eduKate Learning Manual
Science | Earth, Water, Atmosphere & the Celestial World
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The Moving Shadow

Why the Same Stick Draws a Different Shadow Through the Day

Big Question: Why do the length and direction of a fixed object’s shadow change as the day passes?

Quick Answer

Light from the Sun travels approximately in straight lines over everyday distances. An opaque object blocks some of those rays, producing a shadow on the ground.

As Earth rotates, the Sun appears to move across the sky from east toward west. The direction of incoming sunlight changes relative to the stick.

When the Sun is low, rays arrive at a shallow angle and the shadow is long. When the Sun is high, rays arrive more steeply and the shadow is shorter.

Earth rotates → Sun’s apparent direction changes → ray angle changes → shadow direction and length change.

What You Will Learn

• How an opaque object makes a shadow.
• Why shadows point away from the light source.
• Why a low Sun produces a long shadow.
• Why a high Sun produces a shorter shadow.
• Why the daily shadow pattern is linked to Earth’s rotation.
• What solar elevation means.
• Why local solar noon is not always 12:00 on your clock.
• How a sundial uses repeating shadow geometry.
• Why shadow length also changes with season and latitude.
• Why shadows can reveal information about Earth and the sky.
• How to make a fair shadow-tracking experiment in Singapore.

Part 1 — A Shadow Is Missing Direct Light

An opaque object does not transmit most visible light through itself.

If sunlight travels toward the ground and a stick blocks some rays, the region behind the stick receives less direct sunlight.

That darker region is the shadow.

shadow ≠ substance projected from an object.

Part 2 — The Shadow Points Away From the Sun

Imagine a straight line from the Sun through the top of the stick to the ground. The shadow extends on the opposite side of the stick from the Sun.

If the Sun appears in the eastern sky, the shadow extends generally toward the west. Later, when the Sun appears in the western sky, the shadow extends generally eastward.

Exact direction depends on season, latitude and time.

Part 3 — Low Sun, Long Shadow

When the Sun is low above the horizon, its rays approach the ground at a shallow angle.

The top of the stick blocks a ray that does not reach the ground until far away. The shadow is long.

This is geometry, not because morning sunlight is “weaker at making shadows.”

Part 4 — High Sun, Short Shadow

When the Sun is higher in the sky, rays arrive more steeply.

The ray from the top of the stick reaches the ground closer to the base, so the shadow is shorter.

higher solar elevation → steeper rays → shorter shadow.

Part 5 — A Triangle Hides Inside Every Shadow

A vertical stick, its horizontal shadow and the Sun ray joining the stick top to shadow tip form a right triangle.

At higher resolution:

tan(solar elevation) = stick height ÷ shadow length.

This means a measured shadow can be used to calculate the Sun’s elevation angle if the stick height is known.

Primary learners can understand the geometry without calculating trigonometric functions yet.

Part 6 — Why the Sun Appears to Cross the Sky

Earth rotates eastward once roughly every 24 hours relative to the Sun.

Because we rotate with Earth, the Sun appears to move in the opposite direction across the sky, generally from east to west.

The daily changing shadow is therefore evidence of changing orientation between your location and the Sun.

Part 7 — The Stick Is a Gnomon

A stick or pointer used to cast a time-indicating shadow is called a gnomon.

In a sundial, the gnomon and marked surface are arranged so that shadow position can indicate solar time.

A sundial is therefore a calibrated shadow instrument.

Part 8 — Why a Sundial Can Tell Time

Earth’s rotation is regular enough that the Sun’s apparent direction repeats in a predictable daily pattern.

If we mark where the shadow falls at known solar times, the moving shadow can later be used as a clock.

planetary rotation → repeatable sky geometry → repeatable shadow position → timekeeping.

Part 9 — Why Solar Noon Is Special

Local solar noon occurs when the Sun crosses the local meridian and reaches its highest altitude for that day.

For a vertical stick on level ground, the shadow is usually shortest near this time.

Solar noon is not necessarily 12:00 on a civil clock because time zones, longitude within the time zone and the equation of time shift the relationship.

Part 10 — Singapore Has an Extra Surprise

Singapore lies close to the equator. Around dates when the Sun passes nearly overhead at local solar noon, a vertical object can cast an extremely short shadow.

