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So there have been question similar to this, but the answer that I have found isn't quite what I want, because they are specific to that world they are from. This world is an earth-like planet, with a singular moon that orbits it. The orbital period of this world is 256 days, there are 8 months with 32 days, each month has 1 moon phase, and it takes the full 256 days to have a full cycle (Say it was the second month of summer, so Termes in this world's case, that month starts as a waning gibbous, and ends as a last quarter risen, making it so the month after it starts as at last quarter). I was wonder if I could reasonably have a rare occasion where there is an entire 32 day long eclipse that closes the world in darkness.

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    $\begingroup$ At first glance, given your calendar: no. You seem to lack knowledge of what an lunar eclipse actually is and how it is caused. See en.wikipedia.org/wiki/Lunar_eclipse .. study that and understand why a full cycle of occlusion cannot happen. The moon moves, the eclipse is a shadow. Also, a lunar eclipse will never occur everywhere on your planet same time, unless your moon is several times the size of your planet, $\endgroup$
    – Goodies
    Jul 7, 2022 at 8:13
  • $\begingroup$ @Goodies thank you for the input, just finished reading up on Lunar Eclipses. This news is slightly upsetting, but this is a science-fiction fantasy setting I am making, so I will have to make it be a magical occurrence. Also by "Full Cycle of Occlusion" were you thinking I was wanting it to last the entire 256 day moon cycle? I only want it to last a 32 day period, because that is the length of my months, either way if it's not possible by scientific explanation that's fine. Thank you for the help. $\endgroup$ Jul 7, 2022 at 8:44
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    $\begingroup$ @Goodies When you said "a lunar eclipse will never occur everywhere on your planet same time, unless your moon is several times the size of your planet," were you thinking of a solar eclipse? A lunar eclipse is the moon passing through the planet's shadow (requiring a small enough moon) and can be seen from all over the moon-facing side of the planet. I agree on the rest though. $\endgroup$ Jul 7, 2022 at 9:00
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    $\begingroup$ @PastychomperthanksMonica As far as I know, lunar eclipses (aka "blood but actually orangey" moons) doesn't "close the world in darkness". At least not our world :p. $\endgroup$ Jul 7, 2022 at 12:48
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    $\begingroup$ This might be possible is you assume a gargantuan sun to allow for a wide planetary orbit, then have an equally large orbit for the moon to allow for such a long lunar orbit, but then you would have to super-size the moon to get an eclipse that can be seen from the planet, but keep the density low so it can still orbit. That said, I've no idea of the kinds of calculations you'd use to prove this was possible. $\endgroup$
    – Halfthawed
    Jul 7, 2022 at 14:39

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Everyone would die.

You've described your year and lunar cycle as both being 256 days. This means that in one 32-day month, your planet moves 45° around its star. There are two possible cases for the motion of the moon.

Prograde orbit

In this case, the moon would move 90° around the planet per month, such that the star-planet-moon angle changes by 45°. So, at least the proposed lunar cycle is possible. However, for even a single point on the planet to experience a 32-day solar eclipse, the moon would need to be so large that it takes up 45° of the sky. This means having a diameter larger than its orbital distance. In this scenario, the moon would either be too close to have a stable orbit (and crash into the planet) or it would be larger than the planet (which would then crash into the "moon"). Either way, the two bodies collide.

Retrograde orbit

The only other way for a lunar cycle to equal a solar year is if the moon does not move relative to the planet. This would require the moon having no lateral motion, and therefore it would not be in an orbit, but rather a free-fall directly toward the planet. Again, collision is inevitable.

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  • $\begingroup$ Thank you all for your input, while I was hoping it might have been possible for a month long eclipse without further use of the explanation of it being magic you guys have helped me a lot. $\endgroup$ Jul 7, 2022 at 15:04
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    $\begingroup$ @GamerOvertron If you are really set on having month-long solar eclipses without objects just outright stopping in the sky, your story could take place on a moon, and have a big planet do the eclipsing. Let rᵣ = moon-planet radius / planet-sun radius, and let rₘ = planet mass / sun mass. Orbital period is proportional to √(radius³/parent mass), so rᵣ³ = rₘ. But, gravity is proportional to mass and radius⁻², so for the sun to not pull the moon out of orbit, rᵣ² << rₘ. This is a problem, as now we need rᵣ > 1, which isn't possible. So magic would still be required in some capacity. $\endgroup$ Jul 7, 2022 at 20:12
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Short Answer: the orbit of such a moon would be highly unstable.

Long Answer:

Scientists have put a lot of thought into the possiblity of life on very large moons orbiting giant planets in the habitable zones of their stars.

