Moon Geometry

Phases, Eclipses, and
Why Shadows Rarely Matter

Dr. Anna Rosen

January 28, 2026

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Credit: iClicker

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If you can’t scan: open the link and enter the course code ASES.

30–60 sec. Get everyone connected before starting.

Two questions that secretly have the same answer:

Why does the Moon change shape?

Why don’t we get eclipses every month?

Geometry. (Not vibes.)

0–1 min. Hook. Emphasize: “Today is a geometry day. If you can draw it, you can predict it.”

Today’s Learning Objectives

By the end of today, you’ll be able to:

• Explain Moon phases as changing viewing geometry of the Moon’s sunlit half (not Earth’s shadow)
• Predict the Moon’s phase from Sun–Earth–Moon geometry and describe when each phase is visible
• Distinguish phases from eclipses and explain why eclipses do not happen every month
• Define nodes and explain eclipse seasons as repeated alignment windows
• Connect angular size to eclipse type (total vs. annular) using geometric reasoning

1–2 min. Point out: phases (common), eclipses (rare) — same ingredients, different alignments.

Quick Break (2–3 min): NotebookLM

Open NotebookLM: notebooklm.google.com

Make your notebook (now):

1. Create a new notebook: Lecture 4 — Moon Geometry
2. Add sources by pasting the lecture reading web pages (URLs)
3. Ask it to generate retrieval questions + “find-it-fast” summaries

Example source URL to add: https://astrobytes-edu.github.io/astr101-sp26/modules/module-01/readings/lecture-04-moon-geometry-reading.html

Why NotebookLM:

• It’s grounded in your sources (it answers from what you add)
• It can cite where it got the answer (use the citations to verify)
• It’s great for retrieval practice (quiz yourself fast)
• It can produce multimodal study outputs (feature-dependent): audio overview (“podcast”), study guide, concept map, slide-style summary

Caveats: Study tool only. Don’t use it to generate graded solutions. If it doesn’t cite the reading, treat it as untrusted and go back to the source.

Do this as a real break + micro-demo (2–3 min max).

Framing: - NotebookLM is for studying and review; it should not write graded solutions. - If students have the course NotebookLM, open it from the posted invite/link (Canvas/website).

Two demo prompts: - “Make 8 retrieval questions on Moon phases + eclipses. Include 2 misconception checks.” - “Where in the reading do we explain why eclipses aren’t monthly? Summarize in 3 bullets.”

More templates live in handouts/ai-tutor-study-tips.qmd.

Quick Quiz: What Causes Phases?

Moon phases are caused by:

• Earth’s shadow falling on the Moon
• The Moon passing through different parts of Earth’s atmosphere
• The geometry of viewing the Moon’s lit half from different angles
• Clouds on the Moon blocking sunlight

2–3 min. Correct: C. The Sun always lights half the Moon; we see different fractions of that lit half.

Phases Are NOT Shadows

Credit: (A. Rosen/NotebookLM)

Phases are not Earth’s shadow.

If phases were Earth’s shadow, we’d have an “almost-eclipse” basically every night.

3–5 min. Make it observational: crescent moons appear near the Sun in the sky; Earth’s shadow points away from the Sun.

The Key Insight

Credit: (A. Rosen/NotebookLM)

The Sun illuminates half of the Moon at all times.

The phase is: how much of that lit half you can see from Earth.

5–7 min. Say: “The Moon isn’t changing. Your viewing angle is changing.”

A Mental Model: Lamp + Ball

Imagine a tennis ball under one lamp:

• The lamp lights one hemisphere (always 50%).
• Walk around the ball.
• The lit fraction you can see changes smoothly.

Moon phases are this exact demo — just with the Sun as the lamp and Earth as your viewpoint.

7–8 min. Keep it simple. No diagrams yet; set up intuition.

The Earth-Moon System

Credit: Cococubed

7–8 min. Transition from the mental model to the real geometry. Point out: Earth at center, Moon’s orbit around it. The Sun is far off to one side (not shown to scale).

The Phase Cycle (Geometry Map)

Credit: Cococubed

8–10 min. Walk around the orbit: new → waxing crescent → first quarter → waxing gibbous → full → waning gibbous → third quarter → waning crescent.

Why ~29.5 Days?

Credit: (A. Rosen/NotebookLM)

Sidereal month ≈ 27.3 days (relative to the stars)
Synodic month ≈ 29.5 days (new → new)

Earth moves around the Sun, so the Sun-direction shifts during one Moon orbit.
The Moon must catch up to re-align → about 2 extra days.

