tl;dr: Consider the birthday paradox.<p>In astronomy we call these resonances. Sometimes, two seemingly unrelated periodic events will occur together, synchronized by a ratio between some small integers.<p>I think the most typical example is the one they teach you in the first Solar System 101 class to wow you (it works): the 3:2 resonance between the orbits of Pluto and Neptune.<p>Sometimes it might turn out to be a coincidence with more accurate measurements, or when you find evidence that this moment in time might be somehow unusual.<p>For example, Earth and Venus also seem to be in 8:13 orbital resonance, but, in fact probably aren't. On closer inspection, it turns out that there is error of about 0.4% after 8 years and it compounds. It takes a while to compound, but effectively you can't use this "near resonance" to predict where the two will be in their orbits in a few thousand years.<p>In fact, with enough bodies in the solar system and the birthday paradox, there are many compelling candidate resonances with small integer ratios, but the majority of them are probably just random coincidences.