Interplanetary & interstellar travel times with real physics: 1g flip-flop, relativistic rocket
Percepatan a for half the journey, then decelerate a for the other half. Formula: t = 2·√(d/a).
Einstein physics for 1g to the stars: τ = 2(c/a)·arccosh(1+x), T = 2(c/a)·√((1+x)²−1), with x = a·d/(2c²).
The craft cruises at constant velocity v = β·c. Earth time T = d/v; ship
Compare four travel approaches to the same destination.
| Method | Ship time | Earth time | Notes |
|---|
With a flip-flop maneuver (1g acceleration halfway, 1g deceleration the rest), the closest Earth–Mars distance of 54.6 million km takes 1.727 days with a peak velocity of 731.7 km/s. Compare with a Hohmann transfer needing ±259 days — continuous 1g is far faster but requires
True for crew-perceived time (proper time). With constant 1g proper acceleration flip-flop to Alpha Centauri (4.37 light years), the crew experiences 3.582 years while 6.003 years pass on Earth. This difference is purely due to relativistic time dilation — the formula uses the arccosh function,
A flip-flop maneuver is the fastest trajectory between two points with acceleration
Because Newtonian physics knows no speed-of-light limit. Example: a Newtonian 1g flip-flop to Proxima Centauri gives a peak velocity of 2.094 times light speed — a non-physical result. This calculator automatically warns and directs you to the relativistic rocket mode which uses proper acceleration
Ship time (proper time, τ) is time measured by clocks aboard the craft; Earth time (coordinate time, T) is time measured by a stationary observer on Earth. They are linked by the Lorentz factor γ: T = γ·τ. On a 1g trip to Proxima Centauri, the crew ages 3.542 years while 5.873 years pass on Earth
At a constant cruise velocity of 0.9c, Earth elapsed time is 4.718 years, but the crew experiences only 2.057 years due to the Lorentz factor γ = 2.294. The closer to c, the bigger the difference.
Newtonian-wise, total velocity change = 2 × peak velocity. For a 1g flip-flop to the Moon, peak velocity is ±61.4 km/s so total delta-v is ±122.8 km/s — about 10 times Earth's escape velocity. This is why the maneuver is beyond chemical propulsion: the best chemical rockets only deliver
A Hohmann transfer is a fuel-efficient maneuver that coasts along gravity (slow: Earth–Mars ±259 days). This calculator computes continuous-1g acceleration scenarios that are far faster but need fantastic energy. For complete Hohmann calculations (Δv₁, Δv₂, travel time), use the
Yes — 1g is exactly the gravity we feel on Earth, so physiologically it is the most comfortable acceleration for long journeys. The problem is not comfort but propulsion: sustaining 1g for years needs energy sources and propellant beyond current technology.
To the Moon (384,400 km): 3.478 hours with a peak velocity of 61.4 km/s. To Jupiter (closest distance 588 million km): 5.668 days with a peak velocity of 2,401 km/s. Both are still in the Newtonian regime since peak velocities are far below light speed.
This calculator uses an ideal straight-line motion model: it excludes origin/destination planetary gravity, launch windows (planet positions), propellant needs, general relativity effects, and interstellar medium drag. For real orbital maneuvers (rendezvous, gravity assist), use the Hohmann transfer
For constant proper acceleration a over distance d (flip-flop): x = a·d/(2c²), ship time τ = 2(c/a)·arccosh(1+x), Earth time T = 2(c/a)·√((1+x)²−1), and peak Lorentz factor γ = 1+x. At short distances this merges with the Newtonian result t = 2√(d/a); at interstellar distances, relativity takes
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