Though the Scriptures do not give the exact dates for the birth of Isaac or for the impregnation of the foremothers, Chazal, using interpretations of the verses, determined precise dates. The early sages determined that Isaac was born on Passover. How do they know that Isaac was born on Passover? Answer: G-d promised Abraham that Isaac would be born to him using these words: “At the mo’ed I will return to you, according to the time of life, and Sarah shall have a son” (Genesis 18:14). The word mo’ed was understood by the scholars to mean “holiday.” The scholars also learned that G-d’s promise came to pass on a holiday, that Sarah became pregnant on a holiday and would give birth to a son on the next holiday. The scholars clarify on which holiday G-d promised Abraham that the next holiday would see his son born. If G-d made His promise on Passover, stating that Sarah would become pregnant and give birth on Shavuot, only 50 days later, then the child who would be born would not have enough time to develop into a whole and healthy baby. The scholars try to determine if G-d might have made His promise on Shavuot, saying that Sarah would become pregnant and give birth on Rosh HaShanah, but there still is too little time, for the gap between holidays is only five months. The students claim, instead, that G-d made His promise that on Sukkot Sarah would become pregnant and that she would give birth on Passover. The scholars ask: Between Sukkot and Passover there are only six months, and this is not long enough for a healthy pregnancy. Answer: That year was a leap year [with two months of Adar], so Sarah’s pregnancy, from Sukkot to Passover, was seven months long, and seven months is long enough to give birth to a whole and healthy baby. The scholars then asked: On the day when G-d made His promise to Abraham that Sarah would become pregnant, Sarah menstruated, and so it was forbidden for Abraham to have conjugal relations with her until she stopped menstruating and was purified in a ritual bath, a process which took a number of days. So Sarah’s pregnancy was shorter than seven months. Answer: According to the sages there are two paths a woman’s pregnancy can take — one in which the pregnancy lasts seven months and one in which the pregnancy lasts nine months; both paths are natural and normal. A woman on the nine month path will give birth to a baby after precisely 271 days, no more and no less. A woman whose pregnancy is on the seven month path can give birth earlier or later than seven months and the length of her pregnancy is not precise. Therefore Sarah, who gave birth to Isaac on Passover, did give birth in fewer than seven months, but the baby was born healthy. The early sages also determined that Sarah, Rachel, and Hannah became pregnant on Rosh Hashanah.
The pregnancies of Rachel and of Hannah are learned from the following verses. Of Rachel it is written “Then G-d remembered Rachel, and G-d listened to her and opened her womb” (Genesis 30:22) and of Hannah it is written “And Elkanah knew Hannah his wife, and the Lord remembered her” (I Samuel 1:19). Of Rosh Hashanah it is written “Speak to the children of Israel, saying: ‘In the seventh month, on the first day of the month, you shall have a sabbath-rest, a remembrance of blowing of trumpets, a holy convocation'” (Leviticus 23:24). Because the idea of remembrance is used in reference to Rosh Hashanah and the pregnancies of Rachel and of Hannah, the scholars learned that Rachel and Hannah became pregnant on Rosh Hashanah. How did they know that Sarah also became pregnant on Rosh Hashanah? Answer: In reference to both Hannah and Sarah the idea of conception is used. Of Hannah it is written “Hannah conceived and bore a son” and of Sarah it is written “For Sarah conceived and bore Abraham a son” (Genesis 21:2). Just as Hannah conceived on Rosh Hashanah, so did Sarah.
(Babylonian Talmud, Tractate Rosh Hashanah 11a)