I think I've found the dumbest application of Special Relativity
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They use half of what SR would call for, thus invalidating SR by omission.
Relativists try to justify the asymmetry in time dilation by saying "orbit is non-inertial and SR deals with inertial frames". That also invalidates the original argument then.
No, the difference is gravity is an accelerating force vs a constant speed of the orbiting craft.
It is the acceleration that causes the time dilation.
Time is slower at the bottom of a gravity well.
Two different effects. Effects due to different gravitational potential and effects due to velocity.
You're conflating the two. SR deals with velocity and not acceleration.
You are correct, they are different effects.
The salient point is that Time is Relative. Einstein's/Maxwell's equations predict the effects exactly.