Three programs start at the same moment β Cincinnati, Mt. Everest, and a GEO satellite. Which one delivers its answer back to Cincinnati first?
N, each racer finishes NΒ·Ξ΅ seconds earlier (from Cincinnati's frame), then loses time sending the answer back.
Ξ΅ β 7.3Γ10β»ΒΉΒ³ (gravitational +9.5 minus rotational β2.2, both Γ10β»ΒΉΒ³). Signal back: ~40 ms. Break-even: ~1,736 years.Ξ΅ β 5.4Γ10β»ΒΉβ° (~740Γ bigger than Everest β much higher gravitational potential dominates). Signal back: ~120 ms. Break-even: ~7 years.Like every back-of-envelope physics problem, this one assumes a few cows are spherical. Things this viz pretends don't exist:
Tcomm is bare light-time. The real world has TCP handshakes, error correction, and queuing latency that swamp the relativistic effect.The math is sound to ~3 sig figs. But it's still a cow-shaped sphere.