of challenges in the past.

What specific challenges does long duration night pose? What are the methods to over come? Will this pose as an issue for Lunar habitat?

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    $\begingroup$ Even if there are no components like batteries that would be damaged or destroyed by freezing, temperature cycles from very cold to maximum tolerable operating temperature will decrease reliability of the rover. Frequent temperature cycles may cause mechanical stress if materials with different thermal expansion are used resulting in micro cracks. $\endgroup$ – Uwe Jan 10 at 16:22
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In addition to the points in Hobbes answer about increased power consumption is the question of where that power is coming from. If using a solar array you need to use batteries to store power through the two weeks of darkness and keep your electronics warm. This especially matters with the batteries themselves since they loose capacity when cold, so you end up needing to use battery power to keep the batteries warm and working. The batteries are also physically large, increasing heat loss area. See related question.

Radioisotope heaters can help, as used on the Lunakhods and mars rovers but you cannot turn them off so need potentially need to add cooling to avoid problems during the day and before launch. They are also a problem to get hold of if you do not also happen to have a large nuclear power program, and can complicate the approval process.

Going full RTG like Curiosity solves both power and heat problems but makes the political challenges even more substantial, and there is a limit to how much material is actually available at any one time to make RTGs with.

In terms of human habitation burying the habitat would both provide insulation and naturally means the temperature will tend to average out through the day/night cycle, but that average still appears to be well below zero. Actually burrowing that deep is also non trivial, especially if your digging machinery also needs to be kept warm overnight.

Having a full nuclear reactor as part of the first 'day' of landed equipment to a habitat simplifies both heat and power but would be even more complex politically and ties the colony to the continued willingness of an earth based state to keep producing and flying nuclear fuel until they had the industrial base to do it in situ (a separate interesting question).

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  • $\begingroup$ "get hold of" and "approval process" may be less of a challenge when space agency, government, nuclear regulators, nuclear reactors, and military are all ultimately run by the same person. $\endgroup$ – uhoh Jan 11 at 2:15
  • $\begingroup$ Chang'e 4 its Yutu rover currently operating on the far side of the Moon use both an RTG and solar power. They're designed to operate for months, but hoped to last years. $\endgroup$ – Schwern Jan 11 at 3:51
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    $\begingroup$ @Schwern, the admittedly vague details suggest both are pure solar powered but radioactively heated, which means they still need to sleep at night but have a simpler design, and means the worst case 'blows up on the pad' numbers involve grams of material rather than kgs. $\endgroup$ – GremlinWranger Jan 11 at 5:29
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At night, the temperature on the lunar surface drops to something like -100 ºC. This is too low to operate many of the parts of a rover, so you'd have to run heaters to get the electronics and mechanical parts to operating temperatures. This requires a lot of power.

It also complicates operations because you need light to see where you're going. Nighttime driving is far more difficult than daytime driving. When a rover drives autonomously, this goes double because the image maps you made during the day won't match what you see at night. Night driving also requires light, which is another big power drain.

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From Infinity Beckoned: Adventuring Through the Inner Solar System, 1969–1989 Jay Gallentine, U of Nebraska Press, 2016, 504 pp:

Google Books

Realize that an entire lunar day runs approximately one Earth month— four weeks. For two of those weeks the sun is “up” on the moon, and for the other two it’s down. No sunlight on the lunar surface means nothing’s lighting up the solar cells on Lunokhod, which by extension means not enough power to move or run a science instrument or do much of anything. And it’s mighty cold up there when the sun goes down: 250 below, Fahrenheit. “At the nighttime, it is so cold that if you don’t have a heater inside, everything could be frozen,” explained Alexander Basilevsky. “The batteries—they had liquid, so that liquid would be frozen.” Insulation splits. Wiring cracks. Rovers break. Closing the lid helped warm things up by sealing over the massive thermal radiator sitting at the top of the tub. Whatever heat lingered inside would thus be temporarily retained. But that by itself wouldn’t keep the home fires burning. Erupting from the tail end of Lunokhod’s body, like some giant pimple on its butt, hung a twenty-four-pound can of polonium. Next to circus peanuts, it’s some of the most dangerous stuff on planet Earth. Polonium is nasty—radioactive and toxic and murderous—but its natural decay generates free heat and that’s precisely what the idea was in using it. (A compara- tively mundane element like uranium would never produce enough warmth for two constant weeks of sustenance—unless so much was crammed inside Lunokhod that it couldn’t possibly get off the ground. You need material with a rapid period of decay.) An arrangement of pipes arterially wended their way through the rover, fans circulating air to all extremities. Normally 1 he fans and pipes expelled hot air and kept the buggy from overheating during those tropical lunar days. But after the sun went down it had the opposite problem—not enough heat. So at the back of the rover this piping intersected the polonium and voila, instant heater.

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