So your own theory has an equation with the constant c=299792458 m/s in it, and yet you deny that that number is a physical constant: I find that extremely self-contradictory, and that is predominately what made me lose motivation to continue our discussion. I should not have to explain to you that c, the speed of light, is a physical constant locally in GR, just as it is a constant in SR. If you want to use c=299792458 m/s in your own equation, you should not deny that number is a physical constant. With all of that being said, I will still provide some final comments. I don't think of what you did as a "derivation" of any equation, because it seems to be more of an ad hoc "modification" to the existing equation. As an analogy, let's go back to before 1905, before SR. Before SR, everyone thought the tick rate of a stationary clock was the same as the tick rate of an identically constructed moving clock. Let's call the tick rate of the stationary clock Δt (where Δt represents the amount of time elapsed from one tick of the clock to the next tick), and let's call the tick rate of an identically constructed moving clock Δt' (where Δt' represents the amount of time elapsed from one tick of the clock to the next tick). So, before SR we would have this equation: Δt' = Δt But let's say that someone came up with the idea that the moving clock should tick more slowly as a function of its speed, even to the point where it should effectively stop ticking entirely if it moved at the speed of light, c. So using your "boundary conditions" approach, that person might come up with this equation instead: Δt' = Δt * ((c - v ) /c) So for an example case where v=0.8c, we get this: Δt' = Δt * ((1 - 0.8) / 1) Δt' = Δt * (0.2 / 1) Δt' = Δt * 0.2 That is an ad hoc modification to the existing equation. It gives the desired result, but it may or may not be correct. The proper way would be to derive a new equation, using the idea that the speed of light is a constant. Build the two clocks such that a light pulse bounces up and down between two mirrors, with one mirror on top, and the other mirror on the bottom. Let each reflection of the light pulse represent one tick of each clock, and then derive the relationship from there. That is what SR did, and the correct result is this: Δt' = Δt * √(1 - (v² / c²)) So for an example case where v=0.8c, we get this: Δt' = Δt * √(1 - (0.8² / 1²)) Δt' = Δt * √(1 - (0.64 / 1)) Δt' = Δt * √(1 - 0.64) Δt' = Δt * √(0.36) Δt' = Δt * 0.6 That result is different from the ad hoc method, but it could also have been possible that the ad hoc method might have resulted in Δt' = Δt * √(1 - (v² / c²)) if it were done differently, or if someone were very lucky. So, Tony, it may be possible that your equation is good, if it just happens to give the same results as GR. Maybe you got lucky, maybe not. I don't know enough about GR to say one way or the other. But as others have already pointed out, it does not appear to be a Doppler effect, because there is no wavelength involved. It would probably be better described as gravitation as a projectile, based on your explanation that a projectile thrown at a dog might not hurt the dog if the dog runs away at a velocity that is very close to the velocity of the projectile.