The spinning Earth: day, night, shadows and time
By the end of this lesson you will be able to
- Describe the Earth’s rotation — once every 24 hours, west to east, about a tilted axis — and explain why it produces day and night and the Sun’s apparent path across the sky.
- Explain why a shadow is longest near sunrise and sunset and shortest at local noon, and describe how a sundial uses this pattern.
- Calculate time differences from longitude using 15° per hour, and state Botswana’s time zone (UTC+2).
- Outline how Eratosthenes measured the size of the Earth in about 240 BC from two shadows, and calculate a circumference from his method.
- Design an investigation into shadow length through the day with qualified control variables.
The puzzle
Right now, sitting still, you are travelling eastwards at about 1500 km/h — faster than a passenger jet — because the ground under Gaborone is being carried round by the turning Earth. You feel nothing. No wind, no lean, no rumble. Yet the same movement you cannot feel makes the Sun rise, drags every shadow across the ground through the day, and decides that when it is midday in Botswana it is still before dawn in Brazil. How can a movement so large be so invisible — and how could anyone have discovered it?
Predict, before you read on: at what time of day is your shadow shortest, and which direction does it point at that moment in Botswana? Then predict whether a person in Nairobi (on the equator) or a person in London sees the Sun higher in the sky at midday in June.
Compare your answer
Shortest at local solar noon — which in Gaborone is around 12:15 by the clock, not 12:00 — and it points south, because from Botswana the midday Sun is in the northern half of the sky for the whole year. In June the noon Sun stands about 65° above the horizon in Nairobi and only about 62° in London, but the more surprising comparison is with Gaborone, where in June it reaches only 42°: winter shadows in Botswana are long. Everything in this lesson follows from one movement: the Earth turning once a day about an axis that is tilted.
The science — structured notes
1.1 A turning planet
The Earth is a sphere about 12 700 km across that rotates — spins about an imaginary line through the North and South Poles called its axis. One full turn relative to the Sun takes 24 hours: one day. The direction is from west to east, which is why everything in the sky — Sun, Moon, stars — appears to move the other way, rising in the east and setting in the west. The sky is not moving; we are.
| Fact about the rotation | Value | What it does |
|---|---|---|
| Time for one turn | 24 h (23 h 56 min relative to the stars) | Sets the length of the day |
| Direction | West → east (anticlockwise seen from above the North Pole) | Sun and stars appear to rise in the east |
| Speed of the ground at the equator | About 1670 km/h | Circumference 40 000 km ÷ 24 h |
| Speed of the ground at Gaborone (25° S) | About 1500 km/h | The circle of latitude is smaller, so the ground moves more slowly; at the poles it barely moves at all |
| Tilt of the axis | 23.4° from upright | Seasons and changing day length — Lesson 6.2 |
1.2 Day, night and the Sun’s path
The Sun lights one half of the Earth at a time. The half facing the Sun has day; the half facing away has night; the line between them, the terminator, sweeps westward across the surface as the planet turns. You cross it twice a day: at sunrise you are carried into the lit half, at sunset out of it.
1.3 Shadows through the day — the sundial
A vertical stick casts a shadow that points directly away from the Sun. Because the Sun’s position in the sky changes through the day, the shadow both turns and changes length: long and pointing west at sunrise, shortest and pointing south (in Botswana) at solar noon, long and pointing east at sunset. The length depends on how high the Sun is — its altitude above the horizon.
| Sun’s altitude | Shadow of a 10 cm stick | Where you would see it |
|---|---|---|
| 5° | 114 cm | Minutes after sunrise, anywhere |
| 20° | 27.5 cm | About 07:00 in Gaborone in December |
| 42° | 11.1 cm | Noon in Gaborone, June solstice |
| 65° | 4.7 cm | Noon in Gaborone, March equinox |
| 88° | 0.3 cm | Noon in Gaborone, December solstice — the Sun almost overhead |
At the same moment, a 1 m stick casts a shadow 2.5 m long and a tree casts a shadow 20 m long. How tall is the tree?
