Round-Earthists know how their model works.
So, can you give me the mechanism behind gravity?
As another said, it'd be mass. Everything has the tendency to go to a higher mass. And if you didn't know it by now, Earth has slightly more mass than a pencil, apple, etc. I'm a junior in HS, gravity is common knowledge. If earth is accelerating through space, why don't we even get any closer to the moon, sun, other planets, etc?
Inertia.
In the FE theory, there are many different suns that somehow have a mathematical, non-collisonal, series of paths. To support these paths and keep the suns from colliding, the FE's had to rule out gravity. So they had to make the Earth being accelerated, so on, so forth.
The FE theorists don't simplify things, they make them more complex and unknown. True, the RE's have their unknowns, but they've solved the forces applied on big things to smaller things. Quarks (perhaps even strings, if you like the String-theory) - though at a quark's level, some of the laws of physics are utterly shot.
We've narrowed it down to six different probable-point-particles and the Theory of Spacetime, FE's, which we can basically use to expand our arguements.
You still don't know what keeps everything moving like you say it does, or what keeps everything in earth. If nothing else, we have theories. You've got an invisible (or perhaps visible!) hand pushing you through the universe, who's
sole purpose is to explain why we don't float in the air.
Maybe it's not a hand. Maybe it's an superstrong-technicolor oyster with a tophat that's pushing you through the universe, using it's pulse detonation engines to power it, and secretly dining with the Heads of State that are behind the conspiracy!