---
title: "The Speed of Light; Distances in the Universe"
book: "Primary & Middle School Physics"
subject: physics
language: en
chapter: 61
exercises: 12
source: https://one-course.com/books/physics/1/en/chapter/61-the-speed-of-light-distances-in-the-universe
---

# Chapter 61 — The Speed of Light; Distances in the Universe

For seven years this book has whispered that [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) is “as good as instant” — the flash before the thunder, the seen strike starting the stopwatch. This chapter keeps the family’s oldest promise: [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)’s [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) is not infinite, humans measured it against all odds, and the number is so vast that it becomes, in the same breath, astronomy’s ruler and its time machine.

## 61.1 The impossible measurement

**Example 61.1 (Lanterns on two hills).**

Four centuries ago, the great pioneer of experiments set two observers on distant hills at night, each with a shuttered lantern: uncover yours on seeing mine, and the round-trip delay should betray [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)’s [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula). The delay they found was only human reflexes; between the hills, [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)’s true crossing took a few *millionths* of a second. The experiment failed magnificently — proving, at least, that [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) is faster than anything a hilltop could clock, and daring astronomy to find longer race-tracks.

**Example 61.2 (The moon that ran late).**

The race-track came courtesy of Jupiter. Its innermost great moon eclipses into Jupiter’s [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) on a superbly regular schedule — a clock in the sky. Yet a patient astronomer found the clock running *late* by many minutes in the months when the Earth’s [orbit](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit) had carried us to the far side of the Sun from Jupiter, and early again as we swung near. His leap: the moon is punctual — its *[light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)* is delayed, needing extra time to cross the extra width of the Earth’s [orbit](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit). From the lateness and the [orbit](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit)’s size came the first estimate of [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)’s [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) — breathtakingly close, for the sixteen-hundreds, to the truth.

![The moon that ran late: eclipse news from Jupiter reaches the far-side Earth many minutes behind schedule — the delay is light, caught commuting.](https://one-course.com/images/onecourse/chapters/physics-1/g8-speed-of-light/fig-6ab1b6343c09.svg)

*The moon that ran late: eclipse news from Jupiter reaches the far-side Earth many minutes behind schedule — the delay is [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source), caught commuting.*

**Proposition 61.3 (The speed of light).**

In vacuum — and in [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air), to excellent approximation — [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) travels at

$$
c = 300\,000\,\mathrm{km}/\mathrm{s} = 3 \times 10^{8}\ \mathrm{m}/\mathrm{s},
$$

three hundred thousand kilometres each second: seven and a half laps of the Earth between two heartbeats. Every color of the blend travels at this same $c$ in vacuum; nothing that carries matter or news has ever been clocked faster. Later, Earth-bound ingenuity confirmed the astronomers — a [beam](https://one-course.com/books/physics/1/en/chapter/42-rectilinear-propagation-of-light#def-g6-light-propagation-ray) chopped by a spinning toothed wheel, racing eight kilometres to a [mirror](https://one-course.com/books/physics/1/en/chapter/32-mirrors-and-reflection#def-g5-mirrors-reflection-reflection) and back through the next tooth-gap — and modern instruments have polished $c$ to a certainty so complete that the [metre](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units) itself is now defined from it.

**Example 61.4 (Travel times in the neighborhood).**

With $t = d/c$, the [Solar System](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-family) acquires a timetable. The [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon), $384\,000\,\mathrm{km}$: $384000 \div 300000 \approx
1.3\,\mathrm{s}$ — Earth–Moon radio conversations carry that awkward pause. The Sun, $150$ million km: $150000000 \div
300000 = 500\,\mathrm{s}$ — eight minutes twenty: sunshine is always eight-minute-old news. Mars, at a typical $2 \times
10^{8}$ km: about eleven minutes — rover drivers send the day’s plan and wait; no joystick can steer across a twenty-minute round trip.

![A spiral galaxy: light from its stars crosses millions of years of empty space before reaching any telescope.](https://one-course.com/images/onecourse/chapters/physics-1/g8-speed-of-light/img-b4aa74d9ab12.jpg)

*A spiral galaxy: [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) from its [stars](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-star) crosses millions of years of empty space before reaching any telescope.*

## 61.2 The light-year

**Definition 61.5 (Light-year).**

A *light-year* is a *distance*: the stretch [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) covers in one year — about $9.5 \times
10^{12}$ km, nearly ten million million kilometres. The name misleads the hasty (it is no more a time than a “footstep” is a foot); astronomers use it because kilometres collapse under the sky’s true scale.

