---
title: "Phases of the Moon"
book: "Primary & Middle School Physics"
subject: physics
language: en
chapter: 51
exercises: 12
source: https://one-course.com/books/physics/1/en/chapter/51-phases-of-the-moon
---

# Chapter 51 — Phases of the Moon

Years ago you kept a [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) diary and watched the silver shape march from [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) to full and back, promised the “why” for later. Later is now. You own everything the explanation needs: a [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) that [orbits](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit) monthly, sunlight in straight lines, and a sphere that is always — always — half lit.

## 51.1 The one fact underneath

**Proposition 51.1 (Half-lit, always).**

The Sun [lights](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) one half of the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) at every moment — the half facing it — exactly as it [lights](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) half the Earth. The [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) has no changing shape, no growing and shrinking: it is a stone ball wearing a permanent day side and a permanent night side, the boundary sliding as it [orbits](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit). Everything we call a “[phase](#def-g7-moon-phases-phases)” is merely the *view*: how much of the day side happens to face the Earth.

**Definition 51.2 (Phases).**

The *phases* of the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) are its apparent shapes through the month: *new moon* (day side turned fully away — we see nothing), *[crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes)*, *first quarter* (half the disc lit), *gibbous* (more than half), *[full moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes)* (day side turned fully toward us), then gibbous, *last quarter* and [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) again, closing the cycle in about $29.5$ days. From new to full the lit part grows night by night: the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) is *waxing*; from full back to new it shrinks: *waning*.

![The whole secret in one picture: eight stations of the orbiting Moon, each half-lit on its sunward side. What changes is only which slice of the day side faces the Earth.](https://one-course.com/images/onecourse/chapters/physics-1/g7-moon-phases/fig-bc41c68ea3a9.svg)

*The whole secret in one picture: eight stations of the orbiting [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon), each half-lit on its sunward side. What changes is only which slice of the day side faces the Earth.*

**Method 51.3 (Be the Earth, hold the Moon).**

The explanation, performed in one minute:

1. in a dark room, a single bare lamp is the Sun; you are the Earth; a white ball on your outstretched hand is the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) ;
2. face the lamp, ball toward it: the ball’s lit half faces away from you — you see its dark side: new moon;
3. turn slowly on the spot (the ball orbiting you): a lit sliver appears at the ball’s edge — [waxing](#def-g7-moon-phases-phases) [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) ; after a quarter turn, half the ball shows lit: first quarter;
4. keep turning: gibbous — then, lamp at your back, ball fully lit before you: [full moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) ; complete the turn through [waning](#def-g7-moon-phases-phases) half and [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) to new.

One turn of yourself replays one month of sky.

## 51.2 The misconception, retired

**Proposition 51.4 (Phases are not the Earth’s shadow).**

The most popular wrong answer in astronomy: “the [phases](#def-g7-moon-phases-phases) are the Earth’s [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) on the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon).” Geometry refutes it three ways. The Earth’s [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) points *away* from the Sun — it can only touch a [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) standing opposite the Sun, which happens solely at [full moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) (and then only at rare eclipses). A [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) stands *sunward* of us, nowhere near our [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow). And the [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow)’s edge on the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) is always part of a large circle — it could never carve the gibbous shape’s double-curved boundary. The [phases](#def-g7-moon-phases-phases) need no [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow): a half-lit ball, seen from different sides, does everything.

**Example 51.5 (Eclipse versus phase).**

Keep the two Moon-darkenings in separate drawers. *[Phase](#def-g7-moon-phases-phases)*: the slow monthly cycle, 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 own night side turning toward us — no [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) of ours involved. *[Lunar eclipse](https://one-course.com/books/physics/1/en/chapter/50-shadows-and-eclipses#def-g7-shadows-eclipses-lunar)*: a rare hour when the full [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) crosses our [umbra](https://one-course.com/books/physics/1/en/chapter/50-shadows-and-eclipses#prop-g7-shadows-eclipses-umbra) — the Earth’s [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) genuinely falling on it, coppery and swift. The diary’s rhythm is a view; the eclipse is a visit.

