Interplanetary Brachistochrone Calculator

    How fast could you reach any destination in the solar system (and beyond) with constant thrust? Accelerate to the midpoint, flip, and decelerate — arriving at rest in minimum time.

    Flight Parameters

    g

    Include time dilation & Lorentz factor

    Distance:0.524 AU (78.4 M km)
    Flip point:0.262 AU
    Travel Time
    2d 1h
    Max Speed
    876.8 km/s

    Journey Phases

    Accelerate (1d 0h)FlipDecelerate (1d 0h)

    Journey Details

    RouteEarth → Mars
    Distance0.524 AU (78.4 M km)
    Acceleration1g (9.81 m/s²)
    ModeBrachistochrone (flip & burn)
    Max Velocity876.8 km/s
    Max Velocity (% c)0.2925%
    Total Travel Time2d 1h
    Flip Point0.262 AU
    Sustained g-force1.00 g

    At 1g, crew would feel Earth-normal gravity throughout the burn.

    Peak speed of 876.8 km/s is 78× Earth escape velocity.

    All Routes from Earth at 1g

    About Brachistochrone Trajectories

    A brachistochrone trajectory is the fastest-time path between two points when a spacecraft maintains constant thrust. Unlike fuel-efficient Hohmann transfers, brachistochrone flights trade fuel for dramatically shorter travel times.

    Key Equations

    • Newtonian half-trip time: t = √(2d / a)
    • Relativistic proper time: τ = (c/a) · acosh(1 + ad/c²)
    • Relativistic coordinate time: t = √((d/c)² + 2d/a)
    • Max speed at midpoint: v = at / √(1 + (at/c)²)

    Example Trip Times at 1g

    • Earth → Moon: ~3.5 hours
    • Earth → Mars (closest): ~2 days
    • Earth → Jupiter: ~5.5 days
    • Earth → Pluto: ~18 days
    • Earth → Proxima Centauri: ~3.5 years (ship time, relativistic)

    Why "Brachistochrone"?

    From Greek brachistos (shortest) + chronos (time). The spacecraft accelerates toward the midpoint, flips 180°, and decelerates the rest of the way — arriving at rest in the minimum possible time for a given thrust level.

    Related Tools