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Simulations/Cosmology/Travelling Near the Speed of Light
Cosmology

Travelling Near the Speed of Light

Set a speed and a heading and redraw the real sky three ways: as Earth maps it, as the ship measures it, and where the light the ship sees set out from. Underneath, a ladder of scales from the Moon to the Coma Cluster shows how near everything gets for you, and how long it takes on your own clock.

Map
at rest0.9999999 c
Heading for
Show
Numbers
Speed β = v/c—
Lorentz factor γ—
Destination, Earth’s map—
Measured by the ship—
Its light set out from—
Trip, ship clock—
Trip, Earth clock—
The three maps
  • Earth’s map: where everything is now, by the ruler of anyone at rest with the stars.
  • Measured by the ship: where everything is now, by the ship’s ruler. Distances along the motion are divided by γ, across it they stay the same.
  • Seen from the ship: where each object was when it sent the light reaching the ship now, in the ship’s frame. Ahead the distance is multiplied by γ(1 + β), behind by γ(1 − β); the directions are the aberrated ones a camera on board would record.
  • Speeds are held constant: the trip times leave out speeding up and slowing down.
Data sources
  • Stars: HYG database (Hipparcos, Yale, Gliese).
  • Milky Way: arms from Reid et al. (2019), bar and disk from the standard models.
  • Local Group: McConnachie (2012). Galaxies: 2MASS Redshift Survey.

What to observe

  1. At 0.99 c, γ ≈ 7. On the ship’s ruler the galaxy is squashed seven times flatter along the way you are going, and nothing changes across it.
  2. Watch the ladder: the ship’s row is Earth’s row slid left by the same amount everywhere. A year on board never takes you more than a light-year by your own ruler, yet at 0.9999999 c the Galactic Centre is only 12 light-years away, well inside a lifetime’s reach.
  3. The view out of the window is different again. The light you see from ahead set out long ago, from far away: the sky in front is stretched out by γ(1 + β), while everything behind piles up close to the ship.
  4. Andromeda is 2.5 million light-years away. At 0.9999999 c it is 1,100 light-years away for the crew, who arrive after 1,100 years of their own time while 2.5 million pass on Earth.
  5. At walking-pace fractions of c nothing happens: set 0.1 c and the three maps barely differ, because γ is only 1.005. The effects only pile up in the last few nines.

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