Some time ago the Dimonds put together an interesting article on the status on Geocentrism, arguing that the Church has not settled the matter.
They brought up an intereting quote from Pope Benedict XV's encyclical In Praeclara Summorum:
"If the progress of science showed later that that conception of the world rested on no sure foundation, that the spheres imagined by our ancestors did not exist, that nature, the number and course of the planets and stars, are not indeed as they were then thought to be, still the fundamental principle remained that the universe, whatever be the order that sustains it in its parts, is the work of the creating and preserving sign of Omnipotent God, who moves and governs all, and whose glory risplende in una parte piu e meno altrove; and though this earth on which we live may not be the centre of the universe as at one time was thought, it was the scene of the original happiness of our first ancestors, witness of their unhappy fall, as too of the Redemption of mankind through the Passion and Death of Jesus Christ."
Pope Benedict XV explicitly states that something else than geocentrism might be true. Also, the heliocentric work were removed from the Index of Forbidden Books during the pontificate of Pope Benedict XIV, and Pope Pius VII approved printing books on movement of earth in Rome.
While I'm not opposed to geocentrism (I simply don't know, I have not studied the topic and evidence properly), it seems that the Church has not settled the matter yet. Jut as Stubborn said, I highly doubt whether people are judged by God on whether they believed in geocentrism or heliocentrism, provided they remained of good will.
The Dimond brothers are sedevacantists. Their sedevacantism belief is because they hold Vatican II popes as heretics.
Now if Pope Paul V's decree defining and declaring heliocentrism formal heresy - were taken seriously - then popes who believed heliocentrism from 1741 would also be heretics and thus sedevacantism would have to be moved backwards in time and did not begin in 1962. It is in the interest of the Dimond brothers to deny the 1616 decree was papal and for all time.
In 1633 Pope Urban VIII confirmed the 1616 decree was ABSOLUTE, non-reformable. In 1820 the Holy Office also confirmed the 1616 decree was infallible and remained so:
Olivieri: ‘In his “motives” the Most Rev. Anfossi puts forth “the unrevisability of pontifical decrees.” But we have already proved that this is saved: the doctrine in question at that time was infected with a devastating motion, which is certainly contrary to the Sacred Scriptures, as it was declared.’ --- Report to Pope Pius VII
Here above is the judgement of Maurizio Benedetto Olivieri (1769-1845) Commissary General of the Inquisition found in his written report given to Pope Pius VII. It confirms the heliocentrism of Galileo is formal heresy.
Now were I to tell you what happened next you would not believe me, but they found a way to ignore this heresy as belonging only to Galileo's time but not then (1741 -1820). They stated the new science-proven heliocentrism was not heretical so all could be accepted and the old one forgotten. And that is why the heresy was thereafter ignored in the Catholic Church. Popes could then believe in heliocentrism, Copernicus, Galileo, Kepler and Isaac Newton without being accused of heresy. That is how the Dimond brothers and a million other Catholics can deny the heliocentrism of today is not heresy, not Church teaching. In fact the Church was cheated out of its dogma, a dogma that lasted only 100 years.
Now about Pope Benedict XV's encyclical
In Praeclara SummorumFew today are even aware that Pope Benedict XV, on April 30th, 1921, just one year after his teaching encyclical on how the Scriptures reveal all truth, wrote a different kind of encyclical letter, praising the Catholic writings of Dante. Dante, we remind ourselves, is known for his vision of the geocentric world:
Having written in Spiritus Paraclitus of the dangers ‘physical science’ can cause if it is not the truth, watch now as the Pope himself applies an ‘if’ of science to Dante’s most famous work The Divine Comedy, sometimes called ‘the Summa in verse.' Caught up in the universal belief that science has proven its Copernican cosmology, and unwilling to degrade the Catholicity of Dante’s description of a geocentric Heaven, Hell and Purgatory, the Pope feels he has to rescue all this ‘if’ science is correct. The balance between his faith and the pressure from ‘science,’ in this encyclical, given the fact that no pope ever officially denied the 1616 decree, is not committing this letter to endorsing Galileoism, only to the scenario ‘If the progress of science showed later.’