The Sun’s rays hit both at the same angle, so the ratio of height to shadow is the same for both: height of tree20 m = 1 m2.5 m
Height of tree = 20 × 12.5 = 8 m.
Every shadow measurement in this unit rests on this idea: shadows made by the same Sun at the same time are in proportion to the objects that cast them. Thales used it to measure the Great Pyramid in about 600 BC.
A sundial is a stick (the gnomon) with hour lines marked on the ground or a plate. The shadow’s direction tells the time; its length tells roughly the season. A good sundial has its gnomon tilted to point at the celestial pole (parallel to the Earth’s axis), so that the shadow turns at a steady 15° per hour — the Earth’s rotation rate — whatever the date.
A student in Maun photographs the shadow of a flagpole at 07:00, 10:00, 13:00 and 16:00 on the same day. Explain why the four shadows differ in length and direction, using the Earth’s rotation, and state which is shortest.
Reveal answer
The Earth turns 15° every hour, so between photographs the Sun appears to move across the sky, rising in the east and climbing until local noon (about 12:25 by the clock in Maun) and then sinking towards the west. The shadow always points away from the Sun, so it swings from pointing west (07:00) round through south (near noon) to pointing east (16:00). Its length depends on the Sun’s altitude: at 07:00 and 16:00 the Sun is low and the shadow long; the 13:00 shadow is the shortest of the four because it is closest to local noon, when the Sun is highest. None of this is the Sun moving: it is the flagpole being carried round by the rotating Earth.
1.4 Time zones — turning the rotation into clocks
Solar noon happens at a different moment for every longitude: the Earth turns 360° in 24 h, so 15° of longitude = 1 hour. Places to your east reach noon earlier; places to your west, later. Before railways each town kept its own solar time; today the world uses time zones, each ideally 15° wide, counted from the zero line of longitude through Greenwich (UTC).
| Place | Longitude | Time zone | When it is 12:00 in Gaborone |
|---|---|---|---|
| Gaborone, Botswana | 25.9° E | UTC+2 (Central Africa Time, no summer time) | 12:00 |
| London, UK | 0° | UTC+0 (UTC+1 in summer) | 10:00 (11:00 in British summer) |
| Nairobi, Kenya | 36.8° E | UTC+3 | 13:00 |
| Beijing, China | 116° E | UTC+8 | 18:00 |
| São Paulo, Brazil | 46.6° W | UTC−3 | 07:00 |
| Los Angeles, USA | 118° W | UTC−8 (UTC−7 in summer) | 02:00 |
Botswana’s clocks are set to the 30° E meridian (UTC+2). Gaborone is at 25.9° E. At what clock time is the Sun highest?
Gaborone is 30 − 25.9 = 4.1° west of the zone’s meridian, so it reaches noon later. Time difference = 4.1 × 4 min per degree = about 16 minutes (because 1 hour ÷ 15° = 4 min per degree).
Solar noon in Gaborone is therefore about 12:16 by the clock — and it wanders by a further ±15 minutes through the year because the Earth’s orbit is not a perfect circle. Your shortest shadow is not at 12:00. Francistown (27.5° E) reaches noon about 6 minutes before Gaborone; Ghanzi (21.7° E) about 17 minutes after.
A Botswana Premier League match kicks off in Gaborone at 15:00. Calculate the kick-off time for a supporter watching in each place, and explain your method.
(a) Cairo, Egypt (UTC+2 in winter).
(b) Lagos, Nigeria (UTC+1).
(c) Sydney, Australia (UTC+10), and Toronto, Canada (UTC−5).
Reveal answer
(a) 15:00 — same zone, same time, even though Cairo is 2500 km away: time zones follow longitude, not distance, and Cairo (31° E) lies at almost the same longitude as Botswana.
(b) 14:00 — Lagos is one hour behind (UTC+1 is one hour earlier than UTC+2). Method: find the difference in UTC offsets and subtract or add.
(c) Sydney is 8 hours ahead: 23:00. Toronto is 7 hours behind: 08:00 the same day. Sydney’s supporter is nearly at midnight because the Earth’s rotation carried Sydney into daylight 8 hours before Gaborone.
