Still waiting for a explanation of how a flat plane can be the centre of a three dimensional space.

Luke... go farther.

OKAY, YOUR POINT ?

Pope Alexander VII issued the bull Speculatories Domus Israel which he affixed to a new Index condemning all books in any way teaching heliocentrism, commanding and enjoining by his Apolistic Authority "all persons everywhere to yield to this Index a constant and complete obedience. The importance of this docuмent cannot be minimised,it included and reaffirmed not onlt the previous condemnations, but "all the relevant decrees up to the present time, that have been issued since the Index of our predecessor Clement. The creationist scholar Paula Haigh rightly concludes from this that "The evidence for Papal  Infallibility in the Galileo case rests, then, upon the Bull of Alexander VII in 1664. "

Future Popes allowed it as a theory, the Modernists ran with it When Pope Benedict XVI opened the floodgates by permitting the false theory to be taught as theory in schools, and in 1822 Pius VII " bowing to the general opinion of modern astromeners ," began gradually removing books on heliocentrism from the Index. When Gregory XVI finally removed them all in 1835 , the sequel was not hard to predict. Galileo's views on Bibilical exegesis became the norm, and the Bible no longer figured as a scientific authority. The Holy Ghost had to make way for the dictatorial new scholarship.

You must be speaking of the heliocentrics because that is exactly what they did. Didn't like what the Pope said.

If one subscribes to the R&R position, one is free to accept and reject whichever teaching of a Pope one wants. Also, since the R&R position allows for a manifest heretic to be a Pope, there would be no problem with a Pope uttering the "heresy" of Heliocentrism.

Sorry this is off topic of "Heliocentric Hoax", but related to the comment above: Do sedevacantists reject Pope Pius XII's demands when they (sedevacantists) refuse to implement the liturgical changes of 1955?
Back on topic, when the Popes made allowance for Heliocentric writings was it based on verifiable factual information from unbiased sources? 

Back on topic, when the Popes made allowance for Heliocentric writings was it based on verifiable factual information from unbiased sources?

Galileo did not have enough science evidence to support his theories.  He tried to make his case stronger by pressuring the Church to reinterpret Scripture.  He totally deserved his condemnation.  Later heliocentrism was less objectionable, so I can understand the popes softening their views.  I can't think of any docuмentation for what their motives were.

Here is the Wikipedia summary:

In 1758 the Catholic Church dropped the general prohibition of books advocating heliocentrism from the Index of Forbidden Books.^[73] It did not, however, explicitly rescind the decisions issued by the Inquisition in its judgement of 1633 against Galileo, or lift the prohibition of uncensored versions of Copernicus's De Revolutionibus or Galileo's Dialogue.^[73]The issue finally came to a head in 1820 when the Master of the Sacred Palace (the Church's chief censor), Filippo Anfossi, refused to license a book by a Catholic canon, Giuseppe Settele, because it openly treated heliocentrism as a physical fact.^[74] Settele appealed to pope Pius VII. After the matter had been reconsidered by the Congregation of the Index and the Holy Office, Anfossi's decision was overturned.^[74] Copernicus's De Revolutionibus and Galileo's Dialogue were then subsequently omitted from the next edition of the Index when it appeared in 1835.^[75]

https://en.wikipedia.org/wiki/Galileo_affair

Here is an English translation of the 1820 decree:

The Assessor of the Holy Office has referred the request of Giuseppe Settele, Professor of Optics and Astronomy at La Sapienza University, regarding permission to publish his work Elements of Astronomy in which he espouses the common opinion of the astronomers of our time regarding the earth’s daily and yearly motions, to His Holiness through Divine Providence, Pope Pius VII. Previously, His Holiness had referred this request to the Supreme Sacred Congregation and concurrently to the consideration of the Most Eminent and Most Reverend General Cardinal Inquisitor. His Holiness has decreed that no obstacles exist for those who sustain Copernicus’ affirmation regarding the earth’s movement in the manner in which it is affirmed today, even by Catholic authors. He has, moreover, suggested the insertion of several notations into this work, aimed at demonstrating that the above mentioned affirmation [of Copernicus], as it is has come to be understood, does not present any difficulties; difficulties that existed in times past, prior to the subsequent astronomical observations that have now occurred. [Pope Pius VII] has also recommended that the implementation [of these decisions] be given to the Cardinal Secretary of the Supreme Sacred Congregation and Master of the Sacred Apostolic Palace. He is now appointed the task of bringing to an end any concerns and criticisms regarding the printing of this book, and, at the same time, ensuring that in the future, regarding the publication of such works, permission is sought from the Cardinal Vicar whose signature will not be given without the authorization of the Superior of his Order.

http://inters.org/approval-Settele-heliocentric