I was wondering how/if it would be possible to create an earth-like (atmosphere, gravity, average temperature, etc. are close enough) rocky exoplanet with more than two or three significant temperature oscillations (like our seasons and day/night cycle). Creating basically a Game-of-Thrones esque scenario for intelligent life on this planet with seemingly unpredictable seasons until the advent of (advanced) astronomy.
Could orbital mechanics provide for more cycles?
How complex could it get?
One way of doing this is to start with a binary of A- or F-type dwarf stars, orbiting eachother closely (required for long term stability). Then, place a late-K or early M dwarf in an eccentric orbit that's not exactly planar-aligned (when it comes to both star systems) with the pair at a much bigger distance; on the order of $5-10AU$ away.
We want our larger stars to be heavier to create multiple year cycles of different lengths: they need to have a significant luminosity at larger distance, and be heavy enough that the gravitation of the red dwarf does not destabilize them. On the other hand, making the central stars too heavy would reduce their lifespan by too much: having at least a billion years of stable main-sequence burning means anything bigger than an A-type dwarf is too short-lived. We would like our red dwarf to be stable though; and for that it may need to be much older than a billion years.
That can be explained as the smaller star being captured at some point by the pair, which is actually very young still (A- and F-type stars achieve main-sequence stability much faster). It can also be used to use a larger age for the smaller star; giving life more time to develop on the earth analog; albeit on a frozen world in subsurface oceans. Then the analog of the cambrian explosion can happen once system capture occurs and surface temperatures rise above freezing for the first time.
Solar masses of around ~$1.6M_{sun}$ to $1.8 M_{sun}$ for the large stars and $0.5 M_{sun}$ for the smaller star get us reasonably close to the goal.
Place our rocky planet in orbit around the red dwarf, actually outside of its normal habitable zone (further away). The stars each make a significant contribution to the light on the planet, with most of the light coming from the dwarf, and the sum is enough to make the planet habitable. Even though their spectra would normally be significantly different from ours individually, the mix will get us a light spectrum that's actually closer to ours than each individual component.
Then make sure the rocky planet's orbit around the red dwarf also has a mild eccentricity and earth-like axial tilt. Now we have at least 8 causes of seasonal variation in climate with varying periods and strengths, most being significant (more than a few $^{\circ}K$ at mid to high latitudes).
One can also assume (due to the capture history) that the orbital planes of both star systems don't necessarily align: there might be some inclination.
Just like on earth, the axial tilt of the planet will create seasonal variations, with greater effects near the poles. There's a day/night cycle with the red dwarf, and a much longer cycle of axial precession.
There's also a second day/night cycle with the binary system. If there's inclination; this second day/night cycle isn't synchronous with the first: there's a second 'equator' pointing to the binary system intersecting the one with the red dwarf.
The much greater eccentricity of this planet compared to earth makes it a substantial component. Depending on the position in the milankovic cycle, winters and summers on one hemisphere will be more intense, while on the other hemisphere, the effects counteract.
The planet will cycle from being further away than its parent star from the barycenter, to being closer, in a cycle lasting either slightly shorter or longer than its year (depending on whether the orbit around its parent is retrograde or not compared to the orbit of the red dwarf around the binary).
During one half of the Inner/Outer cycle, the whole planet will be to some extent lit. This is due to the planet being in between the stars. Instead of applying to half the planet like axial tilt.
This effect may increase temperatures, because the planet is much closer to the heavier stars while in the inner system, and vice versa.
This is an oscillation with a long time period; up to several hundred of the smaller 'years'. It also affects the amplitude of oscillation [5]; during the 'winter' period wrt the binary the type [5] oscillation will have a smaller effect. The orbit of the red dwarf takes the planet closer and farther from the binary stars.
The stars in the binary star system eclipse eachother. This causes a variation in light where during the eclipse (the closeness and size of the stars mean these eclipses are common and long-lasting) the luminosity from the binary is nearly halved, causing a predictable drop in temperature everywhere it's 'day' wrt the binary every time an eclipse happens.
If the orbit period of the binary is by coincidence close to (a multiple of) the length of a day, then it might occur that the eclipse happens at the time where the binary system is brightest (or not visible) each time it happens at a certain location on the planet. As each member of the binary is similar in luminosity, there's a significant difference in light intensity between these two cases. A slight difference between the lengths of the two cycles creates a precession. A pattern where there's a variation of temperature/climate by longitude; with a thin 'wedge' where the temperatures are colder due to the eclipse repeatedly occurring during the time the binary is visible in the sky.
The effect of [7] only happens while the planes of both the binary and the captured system (nearly) align. If there is enough inclination, then eclipses of the binary could only happen during the 'spring' and 'autumn' phases of oscillation (6). If there's a lot of inclination then neither this effect nor the previous effect happens; the 'eclipse of the binary' becomes a very rare event; observed twice during the binary 'year' and only on certain locations.
I would argue that Cixin Liu did this in The three Body Problem, but maybe more of this than you want:
Over the course of the first book we get to learn a bit about the Trisolarans: theirs system has three suns and orbits are utterly chaotic, the planet may enter a closer orbit for a while and become mercury hot for a few years, decades or centuries, it may be flinged into a very wide orbit and freeze (as in: it's raining nitrogen) and back again. The trisolarans have (or claim to, we don't really meet them as far as I've read) a remarkable ability to dry out and hibernate during their planets inhabitable spells. The point here is that a system of three suns is utterly chaotic and unpredictable even with advanced astronomic knowledge.