## 51.3 Reading the sky like a clock

**Example 51.6 (Where the phases keep their hours).**

The diagram fixes each [phase](#def-g7-moon-phases-phases) to a position — and each position to a schedule. The full [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) stands opposite the Sun: it must rise at [sunset](https://one-course.com/books/physics/1/en/chapter/4-day-and-night-the-sun#def-g1-day-and-night-daynight), reign all night, and set at [sunrise](https://one-course.com/books/physics/1/en/chapter/4-day-and-night-the-sun#def-g1-day-and-night-daynight). The new [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) travels *with* the Sun: up all day, lost in glare — which is why nobody “sees” a new moon. First quarter trails the Sun by a quarter turn: it rises near midday and sets near midnight — the after-dinner [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon). The old [daytime-Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) surprise of your childhood is now a timetable: any [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) not new nor full shares part of its shift with the Sun.

**Example 51.7 (Which way does the crescent point?).**

The lit side of any [phase](#def-g7-moon-phases-phases) faces the Sun — the [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) is a bow aimed at its archer. Evening [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) in the west: horns pointing up-and-away from the [sunset](https://one-course.com/books/physics/1/en/chapter/4-day-and-night-the-sun#def-g1-day-and-night-daynight) glow beneath the horizon. The sky never draws it wrong; painters often do. A [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) with its horns toward the Sun is astronomy’s favorite spot-the-error.

**Remark 51.8 (The face that never turns away).**

One more diary observation, finally honored: 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 dark patches form the same face every night, [phase](#def-g7-moon-phases-phases) after [phase](#def-g7-moon-phases-phases), year after year. The [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) turns exactly once on its [axis](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit) per [orbit](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit) — so the same half faces the Earth forever. No one saw the far side until a space probe flew around with a camera within living memory of your grandparents. Why the turning and the orbiting agree so perfectly is a deep story of tides, kept for the university years of this course.

## 51.4 Exercises

**Exercise 51.1 ★.**

What fraction of the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) is sunlit at any moment? What, then, is a “[phase](#def-g7-moon-phases-phases)”?

**Solution of Exercise 51.1.**

Exactly half, always — the sunward half. A [phase](#def-g7-moon-phases-phases) is only the view: the fraction of that lit half which happens to face the Earth.

**Exercise 51.2 ★.**

Recite the [phases](#def-g7-moon-phases-phases) in order from new moon, and give the cycle’s length. Which half of the cycle is “[waxing](#def-g7-moon-phases-phases)”?

**Solution of Exercise 51.2.**

New, [waxing](#def-g7-moon-phases-phases) [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes), first quarter, [waxing](#def-g7-moon-phases-phases) gibbous, full, [waning](#def-g7-moon-phases-phases) gibbous, last quarter, [waning](#def-g7-moon-phases-phases) [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) — about $29.5$ days around. [Waxing](#def-g7-moon-phases-phases) is the growing half, from new to full.

**Exercise 51.3 ★.**

In the orbit-walk method, where are lamp, ball and you at new moon? At [full moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes)?

**Solution of Exercise 51.3.**

New moon: you face the lamp with the ball toward it — its lit half turned away from you. [Full moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes): lamp at your back, ball before you — its lit half turned fully toward you.

**Exercise 51.4 ★.**

Give two of the three geometric refutations of “the [phases](#def-g7-moon-phases-phases) are the Earth’s [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow)”.

**Solution of Exercise 51.4.**

Any two: the Earth’s [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) points away from the Sun and could only reach a [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) at full position; a [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) stands sunward of us, nowhere near that [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow); and a round [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow)’s edge could never carve the gibbous double curve.

