Imagine this:

On a flat earth, the ground is accelerating upwards, but since all objects in space stand still, it looks as if the objects are falling towards the ground.

Now, if you have two balls, ball10 and ball20, which you drop from ten and twenty meters above the ground, assuming that the earth is flat, the balls will appear to both accelerate towards the earth at the same rate that the earth is accelerating towards them. That means that the balls are accelerating at the same rate in time. This is not the case though. **In reality, the balls would accelerate at different rates.**

Why?

With gravity, yes there'd be a slight variation, but it's a) hardly measurable and b) UA has multiple explanations for the rate at which gravity drops off with altitude. If this is the argument you're making, say so, but it's a far simpler one to state than going through all of this. 10 to 20 metres is barely going to be noticeable.

Otherwise you seem to be saying that the rate of acceleration of a ball depends on the distance it's going to travel, which just isn't true.

If you want to crunch the numbers it's easy. We know the formula for gravitational acceleration:

G=6.67408 × 10

^{-11}m

^{3}kg

^{-1}s

^{-2}, the gravitational constant

m

_{1}= 5.972 × 10

^{24} kg, the mass of the Earth

m

_{2}=0.0585kg, if we use a tennis ball, say.

r=6371000m, the radius of the Earth, plus ten or twenty metres.

Sure, there's some approximation going on, but this suffices to roughly estimate the variation predicted by gravity.

Just for fun, note that at ground level, approximately F=9.8m

_{2} which is, well, familiar. But if you want to calculate the variation in height, let's do that.

Dropping a tennis ball from 10m gives:

F = 0.5744477063 m/s/s

And dropping a tennis ball from 20m gives:

F = 0.574445903 m/s/s

You have a difference of 0.0000018m/s/s.

To put that in perspective, the balls would need for fall for about ten minutes before you'd notice one moving a

*millimetre* per second faster than the other. That's going to be dwarfed by air resistance.

What part of the formula for gravity do you disagree with?