The Universe really is quite pretty and mathematical. It’s just full of natural rhythms and geometries, and this is often apparent in the orbits of stars and planets.

Planets like to be in harmony, tugging each others orbits with gravity and falling into resonances where their orbits have perfect integer ratios. A nice little illustration of this is the Moons of Jupiter, shown in this animation.

Io, Europa, and Ganymede have a perfect 1:2:4 resonance (formally referred to as a Laplace resonance), where the timing of Europa’s orbit is twice that of Io, and the timing of Ganymede’s orbit is twice that of Europa. I find it really quite satisfying to watch.

In theory, objects in stable orbits around the same celestial body tend to find resonances like this – in practice, you tend to find a mix of perfect resonances which are stable and long term, like Jupiter’s moons above, with other apparent resonances being seemingly coincidental^{⭐}. The orbital ratios we see may be nice and tidy, like Mars and Earth which have an apparent 1:2 ratio, or they might be more unusual, like Neptune and Saturn with their 5:28 ratio. But perhaps the most interesting thing is the shapes these orbits can trace out.

Earth and Venus currently have an 8:13 orbital ratio, which means Venus completes 13 solar orbits every 8 Earth years, with the two planets passing close to each other 5 times for each set of orbits. And if you link the two with an imaginary straight line, it traces a rather lovely pattern.

The centre point of that line draws a cherry blossom! 🌸

Again, you can do the same thing for any pair of planets, ending up with a pattern reminiscent of spirographs, mathematical roses, or possibly higher dimensional uniform polytopes.

Here are a few more!

These images were sourced from a page by Ensign Software.

⭐ I’m not really fond of talking about coincidences where science is concerned, but that appears to be the case here. The perfect “mean motion resonances” are relatively rare, with most observed orbit ratios being “coincidental near-resonances” which appear temporarily stable but gradually shift over time. In other words, they appear to be in resonance over short timescales of hundreds to thousands of years, but on astronomical timescales they’re effectively random. Which means things like the apparent 8:13 Earth Venus ratio are actually an illusion. But shhh, you’ll spoil the mathematical prettiness.

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## About Invader Xan

Molecular astrophysicist, usually found writing frenziedly, staring at the sky, or drinking mojitos.

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