**Exercise 51.5 ★.**

What is the difference between the new moon’s darkness and a [lunar eclipse](https://one-course.com/books/physics/1/en/chapter/50-shadows-and-eclipses#def-g7-shadows-eclipses-lunar)’s darkness?

**Solution of Exercise 51.5.**

The new moon is dark to us because its *own* night side faces us — no [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) of ours involved, and the far side is in full sunshine. The [lunar eclipse](https://one-course.com/books/physics/1/en/chapter/50-shadows-and-eclipses#def-g7-shadows-eclipses-lunar) is the full [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) crossing the Earth’s real [umbra](https://one-course.com/books/physics/1/en/chapter/50-shadows-and-eclipses#prop-g7-shadows-eclipses-umbra): our [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) genuinely falling on it, briefly.

**Exercise 51.6 ★.**

Why does the full [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) always rise near [sunset](https://one-course.com/books/physics/1/en/chapter/4-day-and-night-the-sun#def-g1-day-and-night-daynight)? Argue from its position in the diagram.

**Solution of Exercise 51.6.**

The full [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) stands opposite the Sun. As the spinning Earth carries the Sun down below the western horizon, the opposite point of the sky — where the full [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) waits — must be rising in the east: [sunset](https://one-course.com/books/physics/1/en/chapter/4-day-and-night-the-sun#def-g1-day-and-night-daynight) and full-moonrise are one event seen both ways.

**Exercise 51.7 ★.**

Why does nobody ever “see the new moon rise at midnight”? Where is the new moon at midnight?

**Solution of Exercise 51.7.**

The new moon travels with the Sun: at midnight both stand under your feet, on the far side of the Earth. A new moon at midnight is as impossible as the Sun at midnight.

**Exercise 51.8 ★.**

An evening [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) hangs in the west. Which way do its horns point relative to the vanished Sun — and why can a [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) never aim its horns at the Sun?

**Solution of Exercise 51.8.**

Away from the [sunset](https://one-course.com/books/physics/1/en/chapter/4-day-and-night-the-sun#def-g1-day-and-night-daynight) point — the [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes)’s bow bends toward the Sun, horns away. The lit side must face the Sun, and the horns are the lit side’s retreating edges: geometry forbids them to aim sunward.

**Exercise 51.9 ★★.**

Tonight the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) is [waxing](#def-g7-moon-phases-phases) gibbous. Where in its [orbit](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit) does it stand? Roughly when did it rise, and what [phase](#def-g7-moon-phases-phases) — and what schedule — comes five nights later?

**Solution of Exercise 51.9.**

Between first quarter and full — about three-eighths of the way around, on the evening side. It rose mid-afternoon. Five nights later: [full moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) — rising at [sunset](https://one-course.com/books/physics/1/en/chapter/4-day-and-night-the-sun#def-g1-day-and-night-daynight), up all night.

**Exercise 51.10 ★★.**

A [solar eclipse](https://one-course.com/books/physics/1/en/chapter/50-shadows-and-eclipses#def-g7-shadows-eclipses-solar) can only happen at one [phase](#def-g7-moon-phases-phases), a [lunar eclipse](https://one-course.com/books/physics/1/en/chapter/50-shadows-and-eclipses#def-g7-shadows-eclipses-lunar) only at another. Name both, justify with the alignment geometry, and explain why eclipses are nevertheless rare at those [phases](#def-g7-moon-phases-phases).

**Solution of Exercise 51.10.**

[Solar eclipse](https://one-course.com/books/physics/1/en/chapter/50-shadows-and-eclipses#def-g7-shadows-eclipses-solar): only at new moon — Sun–Moon–Earth in line. Lunar: only at [full moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) — Sun–Earth–Moon in line. Rare even then, because 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 tilted [orbit](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit) usually carries it above or below the exact line: [phase](#def-g7-moon-phases-phases) is necessary, alignment is not guaranteed.