1.5 Eratosthenes measures the Earth — 240 BC
In about 240 BC the Greek scholar Eratosthenes, librarian at Alexandria in Egypt, read that at noon on the longest day of the year the Sun shone straight down a well at Syene (modern Aswan), far to the south: a vertical post there cast no shadow. At the same moment in Alexandria a vertical post did cast a shadow, at an angle of 7.2° from the vertical. On a flat Earth this could not happen; on a curved Earth it must. From that one angle and the distance between the two cities he measured the planet.
The shadow angle at Alexandria was 7.2°. The distance from Syene to Alexandria was 5000 stadia (about 800 km). Find the circumference of the Earth.
The 7.2° between the two posts is the same as the angle between the two cities at the centre of the Earth. A full circle is 360°, so the two cities are 7.2°360° = 150 of the way round the Earth.
Circumference = 50 × 5000 stadia = 250 000 stadia ≈ 50 × 800 km = 40 000 km.
The modern value is 40 075 km. Using a stick, a well and a walked distance, he was within a few per cent — 1700 years before anyone sailed round the planet.
A student writes: “Eratosthenes proved the Earth was round because the shadow in Alexandria was longer than the one in Syene, and longer shadows mean you are further from the Sun.” Identify two errors.
Reveal answer
First, the Greeks already knew the Earth was round (from ships’ hulls disappearing before their masts, and the round shadow on the Moon in eclipses); Eratosthenes was measuring its size, not proving its shape. Second, the shadows differ not because Alexandria is further from the Sun — the Sun is 150 million km away and the 800 km between the cities is nothing to that — but because the Earth’s surface curves, so a vertical post at Alexandria points in a different direction from one at Syene. The Sun’s rays arrive parallel; the posts do not.
1.6 Evidence that it is the Earth that turns
For most of history people assumed the sky turned and the Earth stood still — it feels that way. Three pieces of evidence changed minds:
“In Botswana the Sun rises in the east and sets in the west, so it must be moving around the Earth from east to west.”
Reveal answer
False. The observation is right — the Sun does appear to rise in the east and set in the west — but the conclusion does not follow. Exactly the same appearance is produced by an Earth turning from west to east under a stationary Sun, in the way that trees seem to move backwards past a moving bus. The star trails, Foucault’s pendulum and the curving winds show that it is the Earth that turns; the Sun’s apparent motion is the consequence of our own movement.
Suppose the Earth rotated once every 48 hours instead of every 24. Describe two things that would change for a farmer in the Tuli Block, and one thing that would not.
Reveal answer
Days and nights would each last about 24 hours: the afternoon would go on for twelve hours of sunlight, so the ground would get far hotter than now, and the night would be twice as long and much colder — crops and animals would face a 48-hour cycle of extreme heat and frost. Shadows would move across the ground at half the speed (7.5° per hour), so every sundial would need new hour lines. What would not change: the Sun would still rise in the east and set in the west, and solar noon would still be when the shadow is shortest, because the direction of rotation and the shape of the Sun’s path would be the same — only the rate would differ.
Try it — the shadow stick
Stand a 10 cm stick upright on a sheet of paper and measure its shadow every hour from 06:00 to 18:00 local solar time. Start in Gaborone at the December solstice, then switch to the June solstice, then move the stick to the equator and to London. Plot shadow length against time: what shape is the graph, and where is the minimum?
Suppose your Gaborone December results were: 06:00 → 59 cm, 08:00 → 14 cm, 10:00 → 5.2 cm, 12:00 → 0.2 cm, 14:00 → 5.2 cm, 16:00 → 14 cm, 18:00 → 59 cm.
(a) Describe the relationship between shadow length and time, quoting values, and state whether it is linear.
(b) Explain why the 12:00 shadow is almost zero in Gaborone in December but 11 cm in June.
(c) Switching to London in December, the lab reports “off the paper” at 08:00. Explain.
