What Does the Catholic Church Say About the Sabbath Day?

Quotations from the Catholic Church Catechism.

II. THE LORD'S DAY

This is the day which the LORD has made; let us rejoice and be glad in it.¹⁰³

The day of the Resurrection: the new creation

2174 Jesus rose from the dead "on the first day of the week."¹⁰⁴ Because it is the "first day," the day of Christ's Resurrection recalls the first creation. Because it is the "eighth day" following the sabbath,¹⁰⁵ it symbolizes the new creation ushered in by Christ's Resurrection. For Christians it has become the first of all days, the first of all feasts, the Lord's Day (he kuriake hemera, dies dominica) Sunday:

We all gather on the day of the sun, for it is the first day [after the Jewish sabbath, but also the first day] when God, separating matter from darkness, made the world; and on this same day Jesus Christ our Savior rose from the dead.¹⁰⁶

Sunday - fulfillment of the sabbath

2175 Sunday is expressly distinguished from the sabbath which it follows chronologically every week; for Christians its ceremonial observance replaces that of the sabbath. In Christ's Passover, Sunday fulfills the spiritual truth of the Jewish sabbath and announces man's eternal rest in God. For worship under the Law prepared for the mystery of Christ, and what was done there prefigured some aspects of Christ:¹⁰⁷

Those who lived according to the old order of things have come to a new hope, no longer keeping the sabbath, but the Lord's Day, in which our life is blessed by him and by his death.¹⁰⁸

2176 The celebration of Sunday observes the moral commandment inscribed by nature in the human heart to render to God an outward, visible, public, and regular worship "as a sign of his universal beneficence to all."¹⁰⁹ Sunday worship fulfills the moral command of the Old Covenant, taking up its rhythm and spirit in the weekly celebration of the Creator and Redeemer of his people.

Quotations from the Convert's Catechism of Catholic Doctrine.

"Have you not any other way of proving that the Church has power to institute festivals of precept?" 
"Had she not such power, she could not have done that in which all modern religionists agree with her, she could not have substituted the observance of Sunday, the first day of the week, for the observance of Saturday, the Seventh day, a change for which there is no Scriptural authority" Stephen Keenan, A Doctrinal Catechism 3rd ed. p. 174 

How prove you that the Church hath power to command feasts and holydays? 
By the very act of changing the Sabbath into Sunday, which Protestants allow of; and therefore they fondly contradict themselves, by keeping Sunday strictly, and breaking most other feasts commanded by the same Church." Henry Tuberville, An Abridgment of the Christian Doctrine (1833 approbation), p.58 (Same statement in Manual of Christian Doctrine, ed. by Daniel Ferris [1916 ed.], p.67) 

"The Catholic Church,... by virtue of her divine mission, changed the day from Saturday to Sunday. 
" The Catholic Mirror, official organ of Cardinal Gibbons, Sept. 23, 1893. 

"Is Saturday the 7th day according to the Bible and the 10 Commandments?" 
"I answer yes". 
"Is Sunday the first day of the week and did the Church change the 7th day, Saturday, for Sunday, the 1st day?" 
"I answer yes". 
"Did Christ change the day?" 
"I answer no!" Faithfully yours, "J. Cardinal Gibbons" Gibbons' autograph letter. 

Which is the Sabbath day? 
Saturday is the Sabbath day. 
Why do we observe Sunday instead of Saturday? 
We observe Sunday instead of Saturday because the Catholic Church transferred the solemity from Saturday to Sunday." 
Peter Geiermann, The Convert's Catechism of Catholic Doctrine (1946 ed.), p.50. Geiermann received the "apostolic blessing" of Pope Pius X on his labors, January 25, 1910. 

"The Catholic Church changed the observance of the Sabbath to Sunday by right of the divine, infallible authority given to her by her Founder, Jesus Christ. The Protestant, claiming the Bible to be the only guide of faith, has no warrant for observing Sunday. 

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In this matter the Seventh Day Adventist is the only consistent Protestant. The Catholic Universe Bulletin, Aug. 14, 1942, p.4 

"The observance of Sunday by the Protestants is an homage they pay, in spite of themselves, to the authority of the [Catholic] church." Monsignor Louis Segur, Plain Talk About the Protestantism of Today (1868), p. 213 

How Was the Sabbath Day Changed From Saturday to Sunday?

Sol Invictus ("Unconquered Sun") was the official sun god of the later Roman Empire and a patron of soldiers. In 274 the Roman emperor Aurelian made it an official cult alongside the traditional Roman cults.

