Space After Dark

Exhibition 3 · Light and Time

How long does light take to get anywhere?

Light is the fastest thing there is. Radio is light too, just a colour our eyes can't see, so every message to a spacecraft travels at the same speed. This exhibition has one dial. For now it measures distance: how far light has to go.

Pick somewhere, send light, and wait. These are today's real distances, so the waits are real too. A long wait keeps counting on the progress line while you read on, and a message to Mars is kept on this device until it would arrive.

Experiment

The speed limit

How long does light take to get anywhere?

Goal Send light to the Moon and wait for it to arrive

Predict first. How long will light take to reach the Moon?

Not tried yet Today's distances · light at 299,792,458 m/s

When did the starlight you see tonight set off?

Keep turning the dial outward, past Voyager, to the stars. Out here we measure in light-years. A light-year is a distance, not a time: how far light goes in one year.

Display · Looking out is looking back

Proxima Centauri

4.25 light-years

Its light left in about 2022

The light entering your eye from Proxima Centauri left it in about 2022. Everything you see in the sky is a message that is already old.
What just happened

The night sky is a picture made of light that set off at different times. Sirius shows you a few years ago; the faint smudge of the Andromeda Galaxy shows you light that left before the first people lived. For some stars even the best telescopes disagree on the distance, so they get a range, not one year.

SimplifiedDistances come from star parallax measurements (SIMBAD, using Hipparcos and Gaia). For distant stars the uncertainty is tens to hundreds of years, so we show the range. Andromeda's distance is a round figure, and the galaxy has moved since its light left.
The real numbers

One light-year is about 9.46 trillion km. Distance from parallax: d (light-years) = 3,261.56 / parallax (milliarcseconds). Year the light left = this year − distance in light-years.

  • Sirius: 8.6 ly, light left in about 2017
  • Vega: 25.0 ly, light left in about 2001
  • Arcturus: 36.7 ly, light left in about 1989
  • Spica: 237–264 ly, light left sometime between 1760 and 1790
  • Polaris: 323–521 ly, light left sometime between 1510 and 1700
  • Betelgeuse: 440–640 ly, light left sometime between 1390 and 1590
  • Deneb: 1,240–2,620 ly, light left sometime between 600 BCE and 800 CE

Polaris, Betelgeuse and Deneb have disputed distances: studies of Deneb disagree between about 1,400 and 2,600 light-years.

The dial changes: distance becomes speed

So far the dial has measured how far light has to travel. Now it measures how fast you go, and that changes something different: not when you see a clock, but how fast it actually ticks.

A light delay only makes news late; every clock still keeps its own time. What comes next is not a delay. A fast-moving clock really runs slow.

Does a clock on a fast ship keep the same time as one on Earth?

Here are two identical clocks. Each is a pulse of light bouncing between two mirrors, one tick per bounce. One stays on Earth; the other flies on a ship at the speed you set on the dial. Fly for one hour by the ship's clock, then compare.

Experiment

The slow clock

Does a clock on a fast ship keep the same time as one on Earth?

Goal Make one hour on the ship last a full day on Earth

Predict first. At half the speed of light, how long does one ship hour last on Earth?

Not tried yet Constant speed · ideal clocks · one ship hour

If one twin travels to a star and back, who is older when they meet again?

Now a real trip. One twin stays on Earth. The other flies to a star at the speed on the dial, turns round and comes home. The diagram is a map of space and time: across is distance, up is time on Earth, and each mark is a year of a twin's life.

Experiment

The twins

If one twin travels to a star and back, who is older when they meet again?

Goal Bring the traveller home at least 10 years younger than their twin

Predict first. Who is older when they meet again?

Not tried yet Instant turnaround · no fuel limits

The dial changes again: speed becomes depth

Speed isn't the only thing that changes a clock. Gravity does too: clocks lower down run slower than clocks higher up. Now the dial sets how deep a clock sits in gravity.

Does gravity change how fast a clock ticks?

Move a clock up a mountain, into orbit or close to a black hole, and compare it with one on the ground for a day. In orbit two effects pull against each other: being higher speeds a clock up, and moving fast slows it down. Find the orbit where they cancel.

Experiment

Clocks in gravity

Does gravity change how fast a clock ticks?

Goal Find the orbit where a clock keeps time with one on the ground

Predict first. A clock on the space station, about 400 km up: faster or slower than one on the ground?

Not tried yet Non-rotating Earth · circular orbits · one day

If all of history were squeezed into one year, where would we be?

One last scale, and this one stands outside the dial: no distance, speed or depth changes what has already happened. Squeeze the whole 13.8-billion-year history of the universe into one calendar year. The Big Bang is midnight on 1 January, and now is the stroke of midnight at the end of 31 December.

Display · The universe in one year
If all of time were one year, the dinosaurs died out on 30 December, and every person who ever lived fits in the last 12 minutes.
What just happened

Each day on this calendar is about 38 million years, and each second about 437 years. The Sun and Earth don't arrive until September, animals spread in mid-December, and the dinosaurs die out on the morning of 30 December. The Moon landing happened a fraction of a second before midnight.

SimplifiedAges come from current measurements (Planck 2018 for the age of the universe). Most early dates are uncertain by tens of millions of years, which is less than one day here. Carl Sagan's 1977 original used 15 billion years, so his dates differ.
The real numbers

The universe is 13.787 billion years old. Date on the calendar = 1 January + (1 − age ÷ 13.787 billion) × 365 days.

  • The Big Bang: 13.787 billion years ago → 1 January
  • The first atoms; light is set free: 13.787 billion years ago → 1 January
  • The first stars: 13.687 billion years ago → 3 January
  • The oldest galaxies we have seen: 13.387 billion years ago → 11 January
  • The Milky Way starts to form: 13.000 billion years ago → 21 January
  • The Sun and planets form: 4.567 billion years ago → 2 September
  • Early microbial life: 3.500 billion years ago → 30 September
  • Animal life spreads (the Cambrian): 538.8 million years ago → 17 December
  • The dinosaurs die out: 66.0 million years ago → 30 December, 06:03
  • The first people (Homo sapiens): 300,000 years ago → 31 December, 23:48:33
  • The last ice age ends; farming begins soon after: 11,700 years ago → 31 December, 23:59:33
  • Apollo 11 lands on the Moon: 57 years ago → 31 December, 23:59:59

Light takes about a second to reach the Moon, minutes to reach Mars and a whole day to reach Voyager. Our fastest spacecraft are thousands of times slower than light, so those same distances become days, months and decades of travel.

End of Light and Time · Ends with those distances as travel time

Then how do we go at all?

Next: Leaving the Ground Exhibition 4 · Rockets and orbit