Gemara

R. Zeira: The day and night must be from the new (moon. Everything will be explained below.)

This is like R. Simlai's father taught.

Aba, R. Simlai's father: We calculate the Molad. The moon was seen close to sunset only if the Molad was before midday.

Question: Why do we need to know this?

Answer (Rav Ashi): This enables us to contradict witnesses (who testify falsely that they saw the new moon).

R. Zeira: The moon is covered for 24 hours. For us, six hours of the old are covered and 18 of the new. For them, six hours of the new are covered and 18 of the old.

Question: Why do we need to know this?

Answer (Rav Ashi): This enables us to contradict witnesses.

Question: What is the source that the day and night must be from the new?

Answer #1 (R. Yochanan): "(Yom Kipur is) Me'Erev Ad Erev".

Answer #2 (Reish Lakish): "(We eat Matzah) Ad Yom ha'Echad v'Esrim la'Chodesh ba'Erev".

Question: What is the difference between these answers?

Answer #1 (Abaye): They argue only about the source of the law.

Answer #2 (Rava): They argue about midnight.

Yotzer for Parashas ha'Chodesh (by R. Eliezer ha'Kalir, perhaps this is R. Eliezer b'Rebbi Shimon): (Hash-m showed to Moshe)...Zohar l'Sha'os Shesh Ta'aro Lehis'ashesh... less than six, all eyes weary (from trying to see it, but failing)... The time of its Molad was Chatzos (midday or midnight) Wednesday; until 30 Merutzos, it was not visible outside.

Rishonim

Ba'al ha'Ma'or: Most Chachamim say that all the Halachah does not follow any of these three difficult teachings. This is absurd! Can all the teachings about Sod ha'Ibur in the Gemara be unlike the Halachah?!

Preliminaries: The eastern extreme (of the land) is the west shore of the (great) ocean. Opposite this is the west (extreme of the land), which is the east shore of the ocean. Yerushalayim is in the middle of these two, on our side of the earth. Opposite Yerushalayim on the other side of the earth is the Tehom (the middle of the ocean). The sun circles the earth in 24 hours, from east to west. It takes six hours to go from one of these four places to the next. E.g. morning in Yerushalayim is midday in the east. When a day begins in Yerushalayim, that day begins six hours later in the west, 12 hours later in the Tehom, and 18 hours later in the east, even though it is only six hours away from Yerushalayim.

The moon merely reflects light from the sun. The Molad is when the moon is directly in line between the earth and the sun. At this moment the entire side facing earth is dark. Right after this, the moon is a bit east of the sun, and a tiny sliver of the side facing earth is lit, but is too faint for us to see. The moon makes a complete orbit of the earth (relative to the sun) 360 degrees, in 30 days. In one day it goes 12 degrees. Then enough is lit to be visible when the sun goes down. 'The time of the Molad' refers to the time in Yerushalayim at that moment.

R. Zeira taught that the day and night must be from the new. I.e. we may declare today Rosh Chodesh only if at some place in the world the Molad was before the start of this day, i.e. the night before. Since Yerushalayim is 18 hours 'ahead' of the east, if the Molad was before midday in Yerushalayim (let us say, on Shabbos), this is before Shabbos night begins in the east. We may make Shabbos to be Rosh Chodesh, even though the moon is too faint to be seen until Sunday in Yerushalayim (24 hours after the Molad), because it is visible in the east at the end of Shabbos. In Yerushalayim, even on Sunday the moon cannot be seen in broad daylight, only close to dark. This is like R. Simlai's father taught, that the moon was seen close to sunset, i.e. in the east, only if the Molad was before midday, i.e. in Yerushalayim. When Kidush ha'Chodesh was done through witnesses, they would rely on this calculation only in pressed circumstances; this is why the Gemara asked why we need the calculation. It answered that the calculation enables Beis Din to refute lying witnesses.

Usually, when the Bavli says 'for us' it refers to in Bavel, and 'for them' refers to in Eretz Yisrael. However, Bavel is less than two hours east of Yerushalayim. We must say that here, 'for us' refers to the east extreme, and that Malchus Bavel extended to there. We know that Shevor Malka was a great king over Bavel in the days of the Amora'im. R. Zeira's second teaching discusses how long the moon is covered. This is not from the time of the Molad. Rather, even when the moon is far enough from the sun to be seen (12 degrees away, 24 hours after the Molad), it can be seen only from a small part of earth. In daylight it is too weak to be seen. Since it is near the sun, at night (not close to sunrise or sunset) it is blocked by the earth.

Note: The new moon is east of the sun. One day after the Molad, it rises and sets about an hour after the sun. It is visible after sunset, but not after sunrise, for the sun is too strong by then. The old moon is west of the sun. It rises and sets before the sun; it can be seen before sunrise but not before sunset. Presumably, the old moon ceases to be visible more than 24 hours before the Molad, because an hour before sunrise the sky is not dark. We can understand the following if we say that the old moon becomes invisible 36 hours before the Molad.

Ba'al ha'Ma'or: If the Molad was at midday in Yerushalayim, the new moon reaches visibility (24 hours later) and can be seen in the east, where it is then nightfall, but it is not visible in Yerushalayim until evening, six hours later. If the old moon ceased to be visible in the east at sunrise, at the time it was midnight in Yerushalayim. The moon was not visible in Yerushalayim for the 18 hours before that, six of the night and 12 the previous day. This is what R. Zeira taught 'for them six hours of the new are covered and 18 of the old'. He also said 'For us, six hours of the old are covered and 18 of the new.' This is when the old moon became too faint in the morning in Yerushalayim. In the east it was last seen when it was morning there, six hours before this, and for the last six hours of visibility it was covered. If the new moon becomes visible in Yerushalayim at sunset, it is not visible in the east until it is sunset there, 18 hours later.

