10 minute lesson · Astronomy · Original foundation material
Before you start: Angles around a circle; Speed as distance divided by time; Relative motion.
Two motions shape the sky: Earth spins, and objects also move in their orbits. Keep the observer's changing direction separate from the Moon's changing position around Earth.
Why the sky appears to turn
Earth rotates eastward. This produces the apparent daily westward motion of the Sun and stars. Some stars circle a celestial pole without setting, so avoid claiming that every star rises and sets each day.
Earth turns once relative to distant stars in about 23 hours 56 minutes. The mean solar day is 24 hours. Earth moves along its orbit during a rotation, so it must turn a little farther for the Sun to return to the same direction.
Phases are a viewing effect
Sunlight illuminates roughly half of the Moon at a time. The phase depends on how much of that illuminated half we see. At first quarter we see about half of the visible disc illuminated, even though the name refers to one quarter of the phase cycle.
At full Moon, the Moon lies approximately opposite the Sun in our sky. It is near the meridian around local solar midnight. Ordinary phases are not Earth's shadow; Earth's shadow on the Moon produces a lunar eclipse.
Two different lunar months
The Moon takes about 27.3 days to orbit relative to the stars, but about 29.5 days to repeat a phase. Earth has moved around the Sun meanwhile, so the Moon needs extra travel to repeat the Sun–Earth–Moon geometry.
For circular, coplanar orbits in the same direction, when P < Y, relative angular speed gives 1/S = 1/P − 1/Y. P is the moon's orbital period relative to the stars, Y is the planet's year and S is the phase-cycle period; use matching time units.
A worked example
In a circular, coplanar model, a moon completes an orbit relative to the stars every 24 days. Its planet orbits its star every 360 days in the same direction. Estimate the interval between identical lunar phases.
- The moon moves 360°/24 = 15° per day relative to the stars.
- The direction to the star moves 360°/360 = 1° per day in the same sense.
- The moon gains on that direction at 15 − 1 = 14° per day.
- A repeated phase requires a 360° gain: S = 360/14 ≈ 25.7 days.
Approximately 25.7 days
Check your understanding
Why does the Moon appear to keep nearly the same face towards Earth even though it rotates?
Show the explanation
Its spin period matches its orbital period. As its position around Earth changes, it turns enough to keep approximately the same hemisphere facing Earth.