**Exercise 51.11 ★★.**

Astronauts on the near side of the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) look up at the Earth. Describe what “[Earth-phases](#def-g7-moon-phases-phases)” they see through a month, and what [phase](#def-g7-moon-phases-phases) the Earth shows them when we see a new moon. (Run the geometry both ways.)

**Solution of Exercise 51.11.**

The Earth shows [phases](#def-g7-moon-phases-phases) opposite to ours, on the same clock: when we see new moon, the lunar astronauts see a *full Earth* — our whole daylit side facing them; at our [full moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) they see a new Earth. One geometry, read from the other chair.

**Exercise 51.12 ★★★.**

The old [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes)’s secret: on clear evenings, the [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon)’s *dark* part glows faintly — “the old moon in the new moon’s arms”. Your grade-two self met this as a riddle; solve it now completely: trace the [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)’s path, explain why earthshine is brightest precisely at [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) [phases](#def-g7-moon-phases-phases) (what [phase](#def-g7-moon-phases-phases) does the *Earth* show the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) then?), and why it fades toward [full moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes).

**Solution of Exercise 51.12.**

Path: sunlight strikes the Earth, the bright Earth diffuses it moonward, 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 night side diffuses a little back to our eyes — sunlight twice forwarded. At our [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) [phases](#def-g7-moon-phases-phases) the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) sees a nearly *full Earth* (the [opposite-phase](#def-g7-moon-phases-phases) rule): the night side is floodlit by the brightest Earth possible — strongest earthshine. Toward our [full moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) sees a thin [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) Earth: the floodlight dwindles, and [full-phase](#def-g7-moon-phases-phases) glare drowns what remains.

## 51.5 Problem: A Month with the Moon

**Problem 51.1.**

Weekend problem — the observatory’s open month; thirty nights of Moon, one wall-chart; the docent’s quiz

The town observatory runs a public “Month with the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon)”. As junior docent, you keep the wall-chart and answer the visitors.

**Part I — Setting up the chart.**

1. Night 0 is new moon. Fill the chart’s milestones: on about which nights fall first quarter, [full moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) , and last quarter?
2. Beside each milestone, the chart wants rise-times. Match: rises at [sunset](https://one-course.com/books/physics/1/en/chapter/4-day-and-night-the-sun#def-g1-day-and-night-daynight) ; rises near midday; rises near midnight; rises and sets with the Sun.
3. A visitor asks why the chart shows the [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) low in the *western* evening sky but the [full moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) climbing from the *east* at dusk. Explain with [orbit](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit) positions.
4. Another visitor swears they saw the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) at ten in the morning. Which chart [phases](#def-g7-moon-phases-phases) make a morning [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) possible?

**Part II — The docent’s demonstrations.**

5. You perform the lamp-and-ball walk for a school group. A pupil [freezes](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) you mid-turn: the ball shows three-quarters lit. Name the [phase](#def-g7-moon-phases-phases) , and locate lamp, Earth-you and ball for the group.
6. “So the Earth’s [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) makes the [phases](#def-g7-moon-phases-phases) ?” asks the pupil, pointing at your dark-sided ball. Give the demonstration’s own refutation: whose night side are they seeing, and where would the Earth’s [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) actually be?
7. The group asks why they always see “the rabbit” (or “the face”) in the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) , never its back. Answer with the same-face fact.
8. A skeptical parent: “If the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) spins, as you claim, shouldn’t we see it turn?” Resolve the apparent contradiction: how can the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) spin exactly once per [orbit](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit) and thereby *hide* its spin from us?

