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Is it possible to have a stable system wherein the moon of an Earth-like planet is visible only during certain parts of the year (seasons) from a fixed point on the surface, mimicking the way some more distant bodies seem to be below the horizon during specific seasons?

What would be the characteristics of such a system?

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  • $\begingroup$ Please note than those distant stars which are visible (for example) in winter and not visible in summer are not visible in summer not because they are permanently below the horizon but because the sun is up when they are above the horizon. This is exactly the same situation which makes for moonless nights: for a few days before and after a new moon, the moon rises and sets pretty much at the same time as the sun. $\endgroup$
    – AlexP
    Nov 27, 2023 at 13:42
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    $\begingroup$ You might consider also asking this question on: astronomy.stackexchange.com $\endgroup$ Nov 27, 2023 at 20:45

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I think that is what happens when the planet is close to the point of becoming tidally locked to its moon: when the duration of a revolution around its axis is close but not the same as the duration of a revolution of the moon around the planet, there will be times of the year in which the moon will be visible in the sky, and times where the moon will not be visible.

To a certain extent it happens already today with Earth and Moon, but still on the scale of hours, not months.

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    $\begingroup$ also note that for fixed seasons where the moon is visible, the duration of the relative revolution (between planet and moon) has to be the same as the revolution time of the planet around the sun. Otherwise the "moon-season" would shift over time and not be "summertime is moon time" $\endgroup$
    – datacube
    Nov 27, 2023 at 12:57
  • $\begingroup$ @datacube I wonder if that could be achieved by some weird kind of orbital resonance. (It's not obvious to me whether it can.) $\endgroup$
    – N. Virgo
    Nov 28, 2023 at 2:55
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This is definitely tricky to manage for an Earth-Moon-Sun like system.

The daily motion of the Sun is generated by the rotation of the Earth. The seasons are caused by the orbit of the Earth around the Sun. The axis of rotation of the Earth is inclined at about 23.5 degrees to the Ecliptic, which is the plane of the Earth's orbit. The orbital plane of the Moon about the Earth is inclined at about 5 degrees to the ecliptic, which causes the Moon to go off the Sun's path in the sky, and we don't have eclipses every time they pass.

If planets condense from a debris cloud, this tends to give orbiting bodies with a common plane. Most of the orbits of the planets are close to the ecliptic plane, and to a lesser extend the axes of rotation are perpendicular to the ecliptic (noteworthy exception with Uranus). This suggests that if the Earth-Moon system could condense from some debris cloud at a much smaller scale than the Earth-s orbit, then it would be possible for the Earth-Moon system to evolve with a tilted plane.

There is a more subtle effect, called the Kozai-Lidov effect. You can have an Earth-Moon system with a tilted plane, but this can exchange orbital inclination for orbital eccentricity, and back again. Above an angle of about 40 degrees, this means the orbit eventually becomes so eccentric that the two bodies hit each other.

So, what about Uranus? That whole system is tilted over at 90 degrees. The answer is that the Kozai-Lidov effect gets a lot weaker with distance, so what would cause a binary planet to crash in a year at Earth's orbit might take many millions of years for an outer gas giant. Even if your moon is tiny, like Phobos about Mars, and is probably a captured asteroid so it can have any orbital plane it likes, it is only still orbiting because its orbital plane is close to the ecliptic.

The Earth-Moon orbit plane is probably pretty close to the ecliptic. You moon might be below the ecliptic for half a lunar month, and above it for half a lunar month. Our Moon is probably hidden below the horizon at winter at high latitudes for a few days a lunar month. If you want it to stay hidden for seasons, you want your lunar month to last a year. You can do this by moving the moon about 6 times further from Earth. If you want it to look the same size, then it will be bigger, so the system is almost a double planet.

Can you have a lunar orbit with the same period as the solar orbit? Laplace resonance is for planets with a common orbital centre. I feel a lunar orbit would not 'lock in' to the solar orbit, but be destabilised by it. So the Lunar period would be different, but it could still be something close to a year.

There is one other place a moon might hide. It is pretty extreme, but Phobos does it so I mention it for completeness. If you are close to the Martian poles, you can't see Phobos because its orbit is in so close that it is hidden by the curvature of mars. But Phobos is almost on the Roche limit, so it is almost breaking up from total forces. Its orbital period is about 7.5 hours.

There is one possible solution if the moon is a lot smaller and lower. If the moon was in geosynchronous orbit, it would be permanently hid from one side of the planet; if it was in near geosynchronous orbit, then it would be hidden and then reappear. I suspect such an orbit would be unstable on astronomical timescales.

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    $\begingroup$ "The Earth-Moon orbit plane is probably pretty close to the ecliptic", "our Moon is probably hidden below the horizon at winter at high latitudes for a few days a lunar month": I really don't see how one can speak in the 21st century of the Common Era about how the Sun-Earth-Moon system "probably" works. It works in a well-defined way, which has been pretty well known since about three thousand years ago. P.S. A body six times as far from Earth as the Moon which appears to an observer on Earth to have the same angular size as the Moon would be very much larger than Earth... $\endgroup$
    – AlexP
    Nov 27, 2023 at 13:33
  • $\begingroup$ If you move the Moon six times further from Earth, it will be in orbit around the Sun, not the Earth. $\endgroup$
    – Mark
    Nov 28, 2023 at 0:42
  • $\begingroup$ I am trying to guess a geometry that is like the Sun-Earth-Moon system but also fits the question. There is no stipulation about the length of the year, the distance from the sun, or the density of the moon in the question itself. The moon could orbit the earth at six times the distance. $\endgroup$ Nov 28, 2023 at 12:27
  • $\begingroup$ I think a near-geosynchronous orbit can be stable, as long as the Earth's rotation is just slightly faster than that of the moon's orbital period. If Earth's rotation was slower, then tidal forces would gradually slow down the moon until it hits the Earth in millions of years (or enter the Roche limit and disintegrate to form rings). The Pluto-Charon geosynchronous rotation is a prime example of such a stable orbit. $\endgroup$ Nov 28, 2023 at 12:48

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