We teach our students that when a mechanism does not support their observations, the mechanism must either be revised to support the facts or entirely discounted. They are not required to provide an alternative. -James Tour, Synthetic Chemist

This isn't about competetive models. It's about truth. "Globe earth, heliocentric universe" doesn't have the grounds upon which to go on the offensive polemically, it is in dire need of apologetic defense. Unfortunately for it, there is none.

A globe earth would dictate a measurable and detectable curve. This cannot be supplied. The contrary can be. The recent survey work of JTolan covers this nicely. The California aqueduct when measured as a manmade structure measures over distance as with a curved earth, but when the water contained within is measured over distance the results indicate a flat earth.

Yes, we do have accurate maps of the earth. They're flat. That's slightly tongue in cheek. Researching flat earth has had me autodidactically learning about surveying and how maps are made. All maps are made with reference to the sky, as per the coordinate system of latitude and longitude. If there is an intrinsic misunderstanding in the relationship between the sky and the earth, then that error can be included in all calculations without ever being noticed. When you measure earth with reference to the sky on the presumption of a globe earth, you get a ball earth and an arbitrarilly large sky. When you measure the earth with reference to the earth, it comes back flat. If you measure earth with regard to earth at low angles over great distances the measurements vary with regard to temperature and atmospheric conditions. My conclusion there is that the relationship between the earth and the sky is misunderstood, possibly deliberately, resulting in the mathematical transposition of the roundness of the celestial sphere onto the plane of the earth.