So we didn't land on the moon or send men into space? Um, okay. I'm sorry, but I trust the integrity of Lovell and the math of the major enginerds of NASA over "they just couldn't do it" from someone who doesn't seem to have much in the way of astronautical engineering degrees. The Apollo Missions (and Mercury, and pretty much anything NASA has done) were phenomenal feats of engineering, but they were possible and did happen, even though we had to learn how the hard way.
Most of the arguments I've heard that state we didn't land on the moon are based off of bad gouge and a poor understanding of science. For example: the Van Allen belt does contain high levels of radiation, which could conceivably kill a man, if he stays there long enough. However, it turns out you move pretty fast when you've been punted into space on the top of a Saturn V rocket, and the Apollo astronauts got through quickly and dodged any severe effects.
(Evidence:
http://lsda.jsc.nasa.gov/books/apollo/S2ch3.htm)
I think this is completely relevant to the discussion. The fact that humans have survived space travel, to include orbiting and landing on the moon, based off the calculations of a heliocentric model, proves that the earth is not fixed in space, doesn't it?