I need to read this in more detail when I'm less tired because the problem looks interesting, but the first thing that jumped out at me was your use of d/t for calculating c. You are setting up a relativistic situation, but not using the mathematics of relativity. s=d/t doesn't apply in this situation. You have to include the Lorentz factor, √(1-(v/c)^2 ) in your calculations. For the moment, I'm burned out and headed for bed.

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Time is a great teacher, but unfortunately, it kills all its pupils. Hector Berlioz

"To complete the picture all the photons can be seen to be synchronising friction on and off throughout the overall cone which itself is synchronised to the equal and opposite reaction of equilateral triangulation"... by a scientificator in ATM, too priceless to be lost to posterity.