Hi! Thanks for the link. It contains lots of information. Great job!
I am a local stargazer and I read you article on Star of Bethlehem (伯利恆之星). But according to most serious studies on Star of Bethlehem, this possible phenomenon is not related to Jupiter (木星) and Mars (火星), but Jupiter and Saturn (土星).
The night sky as it appeared looking south from Jerusalem on Nov. 12, 7 BC, 6 p.m. to 9:30 p.m.
I'm in my computer lab in school so I can't type Chinese right now...
Please reply me with Chinese if you are comfortable with it, though.
But in any event
The answer to that is yes, and no.
You can "predict" when did past astronomical events occur by assuming that there are no major disruptions in the orbits (in fact, even a physically crazy initial condition that the earth had stopped for a day and resume moving in full speed will most likely have very little effect on its orbit). That's how they predicted roughly when major astronomical phenomena like a double sun rise (as you have quote) had occured.
Also have to remember that this assumption is quite scientific since if earth's orbit had been majorly disrupted in human history, no one will survive.
As for Zheng He's fleets' positions that's actually not a major issue, since some of the Zheng He's reference stars can be millions of lightyears away from earth, they will have to be moving in speed comparable to speed of light to create a major change in what we see in the sky. Moreover, Zheng He's navigation is used to obtain the position of the Zheng's fleet on earth by knowing how angles at which we see the stars derivates, not the other way round. The change of angle moving from, say, Beijing to Hong Kong will inflict a considerable change in the angle at which we gaze one of the stars that will neglect much of the minor change in the star's own movement - leave alone earth's gravitational wave that may never reach the star until the end of the human race XD.
But again, Sherman, you are right on that if you provide the EXACT DAY, or even exact hour of an eclipse, then you may have a quite good check of the orbit of earth, but that is not quite possible 2000 years ago...
... leave alone the fact that we couldn't even manage to find the "great city of Jerusalem" as in the old testament (we might have dug a small village out of the same position...)