Most stars are red dwarf stars. A planet in the habitable zone of a red dwarf star would be too deep in the gravity of the star, and the strong tidal forces from the star would slow down the rotation of the planet until it was tidally locked, so one side of the planet always faced the star in eternal light and heat and the other side of hte planet always faced away in eternal dark and cold.

To avoid that, astronomers consider the case of giant sized moons orbiting giant planets in the habitable zones of red dward stars. Those moons would be tidally locked to their planets and not to their stars, and so they would have day/night cycles equal to their orbital periods around their planets.

So there have been many theoretical investigations about the possibilities of giant habitable moons of giant palnets in the habitable zones of stars.

For example, there is "Exomoon Habitatabiity constrained by illumination and tidal heating", Rene Heller and Roy Barnes, 2013.

https://arxiv.org/abs/1209.5323

On page 3 they write:

The synchronized rotation periods of putative Earth-mass exomoons around giant planets could be in the same range as the orbital periods of the Galilean moons around Jupiter (1.7d−16.7d) and as Titan’s orbital period around Saturn (≈16d) (NASA/JPL planetary satellite ephemerides)4.

So a potentially habitable exomoon of a giant exoplanet in the habitable zone of star might have a day about 1.7 to 16.7 Earth days. Maybe about 1.0 to 20.0 Earth days.

And their next sentence says:

The longest possible length of a satellite’s day compatible with Hill stability has been shown to be about P∗p/9, P∗p being the planet’s orbital period about the star (Kipping 2009a).

That means that if a moon has a stable orbit the orbital period of the planet around the star has to be at least about 9 times the orbital period of the moon around the planet. Which should apply to all moons of all planets.

And here is a link to the article they cite:

https://academic.oup.com/mnras/article/392/1/181/1071655

I supose there is a slight possibiity that you could find some flaws in that article.

Otherwise you will have to accept that all planets will have years at least 9 times as long as the orbital periods of any of their moons. It is possible that a planet might have a moon with an orbital period equal to the planet's year for a brief period of time, but that moon would have a highly unstable orbit and soon it would either crash into the planet or be lost into interplanetary space again.

There is no way that a large regular moon of a planet that orbits the planet for atronomical and geological eras of time could have an orbital period longer than about one ninth of the orbital period of hte planet around the star.

I note that Habitable Planets for Man, Stephen H. Dole, 1964, pages 61 to 63, concludes that a planet would have to develop for at least about 2 or 3 billion (2,000,000,000 or 3,000,000,000) years before it would become habitable for humans. After that time it would have lost all of its moons that were in unstable orbits.

https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf

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See my answer to a related question on Physics for a discussion of how a slow orbit eventually starts to interact with the Lagrange points.

The duration of the eclipse is related to the relative sizes of the bodies involved and their shadows. In our world the Earth is larger than the Moon. The shadow of the Moon on the Earth (the "umbra," in which the eclipse is total) is no more than a few hundred miles across, and totality lasts for minutes. However, the shadow of the Earth on the Moon can be larger than the Moon, so that the entire Moon can be in eclipse at once, and lunar eclipses last for hours.

You could have a "long" eclipse on an Earthlike moon orbiting a giant planet, but the eclipse would always be a short fraction of the (synodic) month. For circular orbits, the longest eclipse is roughly the ratio of the angular size of the occulting body to the full 360⁰ circle of its path through the sky. For example, the Earth is 2⁰ wide in the moon's sky, and 2/360 of a month is about four hours, a little longer than the totality of a deep lunar eclipse. If the eclipsing object occupied 36⁰ across the sky, totality could last as much as 10% of a month. Your fist, held at arm's length, is about 10⁰ wide.

An eclipse would not happen every month if the moon's orbit was far from the ecliptic. For the Earth-Moon system, not every full moon is eclipsed --- only when the full moon happens to be crossing the plane of the sun-earth orbit, typically twice a year. Jupiter's Galilean moons orbit quite close to the ecliptic and are eclipsed in every orbit around Jupiter. (You can watch them vanish or reappear in your small telescope; your favorite astronomy magazine publishes times.) Uranus's moons orbit in its equitorial plane, roughly 90⁰ from the ecliptic, and are eclipsed only near Uranus's equinox.

An observer in deep eclipse would not see the star's corona, which is only a few times the diameter of the star's photosphere. They would see light refracted through any atmosphere on the eclipsing body. A person observing the Earth from the Moon during a lunar eclipse would see the night side of the Earth, with a ring at the edge of all Earth's sunrises and sunsets; this transmitted twilight is why the totally-eclipsed Moon turns red.

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    $\begingroup$ "All Earth's sunrises and sunsets..." $\endgroup$
    – Tom
    Jul 8, 2022 at 0:31

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