1,338. Is There a Difference Between Greek and Jewish Astronomy?

Hilchos Kiddush HaChodesh 17:24

The basis for all of the calculations we have studied, why to add this and subtract that, as well as how we know these things and proofs for each of them, can be found in the great astronomy and geometry books, of which the Greeks wrote many. Our Sages also possessed this knowledge but the texts written by the Jewish Sages from the Tribe of Issachar in the time of the prophets have not been transmitted to us. Nevertheless, since these things can be proven mathematically without any doubts, it makes no difference whether we get the information from a Jewish or a non-Jewish source. This is because something that has been proven undeniably true does not depend on the character of the one who teaches it, it depends on the proofs he has presented.

Hilchos Kiddush HaChodesh 18:1

It is well-known and it should be apparent that even when the calculations tell us that the moon should be visible on a certain night, that is really only a likelihood. It is always possible that the moon won’t be seen because of cloud cover, because one is in a valley, or because there’s a mountain in the west blocking people’s view as if they were in a valley. This is because the moon cannot be seen by someone in a low place even if the moon is large. On the other hand, it will be possible for someone on a tall mountain to see the moon even when it’s very small. It will also be possible for someone on the shore or traveling by boat on the Mediterranean to see the moon even when it’s very small.