**Part III — Quiz night.**

9. Quiz card A: “Tonight’s [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) rose at midnight and shows its *left* half lit (as seen going toward morning). [Waxing](#def-g7-moon-phases-phases) or [waning](#def-g7-moon-phases-phases) — and which quarter?”
10. Quiz card B: “An artist’s poster shows a [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) at midnight, high overhead, horns pointing straight down at the [sunset](https://one-course.com/books/physics/1/en/chapter/4-day-and-night-the-sun#def-g1-day-and-night-daynight) colors on the horizon.” List every astronomical error on the poster.
11. Quiz card C: “During tonight’s [full moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) , could visitors also witness a [solar eclipse](https://one-course.com/books/physics/1/en/chapter/50-shadows-and-eclipses#def-g7-shadows-eclipses-solar) somewhere on Earth?” Settle it with [phase](#def-g7-moon-phases-phases) geometry.
12. Closing speech: in three sentences, give the month’s one underlying fact, the misconception the month buried, and the schedule trick visitors should carry home (what any [phase](#def-g7-moon-phases-phases) tells about its rising hour).

**Solution of Problem 51.1.**

**1.** First quarter near night $7$; [full moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) near night $15$; last quarter near night $22$ (the cycle closing near night $29$–$30$). **2.** [Full moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes): rises at [sunset](https://one-course.com/books/physics/1/en/chapter/4-day-and-night-the-sun#def-g1-day-and-night-daynight). First quarter: rises near midday. Last quarter: rises near midnight. New moon: rises and sets with the Sun. **3.** The young [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) stands only a little behind the Sun on the [orbit](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit): it hangs in the west after [sunset](https://one-course.com/books/physics/1/en/chapter/4-day-and-night-the-sun#def-g1-day-and-night-daynight) and soon follows the Sun down. The [full moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) stands opposite: as the Sun sets in the west, opposite means rising in the east. **4.** Any [phase](#def-g7-moon-phases-phases) sharing part of the Sun’s shift: the [waxing](#def-g7-moon-phases-phases) gibbous through afternoon, and above all the [waning](#def-g7-moon-phases-phases) [phases](#def-g7-moon-phases-phases) — last quarter and [waning](#def-g7-moon-phases-phases) [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) ride high in morning skies. **5.** [Waxing](#def-g7-moon-phases-phases) gibbous: the ball three-quarters lit means you stand between first quarter and full — lamp behind your shoulder, ball ahead and to the side. **6.** They are seeing the ball’s *own* night side — the half turned from the lamp. The Earth-you casts a [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) too, but it stretches behind you, away from the lamp; the ball is nowhere in it except at the full-moon position — and then only if exactly aligned: an eclipse, not a [phase](#def-g7-moon-phases-phases). **7.** The [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) turns exactly once per [orbit](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit), so the same half faces the Earth forever — rabbit, face and all; the far side waited for a camera to fly around. **8.** Spin and [orbit](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit) keep perfect step: as the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) advances along its path, it turns just enough to keep the same face pointed at us — like a dancer circling a partner while always facing them: truly spinning (the room sees every side), yet showing the partner one face only. **9.** Rising at midnight is the last-quarter schedule — the [waning](#def-g7-moon-phases-phases) side: last quarter (the lit half faces the morning Sun’s direction). **10.** Errors: a [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) stands near the Sun, so it can never ride high at midnight; horns point *away* from the Sun, never at it; and [sunset](https://one-course.com/books/physics/1/en/chapter/4-day-and-night-the-sun#def-g1-day-and-night-daynight) colors at midnight are their own impossibility. Three strikes. **11.** No: a [solar eclipse](https://one-course.com/books/physics/1/en/chapter/50-shadows-and-eclipses#def-g7-shadows-eclipses-solar) requires the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) between Sun and Earth — the new-moon position. Tonight’s [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 full, on the opposite side: the two events cannot share a night. **12.** For example: “One fact runs the month: the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) is always half lit, and we circle-watch that half from changing sides. Buried this month: the Earth’s [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) has nothing to do with [phases](#def-g7-moon-phases-phases) — it visits only at rare eclipses. And take the clock home: every [phase](#def-g7-moon-phases-phases) keeps its own rising hour — full at [sunset](https://one-course.com/books/physics/1/en/chapter/4-day-and-night-the-sun#def-g1-day-and-night-daynight), quarters at midday and midnight — so 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 shape tells you its schedule.”