# How much time will this system last?

Imagine the following star system: The star is very much like ours. Orbiting this star is one planet, very much like Earth. Let's call it the Orb. Orbiting the Orb are two moons: a large one, Mona, that is very much like ours and a small one, Wick, that's big enough to be round but small enough to not cause havoc on the Orb with it's rather close orbit. There is nothing else in the system, not even a mote of dust, and the system itself is in a very quiet neighborhood.

An Orb day, specifically a sidereal day, is very close to twenty-four Earth hours long but unlike an Earth day is always exactly the same length, every day. An Orb year, specifically a tropical year, is exactly 364 Orb days long. An Orb month, the length of Mona's phase cycle, is exactly one-twelfth of an Orb year (i.e., there are exactly twelve months in a year.) An Orb week, the length of Wick's phase cycle, is exactly 7 Orb days long, meaning there are exactly 52 weeks in a year.

Now obviously this system can't maintain this level of precision indefinitely. And in fact the system isn't natural, but was created and maintained by outside entities. For story reasons, these entities are to be permanently removed and nature is to take its course. My question is how quickly and how catastrophically would the system as described destabilize. My first guess is that Wick, in a 3:13 resonance with Mona, would start moving pretty fast, but I don't know which way or how soon.

Also: Assume Wick is sturdy enough that its Roche limit is within its orbit. If this simply isn't possible, although I doubt it isn't, please say so.

• "Unlike an Earth day is always exactly the same length, every day": To a first order approximation his simply means that the Orb's orbit is a circle and Orb's axis has zero inclination. Strictly speaking this "always the same length" is not possible, because the tidal forces exerted on Orb by its primary and its satellites will slow down its rotation continuously, so every day will be a tiny weeny little bit longer than the previous day. For example, the our second is defined so that the mean solar day was exactly 24 hours on 1-Jan-1900; today it's about 24 hours plus 2 milliseconds. Commented Sep 15, 2017 at 16:50
• 3 body systems are not solved, we would have no way to know the stability of your specific 3 body system (ignore the star for now) without exact numerical simulations. If all 3 bodies become resonant and stable, then they will remain that way for a long time until the angular momentum loss from tidal forces moves them away from the resonant stability. Commented Sep 15, 2017 at 17:00
• @AlexP, I'm well aware of that, as are the entities in charge of maintenance. They're a little obsessed with harmony and precision, so they spin up the Orb ever so slightly. Or rather, they did, before they were removed. Also, I would like there to be axial seasons, which in my understanding only change the day:night ratio over the course of the year. Would the axial tilt cause its own problems once the stabilizing entities are removed? Commented Sep 15, 2017 at 17:23
• If there is an axial tilt then the Sun will move across the sky on a circle inclined with respect to the celestial equator and the length of the solar day will vary during the year according to the equation of time. Commented Sep 15, 2017 at 17:43
• I am going to comment on what can change the rotation of earth. Large events, such as large earthquakes and tsunamis, have been shown to measurably change the length of an earth day. It is a very small change indeed, but has been documented. The change is analogous the the rate of spin of an ice skater who puts her arms in towards herself (spinning faster.) Sufficiently large events on Earth can change the mass distribution of the planet and thereby the spin and day length. Commented Sep 15, 2017 at 19:09