A few conservative Roman Catholics are pointing to a dozen Bible verses and the church's original teachings as proof that Earth is the center of the universe, the view that was at the heart of the church's clash with Galileo Galilei four centuries ago.The consensus that the Earth revolves around the Sun only lasted from about 1650 to about 1900. Since then, the consensus has been that motion is relative, and that geocentrism and heliocentrism are both valid. As quoted in my book, the early relativists said:
The relatively obscure movement has gained a following among those who find comfort in knowing there are still staunch defenders of early church doctrine. ...
"I have no idea who these people are," said Brother Guy Consolmagno, curator of meteorites and spokesman for the Vatican Observatory. "Are they sincere, or is this a clever bit of theater?"
Those promoting geocentrism argue that heliocentrism, or the centuries-old consensus among scientists that Earth revolves around the sun, is a conspiracy to squelch the church's influence.
Just as our Copernicus said to us: “It is more convenient to suppose that the earth turns round, because the laws of astronomy are thus expressed in a more simple language,” … these two propositions, “The Earth turns round,” and “It is more convenient to suppose the Earth turns round,” have the same meaning. There is nothing more in the one than in the other. [Poincare, 1902]There is nothing inaccurate about referring to a sunrise or sunset, even tho these terms imply a motion of the Sun. These terms refer to the motion of the Sun relative to the Earth, and that is a completely legitimate scientific view. Anyone who tells you that science says that the Sun does not really rise is a century out of date.
Strictly speaking, one should not, e.g., say that the earth moves around the sun in an ellipse, since this statement presupposes a coordinate system in which the sun is at rest, … In the investigation of the solar system nobody will employ a coordinate system at rest relative to the terrestrial body, since that would be impractical. But in principle such a coordinate system is according to the general theory of relativity fully equivalent to every other system. [Einstein, 1918]
Update: Galileo revival addresses this issue, and I left some comments there.