Geocentrism is being promoted by Robert Sungenis and Fr. Joseph Pfeiffer (in a talk he gave saying that Galileo was wrong) and the Saint Marys Resistance website.
The proof for Geocentrism requires all kinds of unmathematical, imaginary hypotheses and really insane ideas. For example, they say the Earth is not spinning on its axis. The Sun rotates around the Earth once every 24 hours. The stars rotate around the Earth every 24 hours.
This is an effort to discredit modern Astronomy and Evolution, as if they are connected. What happened to the idea that Science and Religion agree. Afterall, it is Science that disproves Evolution.
If some people are attracted to the Resistance because they are following the true Catholic Faith, they may be surprised to find this ancient concept being promoted, when in fact, Newtonian mathematics has proved Geocentrism is a false concept.