Main takeaway: phases track the Sun-direction, not the background stars.

10–11 min. The “lol why 29.5?” slide. Emphasize: phases are locked to the Sun-direction, not the stars.

If you want the quantitative version (say it, don’t show it): - Moon’s orbital speed ≈ 360°/27.3 d ≈ 13.2°/day, so catching up ~27° takes ~2.1 days. - Optional compact relation: 1/P_syn = 1/P_sid − 1/P_year.

Quick Check: Where Is “First Quarter”?

At first quarter, the Moon is:

• Between Earth and the Sun
• 90° away from the Sun (as seen from Earth)
• Opposite the Sun in the sky
• In Earth’s shadow

10–11 min. Correct: B. First/third quarter corresponds to a 90° Sun–Earth–Moon angle.

“Waxing” vs “Waning” (Translation)

Waxing = getting brighter each night

Waning = getting dimmer each night

Growing/waning is about time direction, not left vs right on the Moon.

11–12 min. Students often memorize “right side lit means waxing” which fails in the southern hemisphere and confuses orientation. Emphasize time + where it is in the sky.

Moon as a Clock

Credit: (A. Rosen/NotebookLM)

If you know the time and you can estimate the phase, you can usually predict where to look.

12–14 min. Highlight the big anchor times: new near Sun; first quarter highest near sunset; full highest near midnight; third quarter highest near sunrise.

Check Yourself: Evening Crescent

You see a crescent Moon low in the western sky just after sunset. Is it waxing or waning?

• Waxing
• Waning
• Could be either
• Crescent moons are never visible at sunset

14–15 min. Correct: waxing. Waning crescent shows up pre-dawn in the east.

Check Yourself: Highest at Midnight

It’s midnight, and the Moon is highest in the sky. What phase is it?

• New Moon
• First Quarter
• Full Moon
• Third Quarter

15–16 min. Correct: full moon.

Mini-Activity: Sketch the Geometry

✏️ 60-second sketch

Draw sunlight coming from the left, Earth in the middle, and the Moon in four positions: new, first quarter, full, third quarter.

Then: for each Moon, shade the half away from the Sun and ask: what fraction of the lit half can Earth see?

When you’re done: compare with a neighbor. If your sketches disagree, decide which one has the lit half always facing the Sun.

16–18 min.

Enforcement: - 60 sec sketch (timer). - 30 sec pair-check: “Show your sketch to your neighbor.” - Cold-call 2 pairs to describe (no drawing on board needed): “Where is the Sun? Which half is lit? What do we see from Earth?”

Live Demo (3 min): Moon Phases

Open the Moon Phases demo:

astrobytes-edu.github.io/astr101-sp26/demos/moon-phases/

Do three quick checkpoints:

1. First quarter: where is Earth’s shadow?
2. Full moon: where is the Moon in the sky relative to the Sun?
3. Waning crescent: what time of day would you expect to see it?

18–21 min. Make this mandatory (tight 3 minutes).

Script: - First quarter: turn on “Show Earth’s Shadow” and ask for a quick prediction, then reveal the shadow is nowhere near the Moon. - Full: drag to full and connect to “highest at midnight.” - Waning crescent: drag there and ask “sunrise vs sunset?”

Eclipses: when shadows actually matter

Transition. “Now we earn the word ‘shadow’.”

What Is an Eclipse?

Credit: (A. Rosen/NotebookLM)

• Solar eclipse: Moon’s shadow falls on Earth (Moon between Sun and Earth)
• Lunar eclipse: Moon passes through Earth’s shadow (Earth between Sun and Moon)

20–22 min. Keep it geometrical: alignment + shadow cones (umbra/penumbra).

Quick Check: Solar Eclipse Phase

During a solar eclipse, the Moon must be at:

• Full Moon
• New Moon
• First Quarter
• Third Quarter

22–23 min. Correct: new moon. Lunar eclipse corresponds to full moon.

Why Not Every Month?

If eclipses happen at new and full moon…

…why don’t we get two eclipses every month?

Because the Moon’s orbit is tilted by about 5° relative to the ecliptic.

23–24 min. Name the ecliptic: Earth’s orbital plane (Lecture 3).

Orbital Tilt Breaks the Alignment

Credit: (A. Rosen/NotebookLM)

Most months, the Moon passes a few degrees above or below the Sun (new moon) or Earth’s shadow (full moon).

24–26 min. Emphasize: “5 degrees is enough to miss a shadow cone.”

Nodes = Eclipse Gateways

Credit: (A. Rosen/NotebookLM)

Eclipses are only possible when the Moon is near a node (where its orbit crosses the ecliptic).