‘And first of all, inasmuch as the divine poet throughout his whole life professed in exemplary manner the Catholic religion, he would surely desire that this solemn commemoration should take place, as indeed will be the case, under the auspices of religion, and if it is carried out in San Francesco in Ravenna it should begin in San Giovanni in Florence to which his thoughts turned during the last years of his life with the desire of being crowned poet at the very font where he had received Baptism. Dante lived in an age which inherited the most glorious fruits of philosophical and theological teaching and thought, and handed them on to the succeeding ages with the imprint of the strict scholastic method. Amid the various currents of thought diffused then too among learned men Dante ranged himself as disciple of that Prince of the school so distinguished for angelic temper of intellect, Saint Thomas Aquinas. From him he gained nearly all his philosophical and theological knowledge, and while he did not neglect any branch of human learning, at the same time he drank deeply at the founts of Sacred Scripture and the Fathers. Thus he learned almost all that could be known in his time, and nourished specially by Christian knowledge; it was on that field of religion he drew when he set himself to treat in verse of things so vast and deep. So that while we admire the greatness and keenness of his genius, we have to recognize, too, the measure in which he drew inspiration from the Divine Faith by means of which he could beautify his immortal poems with all the lights of revealed truths as well as with the splendours of art. Indeed, his Commedia, which deservedly earned the title of Divina, while it uses various symbolic images and records the lives of mortals on earth, has for its true aim the glorification of the justice and providence of God who rules the world through time and all eternity and punishes and rewards the actions of individuals and human society. It is thus that, according to the Divine Revelation, in this poem shines out the majesty of God One and Three, the Redemption of the human race operated by the Word of God made Man, the supreme loving-kindness and charity of Mary, Virgin and Mother, Queen of Heaven, and lastly the glory on high of Angels, Saints and men; then the terrible contrast to this, the pains of the impious in Hell; then the middle world, so to speak, between Heaven and Hell, Purgatory, the Ladder of souls destined after expiation to supreme beatitude. It is indeed marvellous how he was able to weave into all three poems these three dogmas with truly wrought design.
If the progress of science showed later that that conception of the world rested on no sure foundation, that the spheres imagined by our ancestors did not exist, that nature, the number and course of the planets and stars, are not indeed as they were then thought to be, still the fundamental principle remained that the universe, whatever be the order that sustains it in its parts, is the work of the creating and preserving sign of Omnipotent God, who moves and governs all, and whose glory risplende in una parte piu e meno altrove; and though this earth on which we live may not be the centre of the universe as at one time was thought, it was the scene of the original happiness of our first ancestors, witness of their unhappy fall, as too of the Redemption of mankind through the Passion and Death of Jesus Christ. Therefore the divine poet depicted the triple life of souls as he imagined it in such a way as to illuminate with the light of the true doctrine of the faith the condemnation of the impious, the purgation of the good spirits and the eternal happiness of the blessed before the final judgment.’
Can you imagine how Pope Benedict XV would have loved Dante’s works if he knew geocentrism was as true as it was in Dante’s time? One of the many reasons alluded to by the Copernican apologists is to say that the 1616 decree was not a binding decree for all time because Pope Benedict XV in this encyclical did not uphold that decree of a moving sun and fixed earth at the centre of the universe. In fact, the Pope takes a neutral stand on the matter submitting to the post-1915 position of science that holds there is no scientific proof for either geocentrism or heliocentrism, that is, spatial relativity prevails. The Pope implies this when he writes: ‘If the progress of science showed later that that conception of the world rested on no sure foundation…’ followed by ‘this earth on which we live may not be the centre of the universe as at one time was thought.’ We say let us be thankful the Pope wrote that the earth ‘may not’ be the centre of the universe rather than ‘is not the centre of the universe.’ The difference we can assure you is profound. Given the fact that in his time heliocentrism was still considered the scientific truth by his Jesuits, one surely would have expected the Pope to say ‘is not the centre.’ One could equally say Pope Benedict XV with the words ‘may not be’ did not accept the heliocentrism demanded by the Holy Office in 1820. Like all the popes since 1616, not one of then explicitly denied the 1616 decree officially, or abrogated the decree by way of the Magisterium.