**Example 61.6 (The neighborhood in light-years).**

The nearest [star](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-star) beyond the Sun: about $4$ [light-years](#def-g8-speed-of-light-lightyear) — tonight’s photons left it while you were in your first physics chapters. The bright [stars](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-star) of the winter sky: tens to hundreds of [light-years](#def-g8-speed-of-light-lightyear). The [Milky Way](https://one-course.com/books/physics/1/en/chapter/33-stars-and-the-night-sky#ex-g5-stars-night-sky-milkyway), our city of [stars](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-star): about $100000$ [light-years](#def-g8-speed-of-light-lightyear) across. The nearest great neighboring galaxy: some $2.5$ million [light-years](#def-g8-speed-of-light-lightyear) — its faint smudge, visible to a dark-adapted naked eye, is the oldest [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) a human can see unaided.

**Proposition 61.7 (Telescopes are time machines).**

Because [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)’s news travels at $c$ and the universe is vast, *looking far means looking back*. The [star](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-star) at $4$ [light-years](#def-g8-speed-of-light-lightyear) shows itself as it was $4$ years ago; the neighbor galaxy, as it was when our ancestors first chipped stone tools. The g5 stargazer’s suspicion is now a theorem of arithmetic: every telescope aimed outward is aimed pastward, and astronomy is history read by starlight.

**Method 61.8 (Converting distance and lookback).**

1. distance in [light-years](#def-g8-speed-of-light-lightyear) $\to$ lookback in years: the same number — that is the [unit](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) ’s whole genius;
2. distance in kilometres $\to$ light-time: divide by $300\,000\,\mathrm{km}/\mathrm{s}$ , then tame the seconds into minutes, [hours](https://one-course.com/books/physics/1/en/chapter/8-measuring-time#ex-g2-measuring-time-clock) or years;
3. [light-years](#def-g8-speed-of-light-lightyear) $\to$ kilometres (rarely worth it): multiply by $9.5 \times 10^{12}$ — and remember why astronomers seldom do.

**Remark 61.9 (What “now” means out there).**

Is the [four-light-year](#def-g8-speed-of-light-lightyear) [star](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-star) still shining *right now*? Almost surely — [stars](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-star) live long — but no faster answer than [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)’s own can ever reach us: the freshest possible news is four years stale, always. For the deep sky, the question softens into strangeness: some of the faintest smudges in great telescopes are galaxies whose [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) left before the Earth existed. Physics will sharpen what “now at a distance” can even mean in the university years; for this year, carry the honest version: the sky is not a scene — it is an archive.

## 61.3 Exercises

**Exercise 61.1 ★.**

Give $c$ in $\mathrm{km}/\mathrm{s}$ and in $\mathrm{m}/\mathrm{s}$ (powers-of-ten form). What failed on the two hills, and why?

**Solution of Exercise 61.1.**

$c = 300\,000\,\mathrm{km}/\mathrm{s} = 3 \times 10^{8}\ \mathrm{m}/\mathrm{s}$. The hilltop lanterns measured only human reflexes: [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) crossed the hills in millionths of a second, far beneath any hand’s timing.

**Exercise 61.2 ★.**

Retell the late-moon argument in three sentences: what was punctual, what was late, and what the lateness measured.

**Solution of Exercise 61.2.**

Jupiter’s moon eclipsed on a punctual schedule — a sky clock. The *news* of each eclipse arrived late whenever the Earth stood far from Jupiter, early when near. The lateness measured [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)’s travel time across the width of the Earth’s [orbit](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit) — and so [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)’s [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula).

**Exercise 61.3 ★.**

Compute [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)’s travel time: [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) ($384\,000\,\mathrm{km}$); Sun ($150$ million km). Why is sunshine “old news”?

**Solution of Exercise 61.3.**

[Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon): $384000 \div 300000 \approx 1.3\,\mathrm{s}$. Sun: $150000000 \div 300000 = 500\,\mathrm{s}$ — eight minutes twenty. Sunshine always shows the Sun as it was eight minutes ago: old news by construction.