Reveal answer
(a) The shadow shortens from 59 cm at 06:00 to 0.2 cm at 12:00 and lengthens again to 59 cm at 18:00; the changes are large near sunrise and sunset (59 to 14 cm in the first two hours) and small around noon (5.2 to 0.2 cm between 10:00 and 12:00). The graph is a U-shaped curve, symmetrical about 12:00 — not a straight line and not a proportion, because the length depends on the Sun’s altitude, which rises fastest just after sunrise.
(b) Shadow length depends on the Sun’s altitude. In December the noon Sun over Gaborone is at 88° — almost overhead, because the Sun stands over the Tropic of Capricorn, just north of the city — so the light comes down nearly vertically and a vertical stick casts almost no shadow. In June the Sun stands over the Tropic of Cancer, 47° further north, so its noon altitude in Gaborone is only 42° and the shadow is nearly as long as the stick.
(c) At 08:00 solar time on the December solstice the Sun has not yet risen in London: at 51° N in midwinter it is up for under eight hours, roughly 08:05 to 15:55. With the Sun below the horizon there is no shadow to measure; just after it rises the altitude is so small that the shadow is longer than the paper. The result is not an error — it is the tilt (Lesson 6.2) combined with the rotation.
Common mistakes to avoid
- “The Sun moves across the sky” — say “appears to move”; the Earth rotates west to east.
- Shortest shadow at 12:00 on the clock — the shortest shadow is at local solar noon, about 12:16 in Gaborone.
- Midday Sun “overhead” — it is overhead only between the tropics, on two days a year; from Gaborone it is always to the north.
- “Longer shadows mean further from the Sun” — shadows depend on the Sun’s altitude, set by the Earth’s curve and tilt, not on distance.
- Time zones by distance — they follow longitude; Cairo and Gaborone share UTC+2 despite being 5000 km apart.
- Eratosthenes “proved the Earth was round” — he measured its size; its shape was already known.
How we found out — a well, a pendulum and a very long argument
The Greeks knew the Earth was a sphere by 350 BC: Aristotle pointed to the round edge of the Earth’s shadow on the Moon during eclipses and to the way new stars appear as travellers go south. Eratosthenes (about 276–194 BC) turned that shape into a number with the two shadows of 240 BC. But almost everyone, including Aristotle, believed the sphere stood still while the heavens turned around it — the obvious explanation for what the eyes see. One Greek, Aristarchus of Samos (about 270 BC), proposed that the Earth spins and orbits the Sun; he was ignored for eighteen centuries because nobody could feel the movement and nothing seemed to fall behind as the ground rushed east.
The argument was reopened by Nicolaus Copernicus in 1543, whose model with a rotating, orbiting Earth predicted the sky more simply, and it was settled by evidence that could be seen. In 1851 Léon Foucault hung a 28 kg brass ball on a 67 m wire from the dome of the Panthéon in Paris and let it swing. Hour by hour the swing turned across the floor, exactly as it must if the floor itself was rotating beneath a pendulum that kept its own direction. Crowds queued to watch the Earth turn. Foucault pendulums now hang in science centres on every continent, and each one turns at the rate its latitude predicts — fastest at the poles, not at all on the equator, about 6° an hour in Botswana. The movement that no one can feel became something anyone can watch.
Foucault’s pendulum turns once in 32 hours in Paris (49° N) and would take about 57 hours in Gaborone (25° S). Explain why the rate depends on latitude, and what the pendulum would do at the North Pole and at the equator.
Reveal answer
The pendulum keeps swinging in a fixed direction in space; what turns is the ground under it. At the North Pole the ground makes one complete turn about the vertical every 24 hours, so the swing appears to go round once a day. At the equator the ground moves in a straight line eastwards without turning about the vertical at all, so the swing direction never changes. In between, only part of the Earth’s rotation is a turn about the local vertical — the part that grows with the sine of the latitude — so the pendulum turns more slowly the nearer the equator: 24 h ÷ sin(49°) ≈ 32 h in Paris, 24 h ÷ sin(25°) ≈ 57 h in Gaborone. A pendulum is a rotation meter, and its reading matches a turning Earth everywhere it has been tried.
