I want two moons in my novel's new world, but hope to have minimal changes in tides, etc. Would it be possible to have a very small moon that doesn't wreak havoc on nature? Also, is it possible for a small moon to have an orbit that only brings it around a planet intermittently, e.g. once every few months?
Yes. You could absolutely have two moons and not wreak havoc on tides. The force of gravity that moon exerts on the surface of the planet, pulling the oceans, is the same force of gravity that holds the moon in orbit. If the moons were further out, or if one moon was much further out, the effect on the tides could be negligible. I would recommend a much less dense outer moon, that has a large volume of lighter material, say frozen water instead of rock, that would still reflect a lot of moonlight, and even a comet trail. That's it! Make it a large comet that caught in the orbit of a planet. That's highly improbable, but possible, and the visual effect would be stunning.
The Force of Gravity equation is as follows:
F = (G•m1•m2)/D²
F is the force of gravity G is the Universal Gravitational Constant is 6.67384E-11 m³/kg•sec². m1 is the mass of the first object m2 is the mass of the second object D is the distance between them.
Yes, both of these scenarios are quite plausible.
Our moon influences the tides so much because it is very large compared to other natural satellites in our solar system and is fairly close to Earth.
Check out the table on this wikipedia page : https://en.wikipedia.org/wiki/List_of_natural_satellites
Sort them by 'mean radius' and you can see that our moon is the 5th largest in the solar system. It is also closer to Earth (smaller Semi-major axis) than any of the larger ones are to their planet.
There are moons that are much closer to their host planet than our moon is to us, but most of them are significantly smaller.
The total gravitational effect they have on the planet is therefore much less than our moon's, which means way less tidal forces.
In order for the new moon to only come around every few months, it would need a highly eccentric orbit. https://en.wikipedia.org/wiki/Orbital_eccentricity .
Check out the list of the objects on that page, note that Halley's Comet has an eccentricity of ~0.96 compared to the moon's ~0.05.
Check out this page to see that visualized: https://en.wikipedia.org/wiki/Halley%27s_Comet
So your new moon would have to be quite small, probably only a few 100 kms across at max, and would spend most of its orbit far away from the planet. Then it would come screaming in, pass close by to the planet quickly, and get flung back out again.
As a result, your new moon probably won't be super visible, and it probably won't have a stable long term orbit. It would probably more closely resemble a captured asteroid than an actual moon.