Earth’s and Moon’s Orbits

Finding the Moon and understanding its cycles.

Where’s the Moon?

Until two weeks ago, I never knew where to expect to see the Moon. Twelve minutes and fifteen seconds and two YouTube videos (Moon phases explained and Explaining The Moon Phases) later, I know where to look. The answer relies on an observation and an abstraction:

1. Everything rotates anticlockwise as viewed from above the North Pole: the Earth’s orbit of the Sun, the Earth’s rotation, and the Moon’s orbit of the Earth are all anticlockwise. This likely goes back to the rotation of the swirling disk accreted into the Solar System.
2. To a first approximation, we can think of both the Sun and Moon as fixed in the sky, and focus just on Earth’s rotation to understand when we see them.

The key is to know where in the sky the Moon sits relative to the Sun. If the Moon and Sun are aligned, they will rise and set together and move from East to West in the sky. But, you won’t see the Moon because its illuminated side faces away from Earth! This is called a New Moon.

Falling behind the Sun today means catching up to it tomorrow

To see what happens after a New Moon, you need a second-order effect.

3. The Moon rotates around the Earth every 27.3 days.

Remember, the Moon orbits anticlockwise. If on day 1 it is aligned with the Sun (New Moon), on day 2 it will lag slightly behind—it will rise and set a little later than the Sun, and it brackets dusk. A week later, it’s about 90° behind the Sun (First Quarter), and after two weeks it’s directly opposite: a Full Moon, rising at sunset and setting at sunrise.

After the Full Moon, the Moon keeps moving anticlockwise, so it goes past the 180° mark and starts catching up with the Sun from the other side. It moves away from the sun until 180°, goes round the back of the Earth, and then moves towards the sun. Now, it rises before the Sun and sets before the Sun, and it brackets dawn. It is ahead of the Sun in the sky—just as London is ahead of New York in time.

Although the Moon always moves at the same orbital speed, its position relative to the Sun changes in a cycle. In the first half of the cycle (New to Full), it lags behind the Sun—it rises and sets later each day. After the Full Moon, it keeps going in the same direction but begins to close the angular gap. It rises earlier and earlier, gaining on the Sun from the east. By the next New Moon, they’re aligned again, and the cycle restarts.

In a nutshell, losing time relative to today (rising later each day) means gaining time on tomorrow (getting closer to tomorrow’s sunrise).

Synodic rotation period

After 27.3217 days, the Moon is back to the same position in the sky relative to the stars. However, since the Earth has moved around the Sun, it won’t be back aligned with the Sun, it will be ahead. Thinking about the time the Moon needs to rotate 365.25 / 27.3217 degrees, and adding it, and then the time to move that distance, and summing the geometric series, shows that the Moon will again be exactly aligned with the Sun after \[ \dfrac{27.3217}{1 - \dfrac{27.3217}{365.25}} = \dfrac{1}{\dfrac{1}{27.3217} - \dfrac{1}{365.25}} = 29.5306 \] days.

Putting this information together makes sense of Table 1, Table 2, and Table 3.

Table 1: Location of the Moon by lunar phase.

Phase	Moonrise	Moonset	Visible Time	Position in Sky
New Moon	~Sunrise	~Sunset	Not visible (near Sun)	Near Sun, invisible
Waxing Crescent	Mid-morning	Evening	Early evening	Low in western sky
First Quarter	Around noon	Around midnight	Afternoon to evening	High in southern sky
Waxing Gibbous	Mid-afternoon	Early morning	Late afternoon to night	East to south at night
Full Moon	Sunset	Sunrise	All night	High around midnight
Waning Gibbous	Early evening	Mid-morning	Late night to morning	West in morning sky
Last Quarter	Around midnight	Around noon	Late night to early morning	High in southern sky before dawn
Waning Crescent	Early morning	Mid-afternoon	Pre-dawn	Low in eastern sky

Table 2: Sunrise and Sunset by season.

Season	Sunrise	Sunset	Notes
Winter (21 Dec)	~08:00	~16:00	Shortest daylight
Spring (21 Mar)	~06:00	~18:00	Equinox (12h day, 12h night)
Summer (21 Jun)	~04:45	~21:20	Longest daylight
Autumn (23 Sep)	~06:50	~18:50	Equinox (day = night)

Table 3: Moon rise and set by phase and season.

Phase	Moon–Sun Angle	Winter	Spring	Summer	Autumn	Position Notes
New Moon	0°	08:00–16:00	06:00–18:00	04:45–21:20	06:50–18:50	Near Sun, not visible
Waxing Crescent	~45° behind	10:30–18:30	08:30–20:30	07:15–23:15	09:20–21:20	Low W after sunset
First Quarter	90° behind	12:00–00:00	12:00–00:00	12:00–00:00	12:00–00:00	South at sunset
Waxing Gibbous	~135° behind	14:30–02:30	15:00–03:00	16:00–04:00	14:30–02:30	Rises before sunset in E
Full Moon	180°	16:00–08:00	18:00–06:00	21:20–04:45	18:50–06:50	High at midnight
Waning Gibbous	~135° ahead	18:30–10:30	21:00–09:00	23:45–10:00	21:20–09:20	Sets in W after sunrise
Last Quarter	90° ahead	00:00–12:00	00:00–12:00	00:00–12:00	00:00–12:00	South before sunrise
Waning Crescent	~45° ahead	03:30–15:30	03:30–15:30	03:30–15:30	03:30–15:30	Low E before sunrise