Where it is used now
- Botswana’s clocks. The whole country keeps Central Africa Time (UTC+2) all year, with no summer-time change; sunrise in Francistown comes about 20 minutes before Ghanzi because Francistown is 6° further east. Solar noon is around 12:15 in Gaborone, so the hottest part of the day and the shortest shadows come after one o’clock.
- Solar power. Fixed panels at Botswana’s solar farms face north, tilted at roughly the latitude (about 25°), so that the midday Sun hits them square on; tracking panels turn through the day at 15° an hour — a sundial in reverse.
- Navigation and surveying. Before GPS, a ship’s longitude was found by comparing local noon (from the Sun’s highest point) with the time on a clock set to Greenwich: 4 minutes of difference for every degree. The method Eratosthenes used still calibrates the satellites that replaced it.
- Building design. Architects in Gaborone shade north-facing windows with overhangs sized from the Sun’s noon altitude — 88° in December, 42° in June — so the summer Sun is blocked while the winter Sun comes in.
- Aviation and satellites. Rockets launch eastward to add the Earth’s 1670 km/h to their speed; a satellite’s ground track drifts west on every orbit because the Earth turns beneath it — the reason BotSat-1 passes over Botswana about six times a day rather than continuously.
Science now — and the scientist you need to be
What is happening in 2026
The Earth’s rotation is now measured to a millionth of a second by comparing atomic clocks with radio telescopes fixed on distant galaxies, and the news is that the day is not exactly 24 hours and is not constant. Over centuries the Moon’s tides slow the spin by about two thousandths of a second per century; over months, shifting winds, molten iron in the core and melting ice change it by fractions of a millisecond. Since 2020 several of the shortest days ever recorded have been measured, more than a millisecond under 24 hours, and timekeepers have discussed whether a “negative leap second” might one day be needed. Meanwhile the world’s measurement authorities have agreed to stop adding leap seconds from 2035, letting clocks and the Sun drift apart by a minute or so per century rather than disrupt the software that runs on precise time. And every phone that knows where it is depends on satellites whose clocks must be corrected for the Earth’s turning: get the rotation wrong by a millisecond and positions are wrong by half a kilometre. The oldest measurement in astronomy — the length of a day — has become one of the most precise.
The mindshift
What you need to be able to do
Three examinable skills: explain day and night and the Sun’s apparent path from the Earth’s rotation (naming the direction and the 24-hour period); reason about shadow length from the Sun’s altitude, with proportion; and plan a shadow investigation with control variables that carry values — “the same stick” scores nothing, “a 10 cm stick, checked vertical with a plumb line” scores. The Think task below is that plan.
See an example
Gaborone, a Saturday in September: marks at 08:00 (41 cm), 09:00 (24 cm), 10:00 (15 cm), 11:00 (10 cm), 12:00 (8 cm), 13:00 (8.5 cm), 14:00 (11 cm), 15:00 (17 cm), 16:00 (27 cm). The shortest shadow was between 12:00 and 13:00, pointing almost due south. The AI gave solar noon as about 12:12 for Gaborone that day and explained it as the city lying 4° west of the 30° E meridian that Botswana’s clocks use, with a small correction for the date — the same reasoning as the worked EXAMPLE.
Key terms
| Rotation | The spinning of the Earth about its axis, once every 24 hours, from west to east. |
| Axis | The imaginary line through the North and South Poles about which the Earth rotates; tilted 23.4° from upright. |
| Apparent motion | Movement we see in the sky that is caused by our own movement — the Sun “crossing” the sky as the Earth turns. |
| Terminator | The line between the lit and unlit halves of the Earth; crossing it is sunrise or sunset. |
| Altitude (of the Sun) | The angle of the Sun above the horizon; highest at solar noon. |
| Solar noon | The moment the Sun is highest in the sky at your longitude; the shadow is shortest and points due south in Botswana. |
| Sundial / gnomon | A device that tells the time from the direction of a shadow; the gnomon is the rod that casts it. |
| Longitude | Position east or west of Greenwich, in degrees; 15° of longitude corresponds to 1 hour of time. |
| Time zone | A region that keeps the same clock time; Botswana uses UTC+2 all year. |
| Latitude | Position north or south of the equator, in degrees; Gaborone is 24.65° S. |
Think like a scientist
Criterion B A school in Serowe is building a sundial in its courtyard and wants data first. A student is asked to investigate how the length of the shadow of a vertical rod changes with the time of day. She has a 50 cm wooden rod, a lump of modelling clay, a large sheet of white card, a metre rule, a plumb line (a weight on a string), a spirit level, a marker pen and a clock. The courtyard is paved and in full sun from 07:00 to 17:00.
