# Three Moons and Simultaneous Full Moons?

In my story's world, the planet is roughly Earthlike in terms of size but it has three moons. I have written in something called "brightnight", when all three moons are full at the same time and the light is almost as bright as day. One month is defined as the time it takes for all 3 moons to have done at least 1 full cycle (new moon to full moon to new moon). Brightnight happens once every month. Is this feasible in any way? I'm not writing hard SF, but I want things to be at least slightly astronomically feasible and not literally impossible. Even if it takes an extremely rare planetary set-up for this to occur, I'll take it.

Basically it started with the mental image of a night sky with three moons, all in different phases, in it, and I built my world around that.

• I fairly sure it's not a stable system. Even if stable, to have all three full overhead at the same time would probably only be for rare alignments. So your brightnights when the moons are all full could find them overhead different geographical regions. The planet would get in the way of seeing all three at once. You'd only be able to see one or maybe two on opposite sides of the night sky on any one brightnight. Waiting for a "lunar alignment" (in the sense that you can see all 3 @ once) might be quite the sight, probably once a millenia or two, and almost certainly a major festival event ;) Jun 23 '20 at 15:30
• Just a reality note: The illuminance provided by the Moon is very very very feeble compared to the illuminance provided by the Sun. At best (full "super" moon), the Moon provides an illuminance of about 0.3 lux; the daylight illuminance in a bright summer day at noon exceeds 100,000 lux, about 300,000 times more light. (That's a difference of 18 exposure steps...) Three full "super" moons will not in any way make the night almost as bright as day, for any reasonable meaning of the word "almost". Jun 23 '20 at 16:40
• @AlexP But subjectively it could appear very bright. If you get the chance, go somewhere far from cities & towns, preferably in winter when the ground is snow-covered. A full moon is sufficient to read by once your eyes get dark-adjusted. Jun 24 '20 at 13:45

This might be possible if all three moons are in an orbital resonance with one another - that is, their periods are integer multiples of each other. For example, to fit your desired timescales you could have the periods be 1 week (Moon 1), 2 weeks (Moon 2), and 4 weeks (Moon 3); then the periods are related by $$P_3=2P_2=4P_1$$, and we have what we call a 1:2:4 resonance. This guarantees that all three moons will be full moons at the same time every four weeks (so roughly one month in Earth's Moon terms). We see resonances arise with many moons of Jupiter and Saturn, and it actually can help stabilize their orbits - Ganymede, Europa and Io are locked in a 1:2:4 resonance.
Is this feasible? Well, let's look at Kepler's third law. For a circular orbit, it tells us that the orbital radius $$r$$ is related to the period $$P$$ by $$P^2\propto r^3$$ The innermost moon would have a period one quarter the period of our Moon, and would therefore have an orbital radius approximately 39% that of our Moon; the middle moon would have an orbital radius of about 62% that of our Moon's. We could argue that, even with the stabilizing resonance, the moons might be too close to one another to be stable; the closest approach between any two would be 88,000 km, compared to the roughly 240,000 km separation of Europa and Io.
The other problem is tides, which would, yes, be a bit more complicated. In fact, as the tidal force scales as $$F_T\propto M/r^{3}$$, I calculate that the tidal force on the Earth would be, at peak, 21 times the current value. That's a lot, yes, though it could be mitigated by decreasing the mass of the moons - which would have the added benefit of decreasing the strength of their gravitational interactions with one another.