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or even if we pass something like a planet etc, what about their gravitational forces affecting this 'disk'.
I could ask the same question of the round earth model. The universe is a big place.
To answer your question then, our planet reacts to gravitational forces like every other planet in our solar system. We orbit a sun, and our orbit varies depending on the proximity of other objects in that system.
Now what i'm getting at is that if we are just accelerating upwards at a constant rate, and this is the only reason that stuff sticks to the 'disks' surface, then if we happen to pass something massive, say a planet the size of jupiter, then suddenly things wont just be accellerating down, they would also move towards that gravitational pull as we pass it.I.e. drop a stone, it shoots sideways for a brief moment. Not down.
Now, if you want to start dismissing gravity aswell, then please wander off the side of your flat earth. Because gravity is infact a byproduct of the electromagnetic forces holding everything in this existance together. Our atoms, and their components, are held together by the same fundamental force that keeps our feet on the ground, that also keeps large masses of rock in space like planets sperical, or at least, not flat.