Earth-frame duration
—
what mission control waits
ship proper time
—
what your calendar shows
Lorentz γ
—
1 ship-year = γ Earth-years
arrival, written ten ways
Honesty panel. Pure kinematics: instant acceleration, no fuel, no shielding, no slowing down at the far end unless you tick round-trip (which simply doubles both clocks). Real starships must accelerate — a comfortable 1 g brachistochrone changes these numbers (pleasantly, for the crew). β = 1 is not on the slider because it is not in the universe. Distances are published estimates; the mathematics is exact:
γ = 1/√(1−β²) · t_earth = D/β · t_ship = t_earth/γ