On habitable planets, rotational period can be assumed to vary significantly. What are the limits of human adaptation to these different conditions while maintaining a normal sleep schedule? The humans have to stay awake for a clear majority of the day, and take the clear majority of their sleep during the night.
Studies done on humans removed from the synchronizing effect of solar light exposure show that the circadian rhythm of sleep tends to re-synch around 36 hours.
It seems therefore that the human body can tune itself around that duration, even though it has to be seen how the solar exposure or lack thereof will influence it: people living at very high latitudes, experiencing long night/days during the year, do not seem to diverge from the 24 hours cycle. However it must be noted that there are other forcing factors which might influence the sleep/wake cycle.
How long are we talking about?
Evolution is your friend. Plop a bunch of humans onto a planet with a 100-hour day and a 100-hour night and wait 50,000 years and you'll be surprised what they evolve to do. Given enough time, any modification you wish is within suspension-of-disbelief.
But the shorter the time span, the less believable it is. Plop those same humans down and wait a month and what you should expect to find is some creative shutters that block every possible photon during the day while our intrepid humans happily sleep 7-10 hours a day.
So, the real question is, "given that I want humanity to conform to [insert very specific day/night conditions here], what would be a believable amount of time for humanity to achieve this conformance?"
As others have pointed out, humans are pretty adaptable in this regard, so the limits will be set by factors other than human biology as such.
The lower limit will be on the order of a couple of hours; much less, and the integrity of the planet with regard to centrifugal force comes into question.
The upper limit will be on the order of a couple of years; much more, and it's impossible to store food overnight, and everyone will have starved to death by the time morning comes and agriculture is possible again.
I don't know.
Nobody knows exactly. But several other answers have mentioned various factors to consider. And here is something else to consider.
If future humans build space habitats they will have control over the periods of light and darek in any "outdoors" parts of the space habitats, and of course they will have artifical lighting for inside their homes and workplaces, etc. So they will have total control over the lengths of days and nights in those space habitats.
And if humans build giant arcologies on Earth or other planets, most or all the interiors of those archologies will be illuminated by artificial lighting, so the light levels outdoors will only matter to those who go outside on rare occassions.
And the same goes for underground cities on Earth or other planets.
But if humans settle on naturally habitable worlds, other planets or moons, or terraform other planets or moons to be habitable for humans, and if those humans decide to live as much outdoors as much of the time as modern humans do, the natural cycles of light and darkness will be important to the colonists whenever they are outdoors, and going outdoors will be something people do several times a day.
Thus the colonista - if they choose not to spend all of their time indoors in giant archologies - will have to adjust their cycles of sleeping and waking to the natural cycles on the planet.
And most of the answers so far have discussed how well humans could adjust to day night cycles of different lengths than Earth's.
But suppoe that human settlers on an alien planet aren't advanced enough to have food synthsizers to produce food out of raw materials and instead have to grow food outdoors. If the humans can't find any native plants they can eat, they will have to plant crops of Earth plants.
And those Earth plants will have to be capable of surviving and even thriving on the alien planet, which will mean that the conditions on the settled parts of the planet will have to be similar enough to the conditions on the densely populated parts of Earth for the plants to thrive.
So finding out the limits of day and night lengths that major Earth crops can tolerate would be important for answering the question.
And of course humans need the right atmosphere to breathe. And of course on Earth the oxygen which he need was produced by plants using photosynthesis. If the planet doesn't have native plants, or plants imported from Earth, to produce oxygen humans won't be able to breathe on the planet and will have to live totally indoors in arcologies with totally sealed environments like moon bases would have. And if they do that they will have artificial lighting indoors and will replicate the day/night cycle of Earth, so the question would be meaningless.
Of course it took hundreds of millions or billions of years for photosythetic plants to produce enough oxygen that it accumulated in Earth's atmosphere faster than it combined with minerals and left the atmosphere. If humans bring Earth plants to a planet without oxygen producing plant life, it may take many millions of years longer to build up a breathable atmosphere than the needs of your story allow.
So I guess that the humans in your story will explore, crashland, or settle on a planet which has a naturally oxygen rich atmosphere.
