Constant-Acceleration Relativistic Rocket Travel
For a rocket that accelerates continuously at a constant proper acceleration a (as felt onboard, commonly expressed in multiples of Earth gravity g), special relativity gives exact formulas for a one-way trip covering distance d. The travel time measured by observers at rest (like on Earth) is t = √((d/c)2 + 2d/a), while the proper time experienced onboard the rocket is τ = (c/a) × arccosh(ad/c2 + 1).
Because of relativistic time dilation, the crew ages less than observers back on Earth for the same journey — the longer and faster the trip, the bigger that gap becomes. At a comfortable 1g of constant acceleration, a trip to a nearby star still takes years of onboard time, since acceleration alone (without exceeding light speed) still leaves a probe’s velocity well under c over interstellar distances for a while. This is a standard relativistic-rocket-equation exploration for educational purposes, assuming no turnaround/deceleration phase.