For example, I was looking at this tapestry that supposedly represents a sighting of Halley's comet, and was wondering how it was concluded that the object being represented was indeed Halley's comet, and not say, a meteor fly by or any other astronomical event.
Even old recordings of bright objects in the sky which were initially mistaken for stars have now been identified as supernovae instead. How are these conclusions drawn?
Time and location of the event are most important here. These can utilized to determine the occurrence of periodic astronomical events. Most often the people recording the events have no idea that the event is periodic or even that it is something that would be usable to date their works in the far future. In the given example, the Bayeux Tapestry, the inscription that accompanies the passing of Halley's Comet is "Isti Mirant Stella", which means "They marvel at the star." They had no idea that this is something that they would be able to see again, given the right position and time.
We know better; modern technology allows us to know Halley's periodicity, 75.3 Julian Years, and that gives us the information necessary to determine with great accuracy every day and year in which Halley's comet has been visible, going back to some arbitrary date.
There is, then, the other important matter. We know that Halley's was visible sometime around the start of the Norman Conquest, but how do we know that it was that comet that they are depicting? The final piece, as mentioned earlier, is location. We can take the well defined spin of the Earth and calculate exactly which side of the planet was facing the night sky at the time of Halley's arrival and use this, in tangent with the date, to determine that it was most likely the same bird.
Of course this is subject to interpretations, there could have been another comet the same night, which had similar luminosity and size to Halley's. However, the simplest answer is usually the most right and so it is believed that Halley's Comet is that which is depicted there.
And so it become a matter of abductive reasoning. We narrow the probability pool of astronomical events until there is an overwhelming probability that it is one event over all others.
