CathInfo.com

To be fair, if a pope uses "may not" in an encyclical, that's hardly a definitive teaching.  Not all encyclicals are infallible, by nature.  It depends how they are written.  Benedict's "openness to science" (similar to Pius XII on theistic evolution) is neither a teaching, nor a decisive statement.  In my opinion, both were horribly wrong for opening pandora's box but there is no authoritative nature in any of this.  In other words, Benedict XV was just wrong (as was Pius XII) and St Robert and company are still correct.

The Holy Office of 1633 is correct.  No, the 3rd possibility is that Benedict XV, like Pius XII, were either liberal or listened to liberal advice.  Their encyclicals were not heretical and neither were they authoritative.  When speaking on science, you can't judge such as a "teaching" in the same way as an encyclical on the sacraments.  Infallibility only protects faith/morals.  The matters of science (those discussed in the Bible) are part of Faith but also outside of it.

My opinion = they were convinced that "new facts" had emerged to possibly change the Church's views.  Theology cannot change, but science can still discover.  So since Faith and Reason are not in opposition, it is *possible* for new facts to emerge which can partially (but not substantially) change the Church's views...only in the realm of science.  That's why Benedict used "may" to denote theory and also why Pius XII said that "further investigation" is allowed on evolution.

But we know now that these "new facts" are lies and so all of this is water under the bridge.  We return to the Church Fathers and 1633 as our authority.

From Alberto Martinez' book, this paragraph from a timeline of events regarding the Galileo and Bruno affairs. 

1885 – Father William Roberts publishes his book The Pontifical Decrees Against the Doctrine of the Earth’s Movement.  In this book, Fr. Roberts presents a strong case for the position that the Church’s condemnation of heliocentrism is infallible. He concludes: (1) Alexander VIII’s Speculatores was a papal act of supreme authority by which the pope, in the face of the whole Church, confirmed and approved the decrees with his Apostolic authority, and made himself responsible for their publication, that heliocentrism was false; (2) heliocentrism was false because the Church declared it a heresy, and whoever says an opinion is heresy ipso facto says that the contradictory of that opinion has been revealed by God with sufficient certainty to oblige a Catholic to accept it by an act of divine faith; and, (3) infallible teachings, even those ex-cathedra, do not generally generate any fresh obligation of faith, but protect and vindicate one that already exists.

In any case, that quote from Benedict XV pretty much does away with the argument that it's heretical to reject geocentrism. Obviously a pope can't say, in effect, "it appears geocentrism is not correct" in an encyclical, if geocentrism is a dogma of faith. It would be like a pope saying in an encyclical, "It appears there are four Persons in God." Such a thing is against the nature of the papacy.