The Roman gens Aurelian was associated with the cult of Sol.^[21] After his victories in the East, the Emperor Aurelian thoroughly reformed the Roman cult of Sol, elevating the sun-god to one of the premier divinities of the Empire. Where previously priests of Sol had been simply sacerdotesand tended to belong to lower ranks of Roman society,^[22] they were now pontifices and members of the new college of pontifices instituted by Aurelian. Every pontifex of Sol was a member of the senatorial elite, indicating that the priesthood of Sol was now highly prestigious. Almost all these senators held other priesthoods as well, however, and some of these other priesthoods take precedence in the inscriptions in which they are listed, suggesting that they were considered more prestigious than the priesthood of Sol.^[23] Aurelian also built a new temple for Sol, bringing the total number of temples for the god in Rome to (at least) four^[24] He also instituted games in honor of the sun god, held every four years from AD 274 onwards.

...claiming the Unconquered Sun as a companion to the Emperor, used with particular frequency by Constantine.^[26] Statuettes of Sol Invictus, carried by the standard-bearers, appear in three places in reliefs on the Arch of Constantine. Constantine's official coinage continues to bear images of Sol until 325/6. A solidus of Constantine as well as a gold medallion from his reign depict the Emperor's bust in profile twinned (jugate) with Sol Invictus, with the legend INVICTUS CONSTANTINUS^[27]

(After his conversion to Christianity) Constantine decreed (March 7, 321) dies Solis—day of the sun, "Sunday"—as the Roman day of rest [CJ3.12.2]:

On the venerable day of the Sun let the magistrates and people residing in cities rest, and let all workshops be closed. In the country however persons engaged in agriculture may freely and lawfully continue their pursuits because it often happens that another day is not suitable for grain-sowing or vine planting; lest by neglecting the proper moment for such operations the bounty of heaven should be lost.^[28]

http://en.wikipedia.org/wiki/Sol_Invictus

 On March 7, 321, Sunday, the Day of the Sun, was declared an official day of rest, on which markets were banned and public offices were closed,^[21] except for the purpose of freeing slaves. The Christians reacted to this by moving their Sabbath from the tradition Jewish day to Sunday. There were, however, no restrictions on performing farming work, which was the work of the great majority of the population, on Sundays.^[22]

http://en.wikipedia.org/wiki/Constantine_the_Great_and_Christianity

The very next day, Constantine enacted another law giving pagan soothsayers official acceptance in the Empire. In all Constantine issued five additional Sunday laws over a few years to strengthen the first one.

The meaning of these weekly Sunday rituals is explained as follows:

Constantine sent to the legions, to be recited upon that day, a form of prayer which could have been employed by a worshiper of Mithra, of Serapis, or of Apollo [277], quite as well as by a Christian believer. This was the official sanction of the old custom of addressing a prayer to the rising sun." [280]

Constantine (337-361 AD), in council with the local bishop of Rome, aimed at bringing about conditions which would bring peace and prosperity where there was distrust and persecution among the leading religions of the Empire. Thus the foundations for a compromise were laid transforming the Christian Church away from its scriptural roots in the fourth century A.D.

"The Logos has transformed by the New Alliance the celebration of Sabbath to the rising of the light. He has given us a type of the true rest in the saving day of the Lord, the first day of light. ... In this day of light - first day and the true day of the sun - when we gather after the interval of six days, we celebrate the holy and spiritual Sabbaths. ... All things whatsoever that were prescribed for the Sabbath, We have transferred them to the Lord's day, as being more authoritative and more highly regarded and first in rank, and more honorable than the Jewish Sabbath. In fact it is on the day of the creation of the world that God said, `Let there be light and there was light.' It is also on this day that the Sun of Justice has risen for our souls." [288]  ([288] Eusebius, Commentary on the Psalms, Psalm 91, in Patrologie Cursus Completus, ed. J.P. Migne, p. 23, 1169-1172.) 

http://www.specialtyinterests.net/lords_day_history.html#tld

a) No traces of the observance of the Sunday are found until about the middle of the second century. Those appear first in Justin Martyr's First Apology. The leading reason assigned by him for its observance is founded on a mystical interpretation of certain passages supposed to refer to the millennium. The supposed resurrection of Christ on that day is mentioned incidentally as a secondary reason. About the close of the second century, the idea of commemorating the resurrection by the observance of the Sunday increases, and the term "Lord's Day" begins to be applied to it.

http://www.specialtyinterests.net/lords_day_history.html#tld

Some may say it doesn't matter which day we worship on since we do not live under the law but under grace. If that is true, then it doesn't matter if we lie, cheat, steal, murder or worship idols. These are the other commandments.