[Dog]

Here you go. 

v = c tanh(r/c)

As you can see, v will never be more than c.

Ah, don't remember what train of thought I was on but yes this is correct. To reach c you would need infinite energy.

Anyways this poses a different problem: the Earth should get harder and harder to accelerate as time goes on (since we're reaching c), therefore it should be slowing down as time progresses. I don't think there is any archaeological or experimental evidence that gravity is getting weaker...

[Pete Svarrior]

therefore it should be slowing down as time progresses

(I'm going to assume that by that you mean the acceleration would decrease, not that it would actually start slowing down. Please correct me if that's wrong)

It is indeed "slowing down" if we assume an external frame of reference. That, however, does not affect the Earth's acceleration relative to the Earth itself, or objects located on it.

[Tau]

Let me rephrase my comment:

Is it correct that flat-earth believers do not believe in gravity, but believe in special relativity?

We believe in gravitation, but not gravity. Special relativity can be directly verified. We're skeptics, not blind. We recognize that verifiable things are true. We just have a higher threshold for what's proven than you do. Relativity has been proven beyond reasonable doubt. Gravity hasn't been proven in such a way that would discount UA. Thus, we believe in the one but not the other. And since it has more likely that the Earth is flat than it is that the Earth is round, it therefore follows that it's more likely that UA, which is consistent with FE, is more likely than gravity.

[markjo]

We believe in gravitation, but not gravity. Special relativity can be directly verified. We're skeptics, not blind. We recognize that verifiable things are true. We just have a higher threshold for what's proven than you do. Relativity has been proven beyond reasonable doubt.

If you accept relativity, then why do you not accept that the gravitational field generated by the mass of the earth would cause the earth to collapse into a roughly spherical shape?

[Dog]

therefore it should be slowing down as time progresses

(I'm going to assume that by that you mean the acceleration would decrease, not that it would actually start slowing down. Please correct me if that's wrong)

It is indeed "slowing down" if we assume an external frame of reference. That, however, does not affect the Earth's acceleration relative to the Earth itself, or objects located on it.

Yes that's what I meant. A decrease in acceleration. This would make gravity seem like it's getting weaker over time.