What is this calculator for?

TLDR:

The whole point is essentially just to remind people that time dilation occurs BECAUSE length contraction occurs (and vice-versa). One cannot exist without the other.

I made this calculator specifically to dissuade people from the misinformed notion that one requires faster than light travel to travel vast distances (as much as around 1 billion light years) in a ‘reasonable’ duration (i.e. a timespan such that human beings would actually be willing to partake in the journey). Basically not taking anything else into account apart from the rough rate of expansion of space in between us and the destination plus the effects of length contraction.

The calculator is not for the most accurate nor most precise possible answers, and makes some simplifying assumptions which basically require the distance to destination to be under ~ 1 billion light years (~9.46e15 m).

Note that a Hubble ‘constant’ of 70 km/s/Mpc (aka 0.02146 m/s/ly) was used for simplicity, and the expansion of space in between us and the source was treated (invalidly!) as actual relative motion of objects via the relativistic addition formula, which was a decision made purely to anticipate it in argument against the validity of the below calculator - the point is, this calculator is trying to overstate the effect of the expansion of space over this distance scale rather than ignoring it altogether.

Actual Required Speed Calculator

  • Measure the distance to a faraway destination (up to 1 billion Ly) from the perspective of someone on Earth.
  • Decide on how long you'd like the journey to take - not including acceleration time - from the perspective of someone on the spaceship.
  • This calculator will tell you the required speed one must accelerate up to (measured from an Earth observer's IRF) to do it!
    • ? Metres or light years only.
    Parsecs are not offered because, let's be honest, it's a little bit of a dumb unit.
    ? Everything is converted to seconds before the calculation. A year is 365.25 days and a month is one twelfth of that.
    Speed (v)
    Speed (fraction of c, β)
    Lorentz factor (γ)