I’ve never heard amny claims about this. Part of the problem is the very long time betwen comet’s returns, and another part is identifying the returning comet as the same one observed many years ago. It’s a nontrivial problem, and even when it was first done, predicting the return of Halley’s comet was cionsidered an impressive feat. The guy who did it – his name is unjustly not known by most people – was Johann Georg Palitzsch (Halley himself had died before the comet’s predicted return), and many people were skeptical of his claim, although it was soon vbindicated. Comet predicting is much tougher than you’d think. Why, in fact, ought one to think that comets even DID return? That was a pretty big leap of faith right there.
I’m curious about a much more mundane and likely propect – the observation and measurement of variable stars. As it turns out, Palitzsch was instrumental in this, too. He’s one of two people to measure the period of variation of the star Algol. He’s pretty much neglected for this, too – everyone remembers that John Goodrick did the same thing, at the same time (their articles re[porting the discovery are contiguous in the pages of the Journal of the Royal Society of London, and the values they obtained for the period almost identical) Goodricke was more 'photogenic", though – a teenage deaf-mute, who tragically died on pneumonia contracted from night air shortly thereafter. Palitzsch couldn’t get a break.
In any event, you’d think that the notion of variablre stars would be easy to come by, and the measurement of their periods straightforward – the stars are in the same place, and all you need to do is to observe and count. Yet the first mention of even the idea of a variable star didn’t occur until about the year 1600. Prior to that, there is no clear statement that variable stars even existed. No ancient text – Greek, Roman, Babylonian, Indian, or Chinese – explicitly refers to them. Such claims that they did write about them that I’ve investigated are ambiguous at best, untrue or over-enthusiastic at worst. I’ve argued at length that I thiink people knew about variable stars in the ancient world and even had measured periods (it’s enshrined and fossilized in mythology), but no one explicitly states it, for whatever reason