Special relativity says a moving clock (the ship's) runs slow as measured from a "stationary" frame (Earth's); the faster you go, the bigger the gap. Reaching relativistic speeds also costs propellant exponentially, per the rocket equation.
γ = 1 / sqrt(1 - v²/c²)
t_ship = t_earth / γ
m0/mf = exp(Δv / v_exhaust) (Tsiolkovsky rocket equation)
- Velocity (fraction of c) — the ship's cruise speed; raising it stretches the ship-time / earth-time gap and steepens the fuel-mass-ratio requirement.
- Payload / fuel ratio target — how much of the ship's launch mass you want left as payload after burning fuel to reach cruise speed.
- Exhaust velocity — how fast the propulsion system ejects reaction mass; higher-performance drives (e.g. fusion vs chemical) need far less fuel for the same Δv.
Watch the two clocks diverge as the ship accelerates toward the distant star: at high v/c, years pass for the crew while decades or centuries pass at home — the classic "twin paradox" — while the fuel-mass-ratio stat shows why chemical rockets can never reach these speeds.