Gemara

10b - Beraisa - R. Eliezer: The world was created in Tishrei.

11a: R. Yehoshua says, it was created in Nisan.

12a - Beraisa: Chachmei Yisrael count the (months of the) Mabul like R. Eliezer, and the Tekufah like R. Yehoshua. (There are four Tekufos based on when certain constellations are the first to rise each night. They corresponding to the spring and fall equinoxes and the winter and summer solstices.)

Chachmei Nochrim count both of these like R. Yehoshua.

27a: Nowadays we say in Tefilas Rosh Hashanah 'today was the beginning of Your actions'. This is like R. Eliezer.

Berachos 59b - Beraisa: One who sees any of the following blesses "Oseh Ma'aseh Bereishis":

The sun in its Tekufah (in the same position in which it was created), the moon in its Gevurah, the stars in their paths, or the constellations in their order.

Question: When is the sun in its Tekufah?

Answer (Abaye): This occurs once every 28 years, on the fourth night of the week, when Shabtai (Saturn) is first to dominate at night. (The five closest planets, sun, and moon are called "Kochvei Lechet". At any time one of them 'dominates', according to a fixed rotation.)

Rishonim

Question (Tosfos 27a DH k'Man): If we count the Tekufah like R. Yehoshua, why is our Tefilah on Rosh Hashanah like R. Eliezer?

Answer #1 (Kitzur Piskei ha'Rosh Rosh Hashanah 1:3): We hold like R. Yehoshua. Nevertheless, Rosh Hashanah is the beginning of Hash-m's actions, i.e. the beginning of the act of judgment.

Gurei ha'Ari (brought in Ben Yehoyada Rosh Hashanah 10b DH R. Yehoshua): The Ari Zal says that the 'pregnancy' of the world was in Tishrei, and the birth in Nisan. This is we say 'ha'Yom Haras Olam' on Rosh Hashanah.

Rif and Rosh (Berachos 43b and 9:14): One who sees any of the following blesses "Oseh Ma'aseh Bereishis":

The sun in its Tekufah, the moon in its Tiharah, the stars in their Mishmaros, or the constellations in their times.

R. Yonah (DH ha'Ro'eh Chamah): It is known that every 28 years, Tekufas Nisan returns to the same place it was when it was created. This is on the fourth night of the week. When one sees the sun the next morning, he blesses.

R. Yonah (DH Levanah, according to Hagahos me'Eretz Yisrael): The moon is in its Tiharah when it returns to Mazel Teleh at the beginning of the month and does not tilt north or south. The same applies when any of the other five Kochvei Lechet returns to the beginning of Teleh, due east. R. Yehonason says that astronomers know the period after which the stars return to their position at the time of creation.

Rambam (Hilchos Berachos 10:18): At the beginning of every 28 year cycle, Tekufas Nisan is at the beginning of the fourth night. One who sees the sun the next morning blesses "Oseh Ma'aseh Bereishis": The same applies when the moon returns to Mazel Teleh at the beginning of the month and does not tilt north or south, or when any of the other five Kochvei Lechet returns to the beginning of Teleh, without tilting north or south. One also says this Berachah when he sees Teleh rise from the eastern end (of the sky).

Hagahos Maimoniyos (70): The Aruch brings this Perush, and another Perush that if the sun and stars were covered by clouds for three days in winter, one says this Berachah the next time he sees them.

R. Akiva Eiger (Berachos 59b): In the Aruch's text, Abaye did not explain 'the sun in its Tekufah'. The latter Perush is like the Yerushalmi.

Rambam (Hilchos Kidush ha'Chodesh 10:6): The calculation (of Rav Ada) that says that each year of Tekufos is slightly less than 365 and a quarter days is more accurate. Chachamim used it when deciding whether or not to make a leap year.

Mas'as Binyamin (101): Abaye is like Shmuel, who says that a year of (four) Tekufos is exactly 365 and a quarter days. The Halachah follows Rav Ada, that after 19 years the sun and moon return to the head of Teleh. Nevertheless, regarding Birkas ha'Chamah we follow Shmuel, for then the Berachah is on Yom Revi'i, just like at the time of creation. It is not difficult that we follow Rav Ada regarding Tekufos and leap years, and Shmuel regarding the Berachah. Similarly, the Halachah follows R. Eliezer regarding calculation of years, but we follow R. Yehoshua regarding Tekufos!

