Both theories are patently ridiculous. The only reasonable theory is mine - that objects follow Newton's Three Laws of motion and thus falling objects are merely traveling in straight lines as inertia would dictate. Likewise for satellites like the moon or sun - they are traveling in straight cyclical lines above the flat earth.
I don't see how that works. If they travel in a straight line how is it cyclical?
I do not support the non-Euclidean earth of John Davis, this might help follow that and GR. For a start John Davis talks of objects travelling in "straight lines". I find that confusing, but many writers on General Relativity do the same.
Some explain it as the "straightest line possible", in the way that a Great Circle is the "straightest line possible" on the surface of a sphere. Since this is not a straight line in the Euclidean sense, I, personally, prefer to use a different name and call it a "Geodesic", a term already in use for that in spherical geometry.
But, of course, not everyone follows this, so you just have to be aware and interpret "straight line" appropriately.
So, a geodesic is the path an object will follow with no forces applied.
So often the "trampoline analogy" is used to explain the curvature of spacetime, but that makes us think that it necessarily
space that is curved.
Space can certainly be curved but even near the sun it is quite small.
Now in GR it is not simply space, but
spacetime that is curved, and that is where it gets hard to visualise.
When Einstein's GR is solved (not by me!), near the earth, what is called the
space-like component of spacetime is virtually unchanged (if I remember rightly it leads to an error of something like 1 cm in the earth's radius), while the
time-like component is quite measurably changed, both by mass, gravitation, and by velocity.
Enough from me, or I'll confuse things more!
This reference
Einstein Online, Einstein's geometric gravityIn fact the whole series it worth a look
Welcome to Einstein Online - relativity and more!.
Now, John Davis and I differ on the curvature of space. I claim his "theory", where the flat earth somehow curved to "look like" a sphere is not Einstein's, but Leo Ferrari's "Ferrari Effect", but that's another story.
They used to say, "Everyone's entitled to their own opinions, but not their own facts."
Of course, after Trump that becomes simply "Everyone's entitled to their own
Alternate Facts", much simpler.