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19.8.18

Though it is considered well known that Hillel II set up the calendar, still there is no record in the Gemara of his having done so. The Gemara would not have left this important fact out if it was so.]

There are dates brought in the responsa of the Geonim before Saadia Gaon that have days that come out not like the modern day Jewish calendar. Therefore the calendar that is in use is not halacha leMoshe MiSinai. [From Moses at Mount Sinai]  It was not in use until sometime right before Saadia Gaon.[It can not be tradition if the early geonim were not using it.]]
But when Saadia Gaon wrote about it, he used the Arabic word that means tradition. The Rambam thought he meant a law to Moses at Mount Sinai when all Saadia Gaon really meant was it was accepted. So the calendar seem to me to be not valid. Thus in figuring out when Rosh Hashana comes out I think it is better to go with Tosphot in Sanhedrin page 10b that says you go by the "molad" [conjunction]. [That means Rosh Hashana comes out the night on Sept 9. [That is Sept 10 is Rosh Hashana.]
[This will depend on your time zone. You have to see when the molad come out in your area. In Israel it turns out to be the night of Sept 9 which makes Sept 10 Rosh Hashana. It all depends on the actual conjunction.

[Though it is considered well known that Hillel II set up the calendar, still there is no record in the Gemara  of his having done so. The Gemara would not have left this important fact out if it was so.]
[The whole thing is just a misunderstanding of what Saadia Gaon meant when he wrote the calendar of his time  was traditional (using the Arabic word).  People though he meant Halacha to Moses from Sinai when all he meant that by his time it was the accepted practice to use it,