What is the source that only the Sanhedrin in Eretz Yisrael may establish Rosh Chodesh?
The Rambam derives from 'This month shall be for you' that this testimony is entrusted to the Sanhedrin in Eretz Yisrael and all who stand in their place.
Question 2
How does the Rambam classify the rule that in our time the calendar is set by fixed calculation?
The Rambam states explicitly: 'This matter is a halacha from Moshe at Sinai' — when there is a Sanhedrin they determine by sighting; when there is none — by the fixed calculation.
Question 3
What is the rule for a place more than ten days' journey from Jerusalem?
A place more than ten full days from Jerusalem keeps two days always — Tishrei messengers could never have reached there given Yom Tov and Shabbat travel restrictions.
Question 4
Why do even residents of Eretz Yisrael keep two days of Rosh HaShanah in our time?
Even in Jerusalem, when no witnesses came on day 30 they kept two days. Since this happened during the sighting era too, the Sages enacted that Eretz Yisrael residents always keep two days of Rosh HaShanah.
Question 5
What is the function of the calendar calculations we perform in the diaspora today?
The Rambam emphasizes: we do not establish based on our calculation — we calculate only to discover what Eretz Yisrael's residents determined, since their determination is what sanctifies Rosh Chodesh.