Know that it takes approximately one month for the Moon to orbit the Earth and use this to explain the periodic nature of the Moon's cycle of phases

Published by Patrick Mutisya · 14 days ago

IGCSE Physics 0625 – The Earth and Moon

6.1.1 The Earth

Key Fact: Lunar Orbital Period

The Moon completes one orbit around the Earth in about 27.3 days (sidereal month). Because the Earth‑Moon system also moves around the Sun, the time between identical phases (the synodic month) is about 29.5 days, which we usually refer to as “one month”.

Why the Moon’s Phases are Periodic

The appearance of the Moon from Earth depends on the relative positions of the Sun, Earth and Moon. As the Moon travels around the Earth, the illuminated portion that we can see changes in a regular, repeating pattern.

\$\$

\text{Phase angle } \theta = \omega t

\$\$

where \$ \omega = \frac{2\pi}{T} \$ is the angular speed and \$ T \approx 29.5\text{ days} \$ is the synodic period.

Sequence of Phases

PhasePosition relative to SunIlluminated fraction
New MoonMoon between Earth and Sun0 %
Waxing CrescentMoon moves eastward0 % → 50 %
First QuarterMoon 90° east of Sun≈50 %
Waxing GibbousMoon approaching full50 % → 100 %
Full MoonEarth between Sun and Moon100 %
Waning GibbousMoon moving away from full100 % → 50 %
Last QuarterMoon 90° west of Sun≈50 %
Waning CrescentMoon about to become new50 % → 0 %

Linking the Orbital Period to the Phase Cycle

  1. Each day the Moon travels about \$360^\circ / 29.5 \approx 12.2^\circ\$ around Earth.

  2. Because the Sun‑Earth line also moves, the angle between the Sun and Moon as seen from Earth changes by roughly the same amount each day.

  3. After one synodic month (≈ 29.5 days) the Moon returns to the same position relative to the Sun, so the same phase repeats.

Common Misconceptions

  • The Moon is lit by Earth’s reflected light – the Moon’s brightness comes directly from sunlight; Earthshine is only a faint glow visible during a thin crescent.

  • The Moon rises at the same time each night – because the Moon moves eastward about 12° per day, it rises roughly 50 minutes later each successive night.

Suggested diagram: A side view showing the Sun, Earth, and Moon at the eight principal phases, with arrows indicating the Moon’s orbital direction and the relative illumination.

Quick Check Questions

  1. How many days does it take for the Moon to complete one synodic month?

  2. Why does the Moon rise later each night?

  3. If the Moon were stationary relative to Earth, what would happen to the observed phases?