(a) Write a research question and a hypothesis with scientific reasoning.
(b) Identify the independent and dependent variables, each with its unit and instrument, and explain why “how far the Sun has moved” is not an acceptable independent variable.
(c) Identify three control variables. For each, give the value or condition and say how it is kept the same.
(d) Write a numbered method another student could follow, including the times of measurement, repeats, what is recorded and one safety point specific to this investigation.
(e) Describe how the results would be processed and presented, and predict the shape of the graph.
Model answer
(a) Research question: How does the time of day (07:00 to 17:00, at two-hour intervals) affect the length of the shadow (cm) cast by a vertical 50 cm rod on level ground in Serowe? Hypothesis: If the time moves from 07:00 towards midday, then the shadow will get shorter, and after midday it will lengthen again, with the shortest shadow at about 12:15 rather than 12:00, because the Earth’s rotation carries Serowe round so that the Sun appears to climb until local solar noon and then sink; the higher the Sun, the steeper its light and the shorter the shadow of a vertical rod — and Serowe (26.7° E) reaches solar noon about 13 minutes after 12:00 on the UTC+2 clock.
(b) Independent variable: the time of day, in hours and minutes, read from the clock — 07:00, 09:00, 11:00, 13:00, 15:00 and 17:00 (six values, so that the minimum is bracketed). Dependent variable: the length of the shadow from the base of the rod to the tip of the shadow, in cm, measured with the metre rule to the nearest 0.5 cm. “How far the Sun has moved” cannot be measured directly (and must never be measured by looking at the Sun); time on a clock is the quantity we can set and read, and the Sun’s position is its consequence.
(c) Height of the rod — 50 cm above the card, measured with the rule and not adjusted between readings, because a taller rod casts a longer shadow at every altitude. Verticality of the rod — checked with the plumb line held beside it before every reading and corrected in the clay, because a leaning rod lengthens or shortens the shadow. Surface — the same sheet of card on the same paved spot, checked level with the spirit level, because a sloping surface stretches the shadow. (Also: the same day, since the Sun’s noon altitude changes from day to day; readings taken on the exact clock times, since the length changes by centimetres in minutes near sunrise.)
(d) 1. Set the card on the paving in the spot that is in full sun all day; check it is level with the spirit level and tape the corners down. 2. Fix the rod upright in clay at a marked point near the middle of the card and check it with the plumb line from two sides; measure its height as 50 cm. 3. At exactly 07:00 mark the tip of the shadow on the card with the pen and write the time beside it; measure the distance from the base of the rod to the mark with the rule to 0.5 cm and record it. 4. Take two more marks within one minute and record all three as trials; calculate the mean. 5. Repeat step 3 and 4 at 09:00, 11:00, 13:00, 15:00 and 17:00, re-checking the plumb line each time. 6. If the shortest shadow appears to be between two readings, add readings at 12:00 and 12:30 on the same day. 7. Record every value in a table with the units in the headings. Safety: never look towards the Sun to check its position — read it from the shadow only; work in a hat and drink water, since the readings run through the hottest hours; anchor the card so a gust cannot lift it and the rod cannot fall on anyone.
(e) Calculate the mean shadow length for each time (to 0.5 cm, matching the rule) and record the direction of each shadow. Plot a line graph with time of day on the x-axis (even scale, 07:00 to 17:00) and shadow length in cm on the y-axis, points as crosses, joined by a smooth curve — not a straight line, since the relationship is not linear. Expected shape: a U, steep at the ends and flat near the bottom, with its minimum at about 12:15 and roughly symmetrical about it; the direction of the shadow will swing from west through south to east. A sundial plate can then be marked from the directions, and the length data tell the school how much space the winter shadow needs.
