How this calculator works
The Einstein model keeps the acceleration felt aboard the ship constant. A stopping trip splits distance equally between acceleration and braking; a flyby accelerates for the whole distance. Inverse modes accept total Earth time, total onboard time or peak speed; distance and Earth time can also determine acceleration. Newtonian time is the same in both frames and may predict speeds above c, illustrating its breakdown. The payload energy budget adds acceleration and unrecovered braking energy, then divides by the entered conversion efficiency. Its converted mass equivalent is a lower bound; the separately labelled ideal photon-rocket fuel includes the need to accelerate remaining fuel at 100% conversion. Presets are rounded examples. Custom distance supports any real or fictional destination. Cosmological expansion is omitted, so very distant trips are illustrative only.
Formula
Per relativistic leg d: x = ad/c²; gamma = 1+x; t = sqrt[(d/c)²+2d/a]; tau = (2c/a) asinh(sqrt(x/2)); beta = sqrt[x(x+2)]/(1+x). Acceleration from leg distance and Earth time: a = 2d/[t²-(d/c)²]. Ideal photon fuel/dry mass = exp(total rapidity)-1. Newtonian: t = sqrt(2d/a), v = at.
Worked example
In the Newtonian comparison, a 100 m flyby at 2 m/s2 takes 10 s and reaches 20 m/s. A stopping trip over 200 m takes 20 s and reaches the same peak speed. A 1 kg payload has peak kinetic energy 200 J in either case.
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Frequently asked questions
Which time describes crew ageing?
Onboard proper time. In the relativistic model it is shorter than departure-frame time.
Is the energy-equivalent mass the required propellant?
No. It omits exhaust momentum and carrying fuel. The ideal photon-rocket output is a separate highly idealised propulsion limit.
Why are there only a few destinations?
The presets are documented distance examples. Enter a distance in light-years, parsecs or other offered units for any other real or fictional location.