How this calculator works
The relativistic model keeps acceleration constant in the instantaneous ship frame. The Newtonian comparison keeps ordinary acceleration constant and can exceed c mathematically. A stopping trip splits distance equally between acceleration and braking. Payload kinetic energy is computed at peak speed. The efficiency-adjusted energy budget counts both legs for a stopping trip and ignores energy recovery. Its mass equivalent is only a lower bound; a separate ideal photon-rocket estimate includes the fuel needed to accelerate remaining fuel at perfect conversion. Food and water use the user-entered onboard daily assumptions without recycling or stored-mass feedback. Preset distances are rounded illustrative values, not navigation data; use custom distance for other real or fictional destinations.
Formula
For one relativistic leg: x = ad/c²; γ = 1+x; Earth time = sqrt[(d/c)²+2d/a]; ship time = (c/a)acosh(1+x); β = sqrt[x(x+2)]/(1+x). Photon-rocket fuel/dry mass = exp(total rapidity)-1. Newtonian: t = sqrt(2d/a), v = at. Energy-equivalent mass = sum of leg kinetic energies/(efficiency × c²).
Worked example
In the Newtonian model, a 100 m flyby leg at 2 m/s2 takes 10 s and reaches 20 m/s. For a 1 kg payload its kinetic energy is 200 J. A 200 m stopping trip at the same acceleration takes 20 s and reaches the same peak speed.
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Frequently asked questions
Which clock determines ageing and supplies?
The onboard proper time determines ageing and the entered daily food and water totals.
Is the energy-equivalent mass a fuel tank size?
No. It omits momentum, exhaust and the need to accelerate fuel. The separate photon-rocket value assumes an ideal fully efficient photon exhaust.
Can I use this for an actual mission?
It is a conceptual straight-line model. Real missions need propulsion, trajectory, destination motion, protection and life-support engineering.