**Exercise 61.4 ★.**

A [light-year](#def-g8-speed-of-light-lightyear) — time or distance? Define it, and give its size in kilometres (powers-of-ten form).

**Solution of Exercise 61.4.**

A distance: the stretch [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) covers in one year — about $9.5 \times 10^{12}$ km.

**Exercise 61.5 ★.**

The nearest [star](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-star) sits about $4$ [light-years](#def-g8-speed-of-light-lightyear) away. What is tonight’s lookback — and what were you doing when its [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) departed?

**Solution of Exercise 61.5.**

Four years. Answers vary — four years ago you were several grades back down this very book.

**Exercise 61.6 ★.**

Why can no one joystick a Mars rover from Earth? Use the timetable example’s numbers.

**Solution of Exercise 61.6.**

At eleven-ish minutes one way, a steering correction answers a picture at least twenty-two minutes stale — the rover would be in the crevasse before the joystick’s twitch arrived. Hence plans, not joysticks.

**Exercise 61.7 ★.**

Order by lookback: the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon); the Sun; the nearest [star](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-star); the neighbor galaxy — with each one’s rough figure.

**Solution of Exercise 61.7.**

[Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon): about $1.3\,\mathrm{s}$. Sun: eight minutes. Nearest [star](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-star): four years. Neighbor galaxy: two and a half million years.

**Exercise 61.8 ★.**

“The [metre](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units) is now defined from $c$.” What does this say about which of the two — ruler or [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) — physicists trust more deeply?

**Solution of Exercise 61.8.**

[Light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source). The [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) $c$ proved steadier than any metal bar or national ruler — so the ruler is now derived from the [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source), not the [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) measured by the ruler.

**Exercise 61.9 ★★.**

Radar ranging: a radio pulse (traveling at $c$) bounced off the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) returns in about $2.6\,\mathrm{s}$. Recover the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon)’s distance from this round trip — and name the old sonar rule that carries over.

**Solution of Exercise 61.9.**

Round trip: $300000 \times 2.6 = 780000$ km; the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) stands at half — $390\,000\,\mathrm{km}$. The sonar rule carries over whole: every [echo](https://one-course.com/books/physics/1/en/chapter/27-how-sound-travels#ex-g4-how-sound-travels-echo) pays for the round trip, halve before believing.

**Exercise 61.10 ★★.**

Sort by the archive’s depth: [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) in your room from a lamp ($3\,\mathrm{m}$); the Sun; a [star](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-star) at $100$ [light-years](#def-g8-speed-of-light-lightyear); the neighbor galaxy. For the lamp, estimate the lookback in billionths of a second ($3 \div (3 \times 10^{8})$ — tame it in words).

**Solution of Exercise 61.10.**

Lamp: $3 \div (3 \times 10^{8}) = 10^{-8}$ s — a hundredth of a millionth of a second: even the room is an archive, too shallow to notice. Then the Sun (eight minutes), the [star](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-star) (a century), the galaxy (two and a half million years) — the deeper you look, the older the page.

**Exercise 61.11 ★★.**

A news report says “astronomers watched a [star](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-star) explode last Tuesday, $8000$ [light-years](#def-g8-speed-of-light-lightyear) away.” Rewrite the sentence with honest tenses: when did the explosion happen, and what happened last Tuesday?

**Solution of Exercise 61.11.**

“Last Tuesday, the [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) of a [star](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-star)’s explosion *reached us* — the explosion itself happened some $8000$ years ago, and its news has been traveling ever since.”

**Exercise 61.12 ★★★.**

The late-moon lateness peaks at about $1000$ seconds — [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)’s time to cross the full width of the Earth’s [orbit](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit), about $3 \times 10^{8}$ km. Run the seventeenth-century division yourself and compare with the modern $c$: how honest was the sky’s first answer?

**Solution of Exercise 61.12.**

$3 \times 10^{8}\ \text{km} \div 1000\ \text{s} = 3 \times
10^{5}$ $\mathrm{km}/\mathrm{s}$ — the modern value on the nose (the historical estimate, with rougher [orbit](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit) figures, landed within about a quarter of it: for the sixteen-hundreds, an astonishing first answer).

## 61.4 Problem: Mission Control

**Problem 61.1.**

Weekend problem — a shift at deep-space mission control; light-lag conversations from the Moon to the stars; the operations manual

Tonight you direct the communications desk: every message travels at $c = 300\,000\,\mathrm{km}/\mathrm{s}$, and the light-lag rules every decision.

