Moon phases and eclipses

The Moon never changes shape. Half of it is always lit by the Sun; what changes is how much of that lit half faces you. Once you see why, eclipses stop being mysterious and start being predictable.

Half of the Moon is always in sunlight. The phases are just our point of view.

Look

The Moon does not make its own light. It shines because sunlight falls on it. At any moment, one half of the Moon is lit by the Sun and the other half is dark, just like Earth has day and night.

As the Moon goes around Earth, we see different amounts of its sunlit half:

• New Moon: the Moon is between Earth and the Sun. The lit half faces away from us, so we cannot see it.
• First quarter: we see half of the disc lit.
• Full Moon: Earth is between the Sun and the Moon. We see the whole lit half.
• Last quarter: half lit again, the other side.

In the tool, the left picture looks down on Earth and the Moon from far above, with the Sun off to the left. The right picture shows what you see from Earth. Move the slider and watch both change together.

Sometimes the Sun, Earth and Moon line up exactly:

• A solar eclipse happens when the Moon’s shadow falls on Earth at new Moon.
• A lunar eclipse happens when Earth’s shadow falls on the Moon at full Moon.

Understand

The Moon goes once around Earth, measured against the stars, in 27.3 days (the sidereal month). But the phases repeat every 29.5 days (the synodic month). Why the difference? While the Moon goes around Earth, Earth moves about 1/12 of the way around the Sun. The Moon needs about two more days to catch up with the new Sun direction.

The fraction of the disc that looks lit depends on the angle between the Sun and the Moon as seen from Earth, called the elongation:

Elongation	Phase	Lit fraction
0°	New Moon	0%
90°	First quarter	50%
180°	Full Moon	100%
270°	Last quarter	50%

If the Moon went around exactly in the same plane as Earth goes around the Sun, we would get a solar eclipse every new Moon and a lunar eclipse every full Moon. But the Moon’s orbit is tilted by about 5.1 degrees. Usually the Moon passes a little above or below the Sun-Earth line, and nothing happens.

The two points where the Moon’s orbit crosses Earth’s orbital plane are called nodes. Eclipses can only happen when a new or full Moon falls close to a node. This happens in two “eclipse seasons” each year, about six months apart.

Master

The illuminated fraction k follows from the phase angle i (the Sun-Moon-Earth angle):

k = (1 + cos i) / 2

Because the Sun is about 390 times farther away than the Moon, i ≈ 180° − elongation. The tool computes i with Meeus’s series (Astronomical Algorithms, eq. 48.4), which corrects the mean elongation for the main periodic terms of the Moon’s and the Sun’s orbits. It places new and full Moons to within about half an hour of the precise times, plenty for learning.

The synodic month follows from the two angular speeds: 1/P_syn = 1/P_sid − 1/P_year = 1/27.3217 − 1/365.256, giving 29.531 days.

Whether an eclipse is possible depends on the Moon’s argument of latitude F, its angle from the ascending node. Meeus gives a quick screening rule: at a new or full Moon, if |sin F| > 0.36 (F more than about 21° from a node), there is no eclipse. The tool applies exactly this test. It is a necessary condition, not a prediction of the eclipse type or where it is visible: that needs the Moon’s distance, Earth’s shadow geometry and much more precise positions.

The nodes are not fixed. They drift backwards around the ecliptic once every 18.6 years, which is why eclipse seasons arrive about 19 days earlier each year, and part of why eclipses repeat in the famous 18-year saros cycle.