In what way could a moon change phases according to the month?

Question

Let’s say that a planet has multiple moons, and because I don’t want to type “a planet” many times, let’s call the planet Stan. One of these moons changes phase (“phase” being the best word for it, despite not actually being a phase, I guess) according to the months, and this is, in point of fact, where the residents of Stan get their twelve month, 30-31 day per month (except for the second month) calendar. I’m aware that this is convenient, but that’s the entire point.

TL;DR: A planet gets their version of the Gregorian calendar from a twelve-phased (pseudo-phase) moon.

Anyway, to elaborate on the question; how could a twelve-phased (again, not legitimate phases) moon work, and what might the twelve phases (see ^) be? Some extra information, every moon appears at night, and Stan is roughly the same distance from the sun as Earth is from our own sun.

Answer 1

The moon (let's call it Stan Jr.) has exactly twelve highly-distinctive surface features. It is not tidally locked to Stan, but instead rotates incredibly slowly - so slow, in fact, that one and exactly one of those highly-distinctive surface features becomes visible and one becomes hidden precisely every thirty or thirty-one days, except for the one that becomes visible or hidden sooner or later than that, which is the second month.

Answer 2

The moon orbits Stan perpendicular to the ecliptic*, thus the plane of its orbit rotates around Stan once a year. When the plane is at right angles to the sun, the moon is always half full. When it's parallel to the sun, you get the normal phases of Earth's moon. In between, you get a mix.

*Much like Uranus in our own system, so its large moons would be a good model.

Answer 3

The simplest solution would be to have this moon orbit the planet exactly once a year (the moon's orbital period around Stan is exactly the same as Stan's orbital period around its sun). Then you work your months around six waxing periods and six waning periods: lesser waxing crescent, greater waxing crescent, waxing half moon, lesser waxing gibbous, greater waxing gibbous, full moon, greater waning gibbous, lesser waning gibbous, waning half moon, greater waning crescent, lesser waning crescent, new moon. In fact, you could build similar systems using many integer ratios (the moon completes an orbit every half year, every third year, every quarter year, every sixth of a year). It just so happens that the earth's moon orbit is roughly a twelfth of a year. This would obviously depend on the moon's distance from Stan, and thus impact its visual size and effect on tides and such. I'll leave the math for others, since that's not part of the question.

An alternate possibility — since you've stated the planet has multiple moons — is to have two moons that have integer ratios with respect to each other (as well as the planet). Thus, if moon A orbits the planet every quarter of a year, and moon B that orbits every third of a year, then you could read months off like the hands of a clock: first month both moons are full, second month A is waning half and B is waning crescent, third month A is new and B is waxing crescent, fourth month A is waxing half and B is full, etc...

Answer 4

I'm imagining a moon with regular surface-level phenomena that would observable from Stan. These "phases" would be entirely unrelated to actual phases which refer to changes in illumination, but could still result in a lunar surface which changes appearance in a cyclic and regular manner. Such phenomena could be a result of geological or biological activity - perhaps there's a massive geyser which erupts each year which has lasting and predictable effects on the weather patterns over the following months, or maybe there's a lifeform that covers the moon like an algae that blooms each year and can be seen from Stan. Each year, you'd see the moon change color as it enters its "bloom" phase, which could continue to change as the algae's lifecycle progresses, ultimately repeating the following year.

There's nothing about these "phases" (or phases of the actual moon) that break the year into distinct time periods, it would be more of a continuum of change that's broken up for convenience. "Phases" derived from such phenomena also wouldn't be as long-term stable as most orbits, but could perhaps last long enough for a civilization to develop a calendar.

Answer 5

Use a Binary Star System

On Earth, the Moon goes through a single sequence of phases based on light hitting the moon from one direction, and the moon orbiting the Earth once every month, but if you were to add another light source, then, each month could have a different set of phases than the pervious month.

To make each set of phases unique to the month, you need to have the moon orbit a planet that orbits a star that has another star also orbiting it.

On such a planet, years would not be measured by the seasonal changes of the axial tilt, but by the seasonal changes caused by how close the planet is too the second star; so, their summer will be when Stan is closest to star 2 and their winter when it is farthest from Star 2, and a month will be 1/12th of the time it takes Stan to get from summer to summer, not 1/12th of the time it takes it to revolve around the star.

This would result is a lunar cycle that looks sort of like this:

Answer 6

Stan Junior needs to be a planet, to be big enough to see as a disk most of the year, and needs to be in an independent orbit around the central star with exactly half the period of Stan (and ideally just far enough out of plane that it never passes directly across the star's disk). Note that this is an unstable condition, especially if there's a Jupiter in the system or another terrestrial planet in a fairly close orbit to either Stan or Stan Jr. "Unstable" in this case means this condition could persist for centuries, perhaps, but certainly not for millions or billions of years.

As the two planets orbit, Stan Jr. gets ahead of Stan, eventually by a full orbit over the course of a Stan year. Twice a year, Stan Jr. passes close to the sun, either in full or dark phase (Stan's version of Galileo is likely to discover that there's an incredibly thin crescent exactly at the dark phase conjunction). This will allow the people of Stan (Stanites?) to have their year defined by Stan Jr.'s phases, though without Stan Jr. being an actual moon of Stan.

I had thought Stan Jr. would need to be Jupiter's size, but seemingly it only needs to be about 50,000 km diameter to be 0.1 degrees across -- 1/5 of a full Moon, easily visible as a disk to the naked eye -- at 2 AU distance. Still a giant, but more like Neptune than Jupiter.