Starflight: Flying Near Light Speed

The simulator shows the real night sky: 270,000 stars from the Henry Draper Catalogue, the great survey of starlight made at Harvard a century ago, each in its catalogued place with its brightness and the colour of its spectral type, together with the Milky Way's glow, measured in the near infrared by the COBE satellite, and the light of the dust between the stars. The ship starts beside the Sun, heading for Orion's Belt, and the default view shows the sky standing still on the left and the same sky from the ship on the right, as it speeds up to 99% of light speed and slows down again. You can choose the speed and the heading, look back the way you came, see the whole sky on one disc, fly to Alpha Centauri, or switch each piece of physics off to see what it does. Hold the pointer over any view, setting or number for a short explanation.

Three things change what you see, and all three come from special relativity. Aberration changes the direction light seems to come from, so the stars appear crowded toward the front. The Doppler shift raises the frequency of light from ahead and lowers it from behind, which changes the colours. And because a star's light arrives concentrated into a smaller patch of sky, its brightness changes too: some stars brighten, others fade, and light that was invisible becomes visible.

Calculated, not drawn. Every star is placed by the exact formula for aberration, coloured by its temperature shifted by the Doppler factor, and given the brightness its shifted spectrum would have, all recalculated by your graphics card in every frame. The glow comes from real maps of the sky and measured spectra, shifted the same way. There is nothing in the program that says "make the stars gather" or "make the sky glow"; it all comes out of the physics, and an independent program checks the result (see Method and sources). It runs best on a laptop or desktop. Built with Claude Opus 5.5.

While working on this, I was surprised to find that the most striking thing at high speed isn't the stars at all. The well-known calculations of what a relativistic traveller would see, going back to the 1970s, deal with the stars. But space between the stars isn't dark: it is filled with light our eyes can't see. The Milky Way's billions of faint stars shine most brightly in the near infrared; the dust between them glows at a few tens of degrees above absolute zero, in the far infrared; all the galaxies in the universe add a faint infrared glow from every direction; and behind it all is the cosmic microwave background, the afterglow of the Big Bang, at 2.7 K.

Near light speed, all of that light ahead is shifted to higher frequencies and concentrated into a smaller patch of sky, and one after another these sources become visible. Heading toward Orion, the Milky Way's starlight is the brightest of them up to about 98% of light speed (probably a little less; see the limits); from there the infrared glow of its dust takes over, and the Big Bang's afterglow becomes the brightest thing ahead only at 99.9997%. The chart shows how bright each one is straight ahead. You can switch each of them off in the simulator, under Physics.

In 1962 the rocket engineer Eugen Sänger worked out what the crew of a fast photon rocket would see. He predicted a dark spot around the star they had left and another around the star ahead, with rings of colour between them, violet at the front through to red at the back: a rainbow wrapped around the sky. The science-fiction writer Frederik Pohl gave it a name in his story "The Gold at the Starbow's End" (1972), and the starbow became a fixture of science fiction.

The trouble was that Sänger treated every star as shining at a single wavelength. Real stars shine across the whole spectrum, roughly like a hot glowing body, and shifting that kind of spectrum only moves a star's colour along the line from red through white to pale blue. In 1979 the physicists McKinley and Doherty ran the calculation with real star temperatures and concluded that no starbow appears. The calculation here agrees. The stars ahead turn blue-white and those behind turn orange and red, with no rainbow ring and no dark spot ahead, and the glow ahead varies in the same way, between warm white and blue-white.

The streaks of the movies are a different idea. Star Wars (1977) shows the jump to hyperspace, which is faster-than-light fiction, and the image of stars stretching outward past a ship has stuck as the picture of travelling fast. A ship speeding up toward light speed would see something quite different: the stars sliding inward, toward where it's going.

Nothing human-made has gone fast enough to see the sky crowd ahead, but astronomers measure the same two effects every day at much lower speeds. Aberration was found by James Bradley in 1725–28, while he was looking for something else: the tiny shift of a star caused by our changing viewpoint as the Earth goes round the Sun. Instead he found a larger shift, up to 20.5 arcseconds, caused by the Earth's speed of 30 km/s. Space telescopes that measure star positions to a millionth of that, such as Gaia, correct for the aberration from their own motion as a matter of routine.

The Doppler shift of the Big Bang's afterglow tells us how fast we are moving through the universe. The Sun travels at 370 km/s toward the constellations Leo and Crater, so the afterglow is 0.0034 K warmer in that direction and the same amount colder in the opposite one. The COBE, WMAP and Planck satellites have mapped this "dipole" precisely: Planck measured 3.362 thousandths of a degree. The view below shows the simulator's calculation of it, in false colour like the published maps. In 2014 the Planck team also measured the afterglow's faint pattern of hot and cold spots being slightly crowded toward the direction we're heading, the same effect this page is about at our modest speed, consistent with the dipole. They called their paper "Eppur si muove" ("and yet it moves").

Each comparison below changes just one thing, so you can see what each piece of physics does. Every image was rendered by the simulator, and the settings for all of them are under Physics and Display in the panel.

The "Journey to Alpha Centauri" view flies a ship to our nearest neighbouring star system, 4.4 light-years away, at a constant 1 g: it accelerates as hard as gravity pulls on Earth, so the crew feel their normal weight, for the first half of the trip, then turns round and slows down at 1 g for the second half. It reaches 95% of light speed at the halfway point. By the ship's clock the trip takes 3.6 years; on Earth, 6 years pass. Along the way every star with a measured distance is placed in three dimensions, so the nearby ones shift against the background as you pass them.

At the end the ship turns round. The Sun is now just another bright star, of magnitude 0.5, and it sits in Cassiopeia, adding a sixth star to the familiar W.

For every star, every frame, your graphics card takes the direction of its light in the stars' frame and turns it into the direction seen from the ship, using the exact formula for the aberration of light, tan(θ′/2) = e^−η tan(θ/2), where η is the ship's rapidity. The same calculation gives the Doppler factor, which shifts the star's temperature, and the star's brightness follows from how its shifted spectrum looks to the eye and from its light being concentrated into a smaller patch of sky. The glow is calculated for every pixel by following its direction back to the stars' frame, looking up the measured brightness there, and shifting the measured spectrum in the same way.

A separate Python program, written independently, checks the result. It works the same physics out a different way, by transforming the light's energy and momentum with explicit Lorentz transformations in 50-digit arithmetic, and the two agree to 10⁻¹². The light the graphics card draws, read back and added up, matches the total the physics predicts to within 0.4% (3% where stars sit at the edge of the picture), and the stars land within about a pixel of where the independent program puts them. The method page has the equations, the data sets, all the tests and the references.

Images and recordings you make with this simulator, and the figures on this page, may be used for any purpose, including teaching, publication and commercial work, without asking permission. We only ask that you credit Frosty Wren Studios, for example:

"Save image" adds this line to the corner of each picture by default; you can switch it off under Playback and output. The simulator's source code is not covered by this permission. The sky is built from public data: the Henry Draper Catalogue (Harvard College Observatory, 1918–1936; machine-readable edition by NASA's Astronomical Data Center), the COBE/DIRBE maps (NASA) and the dust map of Schlegel, Finkbeiner & Davis (via NASA's LAMBDA archive). All of these are public domain or free of restrictions.