Probe deeper — exam-style questions
Attempt every question before opening the answer. Marks in brackets show what a full answer is worth.
Explain why the Sun appears to rise in the east.
Reveal answer
The Earth rotates from west to east about its axis [1]; as your part of the surface turns towards the east it is carried into the sunlit half, so the Sun first appears above the eastern horizon [1].
It is 09:00 in Gaborone (UTC+2). Calculate the time in Tokyo (UTC+9) and in New York (UTC−5), and state how many degrees of longitude the Earth turns through in one hour.
Reveal answer
Tokyo is 7 hours ahead: 16:00 [1]; New York is 7 hours behind: 02:00 [1]; 360° ÷ 24 h = 15° per hour [1].
A vertical 1 m post in Kasane casts a shadow 0.1 m long at solar noon in December and 0.9 m long at solar noon in June. Explain the difference, and calculate the height of a baobab whose June noon shadow is 18 m.
Reveal answer
Shadow length depends on the Sun’s altitude: in December the Sun is almost overhead at noon in Kasane (near the Tropic of Capricorn), so the light is nearly vertical and the shadow short; in June the Sun stands far to the north and is only about 49° up, so the light is slanted and the shadow long [1]. In June the ratio of height to shadow is 1 ÷ 0.9 for every object in the same sunlight [1]; the baobab is 18 × (1 ÷ 0.9) = 20 m tall [1].
Outline the method Eratosthenes used to measure the Earth’s circumference, and calculate the circumference he would have found if the shadow angle at Alexandria had been 9° with the same 5000 stadia between the cities.
Reveal answer
At noon on the solstice a vertical post at Syene cast no shadow while one at Alexandria cast a shadow at 7.2°; because the Sun’s rays are parallel, the angle equals the angle between the two cities at the Earth’s centre [1]; that angle as a fraction of 360° equals the distance between the cities as a fraction of the circumference, so circumference = 360 ÷ 7.2 × 5000 = 250 000 stadia [1]. With 9°: 360 ÷ 9 = 40, so 40 × 5000 = 200 000 stadia [1].
True or false, with a reason: “The shortest shadow of the day in Gaborone is at 12:00 by the clock.”
Reveal answer
False [1]: Botswana’s clocks are set to the 30° E meridian but Gaborone is at 25.9° E, about 4° to the west, so the Sun reaches its highest point — and the shadow its shortest — about 16 minutes later, around 12:16 (varying by the date) [1].
A student says the Earth cannot be spinning at 1500 km/h because “we would all be thrown off and there would be a permanent wind from the east”. Explain what is wrong with each part of the argument.
Reveal answer
We are not thrown off because gravity pulls every object towards the Earth’s centre with a force far larger than the tiny force needed to keep it moving in the Earth’s huge circle — at the equator, gravity is about 300 times larger than required [1]. There is no wind because the atmosphere rotates with the Earth: air, ground and people all move together at the same steady speed, and a steady shared motion produces no force and no relative movement (first law) [1]. Only changes in motion can be felt, and the rotation shows up only in things that keep their own direction — a pendulum, the stars, the curving winds [1].
Summary
- The Earth rotates once every 24 hours from west to east about a tilted axis; the Sun, Moon and stars only appear to move across the sky.
- Half the Earth is lit at any time; rotation carries you into daylight at sunrise and out of it at sunset. From Botswana the noon Sun is in the north.
- A shadow points away from the Sun and is shortest at solar noon, when the Sun is highest; shadow length depends on the Sun’s altitude, and objects in the same sunlight have shadows in proportion to their heights.
- 15° of longitude = 1 hour: time zones are counted from Greenwich; Botswana keeps UTC+2, and Gaborone’s solar noon is about 12:16.
- Eratosthenes measured the Earth from two shadows in 240 BC; Foucault’s pendulum in 1851 made the rotation visible. A movement we cannot feel is known through the patterns it produces.
Next time → Seasons and the tilt: why December is summer in Botswana, why it is not because we are closer to the Sun, and how day length changes with latitude.