Is it possible for two moons to align once a year?

Question

The planet is just like earth and the first moon is the same as earth's moon, but there's a second moon further away. I'd like to know how plausible it is for both moons to align once a year. The second, further moon appears smaller in the sky compared to the first one. Would it even be plausible for them to align once a year without changing the orbit of the first moon?

Answer 1

As a first approximation, the closer the orbital distances, and thus the orbital periods of the two moons are to each other, the longer will be the period between successive line ups of the two moons.

And the farther the orbital distances, and thus the orbital periods of the two moons are from each other, the shorter will be the period between successive line ups of the two moons.

For example, in our solar system Earth orbits the Sun at 1 astronomical Uint, or AU, and has an orbital period of 1 Earth year.

The farthest known planet, Neptune, orbits the Sun at 30.07 AU, and has a orbital period about 164.8 Earth years long. It has a synodic period between orbital alignments with Earth of only 367.49 Earth days, slightly more than one Earth orbit of the Sun.

The planet Mars, in the next orbit beyond Earth, orbits at a distance of 1.523 AU, and has an orbital period of 686.980 Earth days or 1.88085 Earth years. It has a synodic period between orbital alignments with Earth of 779.94 Earth days, or 2.1354 Earth years.

so the outer moon in your story will have to orbit les than 1.523 times as far as the inner moon, and have an orbital period less than 1.88085 times as long as the orbital period of the inner moon.

The Moon has a sidereal orbital period of 27.321661 Earth days, shorter than the Moon's cycle of phases. The Earth has several different types of years defined differently, but you probably want the tropical year, the year that defines the seasons and is the basis of solar calendars, 365.24219 Earth days of 86,400 seconds each.

So there are 13.36822787 lunar orbits in a tropical year of Earth. Thus the relative separation of the two moons' orbits would have to be much less than that between Earth and Mars for their synodic period to be 13.36822787 times as long as the orbit of the inner moon.

Two moons of Saturn, Janus & Epimetheus, orbit Saturn in orbits very close to each other. According to Wikipedia, in 2003 the semi-major axis of the orbit of Janus was 151,460 kilometers, and the semi-major axis of the orbit of Epimetheus was 151,410 kilometers. So in 2003 Janus orbited about 1.000330229 times as far from Saturn as Epimetheus did.

With the two orbits so close, the inner moon orbits only very slightly faster than the outer moon does, and so it takes about four Earth years for the inner moon to pull ahead of the outer moon and then catch up with it again. And every time the two moons get close, they switch orbits, so the former inner moon becomes the outer one, and the former outer moon becomes the inner moon.

So if the outer moon in your system orbits only 1.000330229 times as far from the planet as the inner moon does, there should be about 2,404 orbits of the inner moon between each time the two moons line up. If the inner moon has the same orbit as Earth's moon, the time between successive alignments of the two moons will be about 57,489.58641 Earth days, or 157.39 Earth years.

And if the outer moon orbits about 1.523 times as far as the inner moon, the time between line ups of the two moons will be 2.1354 times the orbital period of the inner moon. If the inner moon has the orbital period of Earth's moon, 27.321661 Earth days, the time between successive line ups of the the two moons should be 2.1354 times as long, or 58.3426749 Earth days, or about 0.159 Earth years.

So for the two moons to line up only once a year, the difference between their orbital distances and the difference between their orbital periods has to be between those two extremes.

According to this list: https://en.wikipedia.org/wiki/List_of_exoplanet_extremes

The smallest known semi-major axis ratio between the orbits of two consecutive planets in the same system is between Kepler-36 b and c.

Planet b's orbit has a semi-major axis of 0.1153 Astronomical units (AU) and a period of 13.86821 Earth days. Planet c's orbit has a semi-major axis of 0.1283 AU, 1.11274935 that of b, and a period of 16.21865 Earth days, 1.169484021 that of b.

https://en.wikipedia.org/wiki/Kepler-36

According to this synodic period calculator https://www.omnicalculator.com/physics/synodic-period the synodic period of c as seen from b would be 69.694 days. That is 6.900241632 times the orbital period of the inner planet b.

So if the the inner moon in your system has an orbital period of 27.321661 Earth days, and the outer moon orbits 1.11274935 times as far from the planet, and has an orbital period 1.169484021 as long, the synodic period should be 6.900241632 times 27.321661 days, or 188.5260558 Earth days, or 0.51615621 Earth years.

According to my calculations on this synodic period calculator https://www.omnicalculator.com/physics/synodic-period if the inner moon has an orbital period of 278.321661 days and the outer moon has an orbital period of of 29.53069 days the synodic period should be 365.241 Earth days, while if the outer moon has an orbital period of 29.530699 the synodic period will be 365.239 days.

And that is as close to Earth's tropical year of 365.24219 Earth days as I could get it.

And of course that assumes that the star is exactly like the Sun, the planet orbits with the same distance and orbital period as the Earth and has the same mass as Earth, and the inner moon orbits the planet at the same distance and orbital period as the Moon orbits the Earth.

Anyway, I hope I have shown that the problem of getting a planet's two moons to align once a planetary year is not unsolvable.

Added 11-06-22.

Afer consieration, I strongly suggest that both moons hav emuch less mass than Earth's moon, so that they appears as dots or very tiny shapes in the sky of the planet.

That will make them much less spectacular as seen from the surface of the planet. But by greatly lowering their masses, that will reduce their gravitational interactions and so reduce the probabability than one will be ejected from orbit around the planet.

Each planet orbiting a star, and each moon orbiting a planet, has an exclusion zone where its gravity will tend to eject less massive objects.

Thus the usual spacing of planets areound a star, or moons around a planet, is rather wide, with each orbit being significantly wider than the next inner orbit.

The examples I gave above of planets and moons with narrow separations between orbits are rather unusual examples. Thus you should greatly reduce the size of your two moons so having their orbits so similar will seem more plausible.

Answer 2

If the two moons orbits lay in the same plane it's impossible: though the outer moon might take longer to orbit the planet, the inner moon will necessarily align with it more than once through the entire duration of the outer's orbit.

If the two orbital planes are instead differently inclined, I think you can find a configuration where the nodes are met once a year, more or less in the same way as our moon and sun do not eclipse each other at every new moon/full moon but only at longer intervals.

Answer 3

Assuming by "align", you mean that the moons eclipse each other as seen from an observer on the planet, that happens all the time in multiple-moon systems. On the planet, if the little moon is naked-eye visible, they'd be lunar eclipses and happen predictably & frequently, maybe with different names for Moon B in A's shadow/blocked-from-view vs Moon A/B in Planet's shadow, like ours.

Formal name for a body passing in front of others is an occultation (Int'l Occultation Timing Association, What is an Occultation?).

Here's an EarthSky article from 2021 discussing viewing Jupiter's moons occulting each other. From Earth we can only see them at Jupiter's own equinoxes, so twice in its solar-year (akin to our start of Spring/Fall), but that's due to how the large Jovian moons are aligned with each other & Earth.

From an observer on the central planet, the eclipse frequency would depend on relative "months" for each moon, their relative sizes, orbital distances/speeds, etc. It's mostly-independent from the length of a year.

It's similar to how our lunar month is mostly unrelated to the length of our solar-year. Earth has 12ish lunar months per solar-year, which is how you get a "blue moon" - when that 13th partial-month happens to include a full moon.

So your world might see an eclipse of its lunar-pair "once in a blue moon" :)