This happens near the equinox seasons, though the exact dates depend on latitude and the Sun’s declination.

A nearly disappearing midday shadow is therefore not the Sun turning off the shadow. It is the geometry approaching a nearly vertical ray path.

Part 11 — Why Shadows Change Across the Year

Earth’s rotational axis is tilted relative to its orbit around the Sun.

As Earth travels around the Sun, the Sun’s apparent daily path changes through the seasons. At the same clock time, solar elevation can be different in different months.

That changes shadow length.

Part 12 — Why Latitude Matters

The Sun’s path also depends on where you are on Earth.

A vertical stick in Singapore, London and northern Alaska will not trace the same daily or seasonal shadow pattern.

Shadow geometry therefore contains information about both time and location.

Part 13 — Shadows Help Reveal Earth’s Shape

Ancient scholars compared shadow angles at different places. The most famous example is Eratosthenes, who used geometry and differences in solar angle between Egyptian locations to estimate Earth’s circumference.

The powerful move was not simply “look at two shadows.” It was to combine:

• same distant Sun;
• different locations;
• measured angle difference;
• known ground distance;
• geometric model of a curved Earth.

A tiny shadow can therefore become a measurement of a planet.

Part 14 — Why Shadows Are Not Perfectly Sharp

The Sun is not a point source. It has a visible disc in the sky.

Some parts of a shadow receive light from part of the solar disc but not all of it, creating a softer outer region called the penumbra.

The darkest region where the light source is fully blocked is the umbra.

This same geometry becomes important in eclipses.

Follow One Shadow Tip Through a Day

1. Morning Sun is low in the eastern sky.
2. The stick casts a long shadow generally westward.
3. Earth continues rotating.
4. The Sun appears higher and shifts across the sky.
5. The shadow shortens and changes direction.
6. Near local solar noon, the Sun reaches its daily highest point.
7. The shadow becomes relatively short.
8. Afternoon Sun moves lower toward the west.
9. The shadow lengthens generally eastward.
10. Sunset ends direct solar illumination and the sharp solar shadow disappears.

A Text Diagram You Can Draw Anywhere

MORNING            NOON              AFTERNOON
 Sun low            Sun high           Sun low
   \                   |                 /
    \                  |                /
     | stick            |              | stick
     |________ long     |_ short   long________|
 shadow west-ish                 shadow east-ish

Earth rotation changes apparent Sun direction

Think Like a Scientist — Build a Shadow Record

1. Place a vertical stick in a fixed location with clear sunlight.
2. Check verticality with a simple level or plumb line.
3. Mark the shadow tip every 30 or 60 minutes.
4. Record clock time.
5. Measure shadow length and compass direction.
6. Repeat on another clear day.
7. Compare the paths.

Do not move the stick between measurements. Avoid staring at the Sun. Measure the shadow, not the Sun directly.

How Do We Know Earth’s Rotation Is Involved?

• the shadow changes in a regular daily pattern;
• the Sun, Moon and stars show systematic apparent daily motion;
• Foucault pendulums demonstrate Earth’s rotation mechanically;
• Coriolis effects and satellite observations are consistent with a rotating Earth;
• astronomical models predict shadow positions accurately.

The shadow is one piece of a large converging evidence system.

Observation vs Inference

• Observation: shadow tip moves during the day.
• Observation: shadow is long when the Sun is low and short when the Sun is high.
• Observation: the stick remains fixed.
• Inference: direction of incoming sunlight changes relative to the stick.
• Higher-level inference: daily solar motion is explained primarily by Earth’s rotation.

Common Misconceptions and How to Repair Them

Misconception	Better model
The shadow moves because the stick moves.	A fixed stick’s shadow changes because incoming light direction changes.
The Sun travels around Earth once each day.	The daily apparent solar motion is primarily caused by Earth’s rotation.
Noon always means 12:00.	Local solar noon can differ from civil clock noon.
A shorter shadow means weaker sunlight.	Shadow length mainly records solar angle.
Shadows have perfectly sharp edges.	The Sun’s finite angular size creates penumbra.
The Sun is directly overhead everywhere at noon.	Overhead Sun occurs only at certain latitudes and dates.

