x = (c²/a) · [cosh(aτ/c) − 1] | t = (c/a) · sinh(aτ/c) | v = c · tanh(aτ/c)
Mission Parameters
Results
Distance vs Ship Time
How Far Can You Go?
At 1.5 g acceleration (flip & decelerate mode):
The Physics
How it works: Under constant proper acceleration a, the ship's trajectory follows a hyperbola in spacetime. The key insight is that while coordinate time t (Earth time) grows exponentially, the crew's proper time τ grows only logarithmically relative to distance. This means at 1.5 g, after just 5 years of ship time you've crossed over 30 light-years — but more than 30 years have passed on Earth.
Flip & decelerate: For a realistic trip where you want to stop at your destination, you accelerate for the first half and then flip and decelerate for the second half. This costs you some distance but means you arrive at rest.
Caveat: This assumes perfect propulsion and ignores fuel mass — in practice, carrying enough fuel for sustained high-g acceleration is the unsolved engineering problem.