Chasam Sofer (Teshuvah OC 56): This is difficult. Surely, the Beraisa is according to Halachah. Abaye explained it like Shmuel, but we cannot, for we rule like Rav Ada. Rather, the Berachah mentioned in the Beraisa is for seeing something that he did not see in a while, like the Berachah for seeing the sea for the first time in 30 days. Perhaps the text of the Aruch should say '30 days'. Alternatively, it is after three days, for this is like the creation of the sun and moon after three days. However, the Rambam says to bless every 28 years like Abaye, but in Hilchos Kidush ha'Chodesh he rules like Rav Ada. Even though we have no answer, we keep the custom of Yisrael to bless.

Rambam (6:8,12,15, brought in Tur OC 427): The first Molad was on Sunday night at five hours and 204 parts (of 1080 of an hour). Every Molad is 29 and a half days and 793 parts, so it is 1:12:793 (days, hours and parts) later in the week. In all, the Molad is pushed later 4:8:876 in a simple year of 12 months, 5:21:559 in a leap year, and 2:16:595 after a cycle of 19 years (which has 12 simple and seven leap years). By adding up the amounts for the years since Bereishis, one can calculate the Molad for Tishrei.

Rashi (12a DH ul'Tekufos): The Halachah follows R. Yehoshua regarding Tekufos. The first Tekufas Nisan was at the beginning of the night, and all future ones are in the middle or the beginning of night or day.

Tosfos (8a DH l'Tekufos): Nowadays, the calculation from Bereishis of the Molad is 7:9:642 later than the actual time. Some say that this is because the moon stopped for this time after it was diminished, acting like one who was excommunicated. There is no source for this. Rather, the first Molad was at 14 hours of the day (Tishrei 1, Erev Shabbos), six hours before Adam was commanded (so it would be visible for him to Mekadesh immediately). It follows that Nisan of Tohu (corresponding to year 0), six months earlier, was Tuesday night, exactly 9:642. We count the Tekufos from Nisan of Tohu. The first Tekufas Nisan was at the beginning of Tuesday night.

Question (Tosfos, ibid.): A Beraisa (12a) says that we count Molados from Tishrei and Tekufos from Nisan. The difference between calculating the Molados form Tishrei and Nisan is more than two days. The Tana'im should have verified which is correct!

Note: Our text (12a) says that we count the Mabul like R. Eliezer (from Tishrei), and the Tekufah like R. Yehoshua. Perhaps the answer to Tosfos' question lies in the Rambam (10:7), who says that these calculations are based on the average position of the sun, but based on its true position the Tekufos are two days earlier.

Poskim

Shulchan Aruch (OC 229:2): One who sees the sun in its Tekufah blesses "Oseh Ma'aseh Bereishis": This happens every 28 years. The Tekufah is the beginning of the fourth night of the week. When one sees the sun the next morning, he blesses.

Magen Avraham (5): One should bless immediately at sunrise. The Maharil commanded that people bless immediately in the morning. Mas'es Binyamin says that one blesses upon leaving the Beis ha'Keneses after Shacharis. It seems that one may not bless after three hours, for by then the sun has moved from its place.

Mishnah Berurah (8): It is good to bless amidst many people. The Levush allows until three hours, but many allow until midday, i.e. with Shem and Malchus. If the sun is covered by clouds one may bless only if its impression can be seen. The Chasam Sofer would say before the Berachah "Halelu Es Hash-m Min ha'Shomayim...", and afterwards "Kel Adon Al Kol ha'Ma'asim..." until "v'Chayos ha'Kodesh", "Ha'Shomayim Mesaprim Kevod Kel", Aleinu Leshabe'ach and Kaddish.

Chasam Sofer (ibid.): It is not clear why women do not bless. The reason they do not bless on Kidush Levanah, that they caused its diminution, does not apply here.

Shulchan Aruch (ibid.): Similarly, he blesses when he sees the moon in its Tiharah, i.e. when it returns to Mazel Teleh at the beginning of the month and does not tilt north or south. The same applies when any of the other five Kochvei Lechet returns to the beginning of Teleh, without tilting north or south. One also blesses when he sees Teleh rise from the eastern end (of the sky).

Mishnah Berurah (9): The custom is not to bless these nowadays.