26–28 min. Define node: intersection points of planes. Keep it visual.

Live Demo (2 min): Eclipse Geometry

Open the Eclipse Geometry demo:

astrobytes-edu.github.io/astr101-sp26/demos/eclipse-geometry/

Two fast tests:

1. Set tilt to 0° → new moon and full moon should always produce eclipses.
2. Restore tilt to 5.1° → eclipses only happen when the Moon is near a node.

28–30 min. This is the cleanest “why not monthly” proof students will remember.

Check Yourself: Why Eclipses Aren’t Monthly

Eclipses don’t occur every month because:

• The Moon is too small to cast a significant shadow
• The Moon’s orbit is tilted relative to Earth’s orbital plane
• Earth’s atmosphere bends the Moon’s shadow away
• The Sun is too bright during most new moons

28–29 min. Correct: B.

Sketch It: Eclipse Geometry

✏️ 90-second sketch

Draw the ecliptic as a straight line. Draw the Moon’s orbit as a tilted loop crossing the ecliptic at two nodes.

Mark new moon and full moon positions both near a node and far from a node.

Circle the cases where an eclipse is possible.

When you’re done: hold up your paper (or show your neighbor) so we can check the logic quickly.

30–32 min. Enforcement: 90 sec timer, then quick scan of the room / pair-check. Ask one student to narrate their sketch: “What has to be true at new moon for a solar eclipse?”

Eclipse Seasons (Same Geometry, Repeats)

Credit: (A. Rosen/NotebookLM)

When the Sun is lined up near a node direction, eclipses become possible for a short window: an eclipse season.

31–33 min. Conceptual only; don’t drown in timing. “Alignment windows repeat.”

Eclipse Seasons: Numbers to Anchor It

Helpful reference numbers (global):

• An eclipse season lasts about 34–35 days (≈34.5 days).
• Eclipse seasons happen about twice per year (roughly 6 months apart).
• Globally, there are about 2–5 solar eclipses per year (average ≈ 2.4).
• A single season can produce up to three eclipses (solar, lunar, solar) if the timing lines up.

33–34 min. Emphasize “global numbers” vs “what you personally see.” This sets up why eclipse chasing is a thing.

Eclipse Varieties

Credit: (A. Rosen/NotebookLM)

33–35 min. Quick tour: partial vs total; umbra vs penumbra; solar vs lunar.

Why Does the Moon Turn Red?

Credit: (A. Rosen/NotebookLM)

During a total lunar eclipse, the Moon is lit by sunlight filtered through Earth’s atmosphere.

35–37 min. Tie to Rayleigh scattering: blue scattered out, red survives and bends into the shadow.

Angular Size Decides: Total vs Annular

Recall (Lecture 3): Sun and Moon are both about 0.5° across in our sky.

But the Moon’s distance changes — so its angular size changes.

If the Moon looks bigger than the Sun → total eclipse possible.

If the Moon looks smaller than the Sun → annular eclipse (ring).

37–39 min. Keep it conceptual: angular size ∝ physical size / distance.

Check Yourself: What If the Moon Were Farther?

If the Moon were 20% farther from Earth than it is now, solar eclipses would be:

• More frequent
• Always total
• Always annular (never total)
• Exactly the same

39–40 min. Correct: always annular. Farther → smaller angular size.

One Wild Fact (Optional)

Total solar eclipses are temporary.

The Moon is slowly receding from Earth (about 3.8 cm/year).

Far in the future, the Moon will look too small to fully cover the Sun.

Optional 60 sec. Keep it as “cool preview” tied to tides/rotation later.

The Big Picture (One Slide Summary)

Phases: not shadows → changing viewing angle of the Moon’s sunlit half.

Eclipses: shadows → rare alignment + near a node.

Total vs annular: angular size (Moon distance) decides whether the Sun can be fully covered.

Wrap. Ask: “If you remember one thing: draw the geometry.”

Exit Ticket

1. During a full moon, the fraction of the Moon that is illuminated by the Sun is:

• 0%
• 50%
• 100%
• It depends on the season

2. A lunar eclipse can only happen at:

• New moon
• First quarter
• Full moon
• Any phase

Collect answers quickly. 1) pre-dawn east, 2) full moon.

Exit Ticket (Open Response)

✏️ 60 seconds: draw + explain

Draw the geometry for a lunar eclipse.

In one sentence: Why must it be full moon?

Collect a few responses out loud, or have students swap papers with a neighbor for a 10-second check.