“The 1st available allowed day for R”H has to be R”H? ”
Generally yes. Rosh Hashana is on the day of the molad Tishrei. I’m not a 100% sure wha t you are suggesting “why can’t the molad be on Sunday and not have r”h till tues?” Are you suggesting it just be arbitrary? why would Rosh Hashana be Tuesday if the molad was Sunday?
The Troah tells us “Hachodesh Hazeh Lachm” as the Gemara learns “Kezeh re’eh vekadesh” when the new moon is seen Beis din is mikadesh Rosh Chodesh. Today of course we (ie chazal) do it al pi cheshbon, but it still isnt arbitrary. The cheshbon is based on the molad * (either becasue a moment after that is the new mooon, although it is invisible for few hours, or because at some point on Earth the moon could be visible on Rosh Hashana which is sort of how the Baal Hamoar explains.
Regardless, the date of Rosh hashana is determined by the molad, al pi cheshbon. It is not arbitrary.
However as mentioned, and as outlined in Rambam Kiddush hachdesh perek 7. There are 4 dechiyos/postponements when Rosh Hashana is pushed off.
Most famously Lo adu Rosh
Second one is molad Zaken if molad is at noon or later R”H is pushed off (this can combine with the Lo adu Rosh for a 2 day push if Molad occurs after noon on Tuesday, R”H would be pushed to Wed, then Lo adu Rosh so pushed to Thursday.
There are 2 other dechiyos that are more technical, and less common.
But none of these dechiyis are arbitrary. IF the molad is Sunday why would R”H be Tuesday?
“I messed up on my correction, too. Pesach can land on a Sunday, in which case Chanukkah on Tues should be possible in a leap year.”
Yes theoretically possible in a leap year, except to Rosh Hashanas on Tuesday in a row are impossible
* A good question is why this only applies to Rosh Hashana and not every month. which are somewhat arbitrary compared to the molad. I assume this is because the calendar would be way too complicated trying to adjust every month to coincide with the molad. As long As Rosh Hashana is accounted for , that enough.
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