How Time Bends When You Travel Near Light Speed

Three ways to explore relativistic space travel. Pick one to begin.

Built with vanilla JS. Equations documented in physics_reference.md.

Space View

scroll = zoom · drag = pan · click = select

Controls

Perspective (whose frame are we playing?)

Time 0.00 yr

Playback speed 1.0 yr/s

Rocket acceleration 1.00 g

Trip profile

Auto No coast Coast

Cruise speed (for coast) 0.9990 c

Propulsion

Ship dry mass 100,000 kg

Scene

Objects

Data Exploration

Three charts updating live from the current scene. Change parameters in the Space View to see them respond here.

Fuel Remaining vs Perceived Time

m(τ) = M₀ · exp(−a·τ / v_ex)

Earth Time vs Perceived Time

t = (c/a) · sinh(a·τ / c)

Distance from Earth vs Speed (β)

γ(x) = 1 + a·x / c² · β = √(1 − 1/γ²)

Time Dilation (γ) vs Earth Time

γ(t) = √(1 + (a·t / c)²)

Fuel & Ship Design

How much fuel does an interstellar rocket actually need? The relativistic rocket equation reveals why chemical propellants can't reach relativistic speeds, and why fusion or antimatter is required for any realistic interstellar mission.

Results

M₀ / M_f = ((1 + β) / (1 − β))^(c / (2·v_ex))

Full trip ratio = (single-burn ratio)² · M_fuel = M_dry · (ratio − 1)

Mass ratio vs peak β

log y-axis. Each line = one propellant. Your current operating point is marked.

M₀/M_f is squared for accel+decel trips, and to the 4th for round trips.