**Part I — Near operations.**

1. The lunar base ( $384\,000\,\mathrm{km}$ ) requests confirmation of a supply drop. How long after your “confirmed” does the base hear it, and what is the soonest you can hear their acknowledgment?
2. A satellite in high [orbit](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit) at $36\,000\,\mathrm{km}$ relays a television feed. Compute its one-way lag — and say why intercontinental phone calls via such satellites carry a just-noticeable hesitation (round trip up and down).
3. The solar observatory reports a great flare “as it happens”. Correct the operator’s phrase: when did the flare truly erupt?
4. Protocol asks all clocks to allow for lag. Which near-Earth link — [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) or high satellite — needs the larger allowance, and by roughly what factor?

**Part II — The Mars window.** Mars stands tonight at $1.8 \times 10^{8}$ km.

5. Compute the one-way lag in seconds, then in minutes.
6. The rover meets an unexpected crevasse and its cameras show it approaching at walking pace. Explain, with the round-trip figure, why a joystick rescue is hopeless — and what the rover must therefore carry on board.
7. The evening’s plan upload takes $3\,\mathrm{min}$ of transmission plus the lag. When must the upload start to be fully received by the rover at 21:00 control time?
8. Six months hence, Mars will stand at $3.8 \times  10^{8}$ km. What becomes of the lag, and what does this teach about “the” distance to a [planet](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-planet) ?

**Part III — The far desk.**

9. An interstellar probe has reached one full light- *day* from Earth. Express that distance in kilometres (powers of ten; a day holds $86400$ seconds), and state the round-trip conversation time with the probe.
10. Dreamers at the back desk draft a “message to the nearest [star](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-star) ”. Draft the schedule instead: sent tonight, when is the soonest any reply arrives?
11. The archive wall shows tonight’s deep [image](https://one-course.com/books/physics/1/en/chapter/32-mirrors-and-reflection#prop-g5-mirrors-reflection-image) of the neighbor galaxy, $2.5$ million [light-years](#def-g8-speed-of-light-lightyear) out. Add the caption’s honest tense — what era of Earth’s past does this snapshot broadcast back, were anyone there to look?
12. End-of-shift log: write the desk’s three rules — one about instantaneous (that nothing is), one about joysticks and lag, one about telescopes and the archive.

**Solution of Problem 61.1.**

**1.** About $1.3\,\mathrm{s}$ after you speak; the soonest acknowledgment returns after the round trip, about $2.6\,\mathrm{s}$. **2.** $36000 \div 300000 = 0.12\,\mathrm{s}$ one way; a question-and-answer rides up and down twice — near half a second of hesitation, just at the ear’s threshold. **3.** “The flare erupted eight minutes twenty before our screens lit — we watch it as it *was*.” **4.** The [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) link: $1.3\,\mathrm{s}$ against $0.12\,\mathrm{s}$ — roughly ten times the allowance. **5.** $1.8 \times 10^{8} \div (3 \times 10^{5}) = 600$ s: ten minutes one way. **6.** The round trip is twenty minutes: the rescue picture is ten minutes old and the rescue command ten minutes late — the crevasse wins by nineteen minutes. The rover must carry its own reflexes: on-board hazard-stopping. **7.** Last bit must arrive by 21:00; it leaves Earth at $21{:}00 - 10$ min $= 20{:}50$; transmission began three minutes earlier: start at 20:47. **8.** The lag doubles to about twenty-one minutes one way: [planets](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-planet) have no “the” distance — both worlds [orbit](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit), and every conversation is scheduled against a moving target. **9.** $300000 \times 86400 \approx 2.6 \times 10^{10}$ km — twenty-six thousand million kilometres; a question-and-answer takes two full days. **10.** [Light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) reaches the [star](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-star) in about four years; the soonest reply lands about eight years after tonight’s transmission. **11.** “This [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) left its galaxy two and a half million years ago: the snapshot broadcasts the Earth of the earliest stone tools — our deepest naked-eye page of the archive.” **12.** For example: “Nothing is instantaneous — every signal, ours included, travels at best at $c$. Joysticks lose to lag beyond the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon): distant machines must think for themselves. And every telescope is an archive reader — the farther the object, the older the news, with no fresher edition printable.”