It's interesting how the approach to science has changed in the last four centuries.
It's easy to have the (mistaken) impression that as long as we humans have been doing anything scientific, we've always done it the same way -- looked at the evidence and data, then tried to come up with an explanation. But science in Europe before the eighteenth-century Enlightenment was largely done the other way around; you constructed your model from pure thought, based on a system of how you believed things should act, and once you had the model, you cast about for information supporting it.
It's why Aristotle's statement that the rate of speed of a falling object is directly proportional to its mass stood essentially unchallenged for over a millennium and a half despite the fact that it's something any second grader could figure out was wrong simply by dropping two different-sized rocks from the same height and observing they hit the ground at exactly the same time. As odd as it is to our twenty-first century scientific mindset, the idea of figuring out if your claim is correct by testing it really didn't catch on until the 1700s. Which is why the church fathers got so hugely pissed off at Galileo; using a simple experiment he showed that Aristotle got it wrong, and then followed that up by figuring out how things up in the sky moved (such as the moons of Jupiter, first observed by Galileo through the telescope he made). And this didn't result in the church fathers saying, "Whoa, okay, I guess we need to rethink this," but their putting Galileo on trial and ultimately under permanent house arrest.
That "think first, observe later" approach to science plagued our attempts to understand the universe for a long time after Galileo; people first came up with how they thought things should work, often based on completely non-scientific reasons, then looked for data to support their guess. That we've come as far as we have is a tribute to scientists who were able to break out of the straitjacket of what the Fourth Doctor in Doctor Who called "not altering their views to fit the facts, but altering the facts to fit their views."
One of the best examples of this was the seventeenth-century astronomer Johannes Kepler. He was a deeply religious man, and lived in a time when superstition ruled pretty much everything -- in fact, Kepler's mother, Katharina (Guldenmann) Kepler, narrowly escaped being hanged for witchcraft. Kepler, and most other European astronomers from his time and earlier, were as much astrologers as scientists; they expected the heavens to operate by some kind of law of divine celestial perfection, where objects moved in circles (anything else was viewed as imperfect) and their movements had a direct effect on life down here on Earth.
At the beginning, Kepler tried to extend his conviction of the mathematical perfection of the cosmos to the distances at which the planets revolved around the Sun. He became convinced that the spacing of the planets' orbits was determined by conforming to the five Platonic solids -- cube, dodecahedron, tetrahedron, icosahedron, and octahedron -- convex polyhedra whose sides are made up only of identical equal-sided polygons. He tried nesting them one inside the other to see if the ratios of their spacing could be made to match the estimated spacing of the planets, and got close, but not close enough. One thing Kepler had going for him was he was firmly committed to the truth, and self-aware enough to know when he was fudging things to make them fit. So he gave up on the Platonic solids, and went back to "we don't know why they're spaced as they are, but they still travel in perfect circles" -- until careful analysis of planetary position data by the Danish observational astronomer Tycho Brahe showed him again that he was close, but not quite close enough.
This was the moment that set Kepler apart from his contemporaries; because instead of shrugging off the discrepancy and sticking to his model that the heavens had to move in perfect circles, he jettisoned the whole thing and went back to the data to figure out what sort of orbits did make sense of the observations. After considerable work, he came up with what we now call Kepler's Laws of Planetary Motion, including that planets move in "imperfect" elliptical, not circular, orbits, with the Sun at one focus.
Start with the data, and see where it drives you. It's the basis of all good science.
What got me thinking about Kepler and his abandonment of the Platonic-solid-spacing idea was a paper this week in Astronomy & Astrophysics showing that even though Kepler initially was on the wrong track, there are sometimes odd mathematical regularities that pop up in the natural world. (A well-known one is how often the Fibonacci series shows up in the organization of things like flower petals and the scales of pine cones.) The paper, entitled "Six Transiting Planets and a Chain of Laplace Resonances in TOI-178," by a team led by Adrien Leleu of the Université de Genève, showed that even though hard data dashed Kepler's hope of the motion of the heavens being driven by some concept of mathematical perfection, there is a weird pattern to the spacing of planets in certain situations. The patterns, though, are driven not by some abstract philosophy, but by physics.
In physics, resonance occurs when the physical constraints of a system make them oscillate at a rate called the "natural frequency." A simple example is the swing of a pendulum; a pendulum of a given length and mass distribution only will swing back and forth at one fixed rate, which is why they can be used in timekeeping. The motion of planets (or moons) is also an oscillating system, and a given set of objects of particular masses and distances from their center of gravity will tend to fall into resonance, the same as if you try to swing a pendulum at a different rate than the rate at which it "wants to go," then let it be, it'll pretty much immediately revert to swinging at its natural frequency.
The three largest moons of Jupiter exhibit resonance; they've locked into orbits that are the most stable for the system, which turns out to be a 4:2:1 resonance, meaning that the innermost (Io) makes two full orbits in the time the next one (Europa) makes a single orbit, and four full orbits in the time it takes for the farthest (Ganymede).
This week's paper found a more complex resonance pattern in five of the planets around TOI-178, a star two hundred light years away in the constellation Sculptor. It's a 18:9:6:4:3 resonance chain -- the nearest planet orbits eighteen times as the farthest orbits once, the next farthest nine times as the farthest orbits once, and so on. This pattern was locked in despite the fact that the planets are all quite different from each other; some are small, rocky planets like Earth, others low-density gaseous planets like Neptune."This contrast between the rhythmic harmony of the orbital motion and the disorderly densities certainly challenges our understanding of the formation and evolution of planetary systems," said study lead author Adrien Leleu, in an interview with Science Daily.