R. Yochanan learned from "Me'Erev Ad Erev" that just like Yom Tov is observed from night to night, also days of the month. Therefore, likewise the Molad must be visible the entire night (and hence, also the entire day) According to Rava, Reish Lakish learns from "... la'Chodesh ba'Erev". If it discussed eating Matzah, it would have said 'Ad Erev'. Rather, it teaches that the end and beginning of the month depend on the Erev. Until midnight is called Erev. Reish Lakish holds that it suffices for the Molad to be from midnight; the Halachah does not follow him.

Rebuttal (Ra'avad, Kasuv Sham DH Achar): This is like the Kuzari (5:2) and R. Avraham bar R. Chiya ha'Sefardi. We follow only Anshei ha'Talmud. Rav Yitzchak bar R. Baruch was an expert astronomer, and he refuted them. It is unreasonable to follow the far east. The Mo'adim depend on Eretz Yisrael.

The Kuzari (2:6, cited by Ra'avad, ibid.) Shabbos starts in Eretz Yisrael. The days were fixed in Eretz Yisrael by Adam ha'Rishon when he left Gan Eden. We all follow him. If the Molad is before six hours of the day in Yerushalayim, it is visible six hours later, before dark (and we can make the day Rosh Chodesh). It is visible 18 hours later in the east. This is the end of Shabbos in the east, even though it is Sunday in Yerushalayim.

Rebuttal (Ra'avad): According to this, we cannot explain 'the day and night must be from the new'. We can make a day Rosh Chodesh only if the Molad is before six hours of the day in Yerushalayim, so it is visible at night. Why does it suffice to fulfill "Me'Erev Ad Erev" in the east? In Yerushalayim, there were only six hours of the new!

Ra'avad (DH Motza): We cannot explain that the moon is covered 24 hours in one place, six hours of the old and 18 of the new or vice-versa. (This is because the old is always seen last in the morning, and the new at evening.) Rather, in every place at least six hours of the old from the time of the Molad and at least six of the new are covered. The Kalir wrote that if the Molad was at midday, it is not seen for 30 hours, until evening the next day.

Note: The Ba'al ha'Ma'or counted not from the Molad, rather, from when it is bright enough to be seen somewhere. Therefore he could explain six and 18 to be in the same place.

Ra'avad (DH v'Atah): R. Zeira taught that the moon is covered 24 hours regarding contradicting witnesses. Even though the moon can be seen after six hours, this is only at sunset. When we Mekadesh the month through witnesses, an hour is needed for them to see the moon, to come to Beis Din, for investigation of their testimony and for Beis Din to declare the month Mekudah. To enable Kidush ha'Chodesh that same day, the moon had to be seen by 11 hours of the day, when the sky is not so dark. The moon is too faint to be seen then unless it is at least 24 hours after the Molad.

Yesod Olam (cited in Chazon Ish OC 64:2,4): The Ba'al ha'Ma'or's Perush caused him to say that the day starts six hours to the east of Yerushalayim. There are difficulties with his Perush. It is absurd to say that the date line interrupts settled places, that it is different days in different parts of a city. Rather, the day begins in the ocean.

Acharonim and Poskim

Nichmad v'Na'im (brought in Encyclopedia Talmudica: Yom (citation 595)): The Yesod Olam understood (like people of his time) that there is one big ocean west of Europe/Africa and east of Asia/Australia, without any dry land. We do not care what day it is for the fish.

Rebuttal (of Yesod Olam - Chazon Ish): The Ran and Ritva agree with the Ba'al ha'Ma'or's Perush. Also, his Perush did not Mechadesh that the day starts six hours to the east; the Rishonim agreed about this.

Ya'avetz (Mor u'Ketzi'ah OC 344): Even if one travels around the world, he counts days according to sunsets, until he reaches a community with Yisraelim. Then, he adopts their day.

Chazon Ish (64:10): The line of longitude six hours east of Yerushalayim is the date line, where there is water. If this line of longitude passes through a land mass (e.g. Australia), the day is the same for entire land mass; it precedes Yerushalayim.

Note: The custom in Australia follows the Chazon Ish.

Encyclopedia Talmudica: Yom (citations 628,608,623,615,618,620,631 and p.686): The Levush (OC 428) says that each day begins nine hours east, because the Me'oros were put in the sky at three hours of the day (in Yerushalayim), so nine hours to the east it was sunset. Some put the date line six hours east from the Jordan river. Some put it (12 hours) opposite Yerushalayim. Some say that the Rishonim discussed a date line to explain the Gemara, but they did not mean that a community that conducted differently until now should change its practice. Many Acharonim say that one changes his day immediately upon crossing the line. Kav ha'Ta'arich ha'Yisraeli gives a total of 13 opinions about the date line. Many recent opinions say that every place should continue to conduct according to its current practice.

Note: The practice of communities in (eastern) Australian and Asian islands, even those entirely more than six hours east of Yerushalayim (e.g. Japan), precede Yerushalayim. Some say that one who goes such a place should be stringent for both opinions regarding Melachah on Shabbos.