Checkpoint Questions

1. How does an opaque object make a shadow?
2. Which way does a shadow point relative to the Sun?
3. Why does a low Sun make a long shadow?
4. Why does a high Sun make a short shadow?
5. What is solar elevation?
6. What makes the Sun appear to cross the sky each day?
7. What is a gnomon?
8. Why can a sundial tell time?
9. What is local solar noon?
10. Why do shadows change across the year?
11. Why does latitude matter?
12. What did Eratosthenes gain by comparing shadows in different places?

Apply It — Three Sticks

• A: vertical stick in Singapore near local solar noon.
• B: same-height vertical stick in Singapore one hour after sunrise.
• C: same-height stick at a high northern latitude in winter.

Predict relative shadow lengths. State what additional date, latitude and solar-elevation information is needed before making a precise numerical ranking between A and C.

Answer Key

Open after attempting the application

B should have a long shadow because the Sun is low soon after sunrise. A can have a very short shadow when the Sun is high, especially near overhead-Sun dates. C is usually long in high-latitude winter because the Sun remains low, but exact comparison requires the actual solar elevation angles.

Can You Explain WHY?

• Why can a stationary object make a moving shadow?
• Why does solar elevation control shadow length?
• Why does a sundial depend on Earth’s rotation?
• Why might Singapore have an almost shadowless noon on some dates?
• Why do two cities get different shadow lengths at the same moment?
• Why can a shadow measure something as large as Earth?

Singapore Field Connection

Singapore’s near-equatorial location makes shadow tracking especially interesting. The Sun can pass north or south of the zenith during different parts of the year, so a midday shadow can switch which side of a vertical object it falls on.

Record a gnomon’s noon shadow over several months. A simple schoolyard experiment becomes a local record of Earth–Sun geometry.

Primary Science / PSLE Bridge

• light travels from a source and can be blocked;
• opaque objects form shadows;
• shadow position depends on light-source position;
• Earth rotates;
• patterns can be measured over time;
• simple geometric models can explain observations.

Go Beyond Primary Science

Primary idea	Higher-resolution science
Shadow gets shorter	Solar elevation and tangent geometry
Sun appears to move	Earth rotation and celestial coordinates
Sundial tells time	Local solar time and equation of time
Season changes shadows	Axial tilt and solar declination
Different places differ	Latitude, longitude and spherical geometry
Shadow edge is soft	Umbra, penumbra and angular source size

Deep Science Window — Solar Noon Can Move on Your Clock

Civil time is designed for societies, not for the Sun to cross every local meridian at 12:00 sharp.

Longitude within a time zone shifts local solar noon, and Earth’s elliptical orbit plus axial tilt cause the equation of time to vary through the year.

A sundial and a wristwatch therefore measure related but not identical definitions of time.

Deep Science Window — One Shadow Can Encode Several Variables

A single shadow depends on object height, solar elevation and azimuth. The solar angles depend on latitude, longitude, date and time.

That means a shadow is not merely a dark shape. It is compressed information about geometry between a local observer, rotating Earth and the Sun.

Evidence Boundaries

• Shadow moves ≠ Sun physically circles Earth each day.
• Short shadow ≠ stronger sunlight by definition.
• Solar noon ≠ always 12:00 civil time.
• Near-zero shadow in Singapore ≠ every noon all year.
• Sundial shadow ≠ perfect clock without calibration.
• Eratosthenes story ≠ one measurement with no assumptions. Geometry, distance and solar-ray assumptions matter.

Manual Summary — KNOW → CONNECT → EXPLAIN → APPLY → CHECK

KNOW: shadow, opaque, ray, solar elevation, gnomon, solar noon, rotation.

CONNECT: Earth rotation → apparent Sun motion → changing ray angle → moving shadow.

EXPLAIN: low Sun makes long shadows; high Sun makes short shadows.

APPLY: sundials, latitude, seasons, overhead Sun and Earth measurement.

CHECK: distinguish the shadow observation from the planetary explanation.

Where to Go Next

• Earth, Water, Atmosphere & Celestial World
• Why the Moon Seems to Follow You
• The Bent Pencil: Refraction

Research Sources and Further Reading

• NASA Solar Dynamics Observatory — Sundials and Earth Rotation
• Smithsonian Science Education Center — Sundials
• NASA Solar System Exploration — Earth’s Rotation

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eduKate Learning Manuals are written so that a learner can begin simply, a parent can teach confidently, and both can keep going until the simple school model opens into real Science.