Halakhah zu Bamidbar 28:9

In the morning we arise early to the Synagogue and we arrange the blessings, the biblical paragraphs of the sacrifices, and the Mishanayos of (the Chapter) אֵיזֶהוּ מְקומָן (What is the Location, Zevachim Perek 5) like the order of the other days only we add וּבְיום הַשַּׁבָּת (And on the Sabbath Day, Bamidbar 28:9-10). And we say בָּרוּךְ שֶׁאָמַר (Blessed is the one that said) and 'Pesukei Dezimra' (Verses of Song), and we are accustomed to add Psalms because there is no work for the Nation.

The commandment of the additional sacrifice of Shabbat: That Israel was commanded to sacrifice two lambs [as a] sacrifice on every Shabbat day, in addition to the regular sacrifice of every day. And it is called the addition of Shabbat, as it is stated (Numbers 28:9), "And on the Shabbat day, two lambs, etc."

Laws of Rosh Ḥodesh that happens to fall on Shabbat, which has three clauses: On Rosh Ḥodesh that happens to fall on Shabbat, for the 'aravit, shaḥarit, and minḥah services pray the regular seven blessings, but say Ya'aleh v-Yavo in the 'avodah prayer, and it is not necessary to menton Shabbat in the Ya'aleh v-Yavo. And take out two Torah scrolls, and read from the first the seven regular readings for the day, and from the second read the mafṭir — "and on the Sabbath day" and "and on your new moons" until the end of the portion, Numbers 28:9-15. And as a prophetic conclusion read Isaiah 66, "The heavens are My throne" except for Rosh Ḥodesh Elul that falls on Shabbat, on which we read Isaiah 54:11–55:5, "Unhappy, storm-tossed..." (Rema: And some do say Isaiah 66, and thus is the custom in our lands, but on Rosh Ḥodesh Av that falls on Shabbat we as a prophetic conclusion read the portion starting with Jeremiah 2:4, "Hear ye," and this is the general practice where there is no custom. And if Rosh Ḥodesh happens upon one of the four special Shabbatot, we read the final prophetic reading for that reading, and see below, siman 785.)

“It is a good custom to shorten the Morning Prayer” - Containing one paragraph.
It is good to shorten the poems and the penitential prayers of the Morning Service so as to speed up the matter so that one can pray the Additional Service¹⁶⁶Musaf, מוסף, the Additional Service; is a special section of prayers that is added to the Morning Service on Sabbaths, festivals, and New Moons which corresponds to the additional sacrifice that was made on these days in the Temple. In the Bible (Numbers 28-29) additional offerings are prescribed to be brought on Sabbaths, the three pilgrimage festivals, Sukkot, Pesaḥ, and Shavuot, Rosh HaShanah, Yom Kippur, and Rosh Ḥodesh (New Moons). Talmud tractate Yoma 33a states that this Additional Sacrifice was to be made after the regular Morning Sacrifice. After the Temple was destroyed the Musaf Service found its place after the Shaḥarit (see footnote 17) Service in the prayers on these Sabbaths and festivals. The Musaf Service now comes immediately after the Torah Service, where the Torah and Haftarah (see footnote 170) are read, which follows the Morning Prayers on Sabbaths, festivals, and New Moons. Musaf can be recited anytime during the day, but one who recites it after the seventh hour (1:00 P.M. according to our time system except on Yom Kippur, see footnote 167) is considered a transgressor.
The Musaf Service begins with the reader's recitation of the half-Kaddish, or praise of God (see footnote 177), which is followed by the Musaf Amidah (see footnote 43). This Amidah normally consists of seven benedictions, the first and last three being the same as is always said, and the middle benediction known as Kedushat ha-Yom, "Sanctity of the Day". In the case of the Musaf Service the middle benediction has an introductory paragraph followed by a prayer for the restoration of the Temple Service, and it concludes with the section from the Torah which deals with the particular Additional Sacrifice made on that Sabbath or festival.
On Rosh HaShanah the Musaf Amidah takes on a unique configuration. It has three central benedictions, thus making a total of nine benedictions in the Amidah. The three benedictions cover the theme of the holy day, malkhuyyot (kingships), zikhronot (remembrances), and shofarot (Ram's Horns, see footnote 221).
The Musaf Amidah after being recited silently is repeated outloud by the reader (see footnote 42). On the Sabbath, the Musaf Amidah is made up of twenty-two verses following the Hebrew alphabet backwards, and a description of the Musaf Sacrifice found in Numbers 28:9-10. The Musaf Amidah takes on a slightly different form for each festival. On the Day of Atonement, the Amidah opens with the usual three benedictions. This is followed by the description of the Additional Sacrifices made on Yom Kippur found in Numbers 29:7-8. After this a prayer for the forgiveness of sins is found. The Confession, the Al Ḥet and Ashamnu Prayers (see footnote 45), form the most important part of the Amidah as they do in the other Amidot of Yam Kippur. Various piyyutim (see footnote 149) are added in the reader's repetition of the Musaf Amidah on Rosh HaShanah and Yom Kippur.
Aaron Rothkoff, E. J., v. 12, pp. 532-34. before the seventh hour (1:00 P.M.).¹⁶⁷In halakhic literature the daylight hours were divided up into twelve equal parts regardless of how short or long the day was at various times of the year. In rough terms we can think of daylight beginning at 6:00 A.M. and ending at 6:00 P.M. Therefore the first hour of the day, in halakhic terms begins at 6:00 A.M. and ends at 7:00 A.M. We need then only add six to the halakhic hour to get the approximate corresponding time in our system. Therefore the seventh hour for us would be seven plus six, which is thirteen o'clock or, in other words 1:00 P.M.