Ok, I've read over a good bit of what he has on the site relating to this issue. His position can be summarized as follows:
1) Based on his understanding of the Fathers and Papal Encyclicals, he believes that we are to understand Scriptural passages literally unless there is very persuasive evidence that they should not be taken literally.
2) He believes that the Scriptures teach geocentricity.
3) He affirms that the Scriptures are not a "science book" per se, but maintains that when "science and faith intersect" the truth will always be the same (ie. scripture is not a science book, but it also does not make inaccurate scientific statements)
4) He believes that heliocentricity is, at best, a theory with a number of flaws
5) He believes that all of the mathematical and scientific data, and that all of the practical things we do (e.g., launching satellites, shuttles, etc.) can be accounted for and will work within a geocentric solar system and universe. He believes that these shuttles/satellites/etc will work or function even when the builders/designers think that the solar system/universe is heliocentric.
6) Therefore, a good Catholic should affirm geocentricity since it is what the Scriptures appear to teach, and since science has not persuasively demonstrated heliocentricity.
His challenge, of course, is one that cannot be answered, which is why he made it: he's making a point that you cannot prove
heliocentricity. You cannot scientifically prove heliocentricity any more than you could prove evolution or the big bang; at most, you can provide evidence and show how such theories answer for and take into account the numerous variables involved.
So, I understand what he seems to be doing on a certain level; however, I think he is misunderstanding the problem. He sees things such as this undermining the Catholic Faith: people are placing more faith in science than in the Church in his mind. Therefore, he does not merely see a slight correlation between this issue and the deterioration of the Church (ie. heliocentricity might be part of a larger problem that is causing Christians to stumble), but sees a definate causation involved (ie. heliocentricity in itself unquestionably causes Christians to stumble). From a Catholic vantage point, the truth is probably very difficult to see: almost all of Catholic and Protestant belief is based on a humanistic and rationalistic foundation. It's not heliocentricity and evolution that are causing Catholics to lose faith in their Church, but it is the underlying premises and mindset that these theories sprang from that is undermining the faith.
I guess I'm not really sure what to say about his arguments for geocentricity--or in any event, his arguments demonstrating that geocentricity is just as plausible as heliocentricity. He does have me somewhat interested, though, so I might get a few books from the library. In the end, I don't find the issue to be of crucial importance to the Orthodox Christian, though, like other matters of science, it is interesting and should not be totally ignored.
PS. To my shock and amazement, this fella seems to affirm an open view of God. One time an open theist had told me that a Catholic priest friend of his was considering the open view position, but I hadn't really given it much thought. To be quite honest, I'm at a loss to understand how someone in a traditional Church can affirm the idea that God "changes his mind". Well, on the other hand, I guess I can understand it (to a degree), some people need everything to fit "logically," and so if "God answers prayers," God must be able to change his mind