And maybe the humans would keep an Earth like approximatley 24 hours cycle of light and dark inside their homes, and only go outside when the outside light period coincides with their waking period of light inside. Depending on the mathematical relationships between the two periods, the times when the interior human day and the exterior planetary day can be as common or as rare, as long or as short, as fits the story.
See also the discussion of the possible length of day on a habitable planet in Habitable Planets for man, 1964, Stephen H. Dole, pages 58-61. Dole worried that plants might die in the sunless nights if they were too long.
And also see discussions whether planets which are tidally locked to their stars, having their rotation periods slowed so that one side always faces the star and the other side always faces away from the stars, can be habitable. The day side of the planet might get too hot, and all the water and even air might freeze solid on the bitterly cold night side. But possibly the water and atmosphere might carry enough heat from the Eternal day side to the eternal night side to keep both sides at temperatures suitable for life. But possibly an atmosphere thick enough to carry enough heat from the day side might be so dense it would block starlight from reaching the surface of the planet, making photosynthesis and oxygen production impossible.
Astronomers for many years ruled out red dwarfs as potential abodes for life. Their small size (from 0.08 to 0.45 solar masses) means that their nuclear reactions proceed exceptionally slowly, and they emit very little light (from 3% of that produced by the Sun to as little as 0.01%). Any planet in orbit around a red dwarf would have to huddle very close to its parent star to attain Earth-like surface temperatures; from 0.3 AU (just inside the orbit of Mercury) for a star like Lacaille 8760, to as little as 0.032 AU for a star like Proxima Centauri (such a world would have a year lasting just 6.3 days). At those distances, the star's gravity would cause tidal locking. One side of the planet would eternally face the star, while the other would always face away from it. The only ways in which potential life could avoid either an inferno or a deep freeze would be if the planet had an atmosphere thick enough to transfer the star's heat from the day side to the night side,...
This pessimism has been tempered by research. Studies by Robert Haberle and Manoj Joshi of NASA's Ames Research Center in California have shown that a planet's atmosphere (assuming it included greenhouse gases CO2 and H2O) need only be 100 millibars (0.10 atm), for the star's heat to be effectively carried to the night side. This is well within the levels required for photosynthesis, though water would still remain frozen on the dark side in some of their models. Martin Heath of Greenwich Community College, has shown that seawater, too, could be effectively circulated without freezing solid if the ocean basins were deep enough to allow free flow beneath the night side's ice cap. Further research—including a consideration of the amount of photosynthetically active radiation—suggested that tidally locked planets in red dwarf systems might at least be habitable for higher plants.
But could alien plants survive in eternal day?
I'm sure that there has ben some research in subjecting Earth plants to artifical light for periods longer than normal daylight, and possibly even to constant 24 hours a day light. If that research show that it is easy for Earth plants, adapted to a day-night cycle, to flourish with 24 hours a day illumination, then alien plants adaped to their world should do fine with 24 hours a day light. So that is something to look up.
And of course if alien plants could flourish in eternal day, other alien plants should be able to flourish during alien days and nights which last for several Earth hours, Earth days, Earth weeks, Earth months, Earth years, Earth decades, Earth centuries, Earth millennia, etc., so long as the temperatures don't get too hot or too cold.
The people would just have to stay inside with artificial cycles of light and dark, and only go outside when their artifical light and waking time coincided with the natural day outside on the planet.
I don't have hard scientific facts, but these:
- The brain needs dreaming for "garbage collecting", typically done when sleeping, so there needs to be some balance between sleeping and being awake.
- The eyes need a darkness phase to recover
- Skin needs light for vitamin D production
- Sunny days can reduce the amount of sleep needed, while the opposite may be true, too
- On short term (a few days) one can reduce sleep significantly, but eventually the brain will switch to "emergency shutdown mode" (meaning you can fall asleep while standing, or even while driving a car)
- Digestion also needs periods of rest; they say sleeping actually helps loosing weight
- Heart and muscles probably also need periods of rest.
So (as others said already) the day and night cycle influences the sleep/wake cycle, but the limits are not very flexible. I also think there are no real long-term experiments exploring the limits