General Structure of the Solar System
Senior 4 · Physics
General Structure of the Solar System
Lesson 2 of 4
25 min
Look for the Moon just after sunset on a few evenings in a row. On the first evening it may be a thin crescent low in the west; a week later it is half lit and high overhead at sunset; a week after that a full, round Moon rises in the east as the Sun sets. Then it rises later and later each night, shrinking again. Twice in a while something more dramatic happens: the full Moon slowly turns dark red, as it did across Africa, Europe, Asia and Australia for 1 hour and 22 minutes on 7 September 2025 (NASA), or, far more rarely at any one place, the Sun itself goes dark in the middle of the day. All of this comes from three bodies, the Sun, the Earth and the Moon, moving in simple ways. This lesson explains the phases of the Moon and the two kinds of eclipse.
The Moon gives no light of its own; we see it by reflected sunlight. At every moment the half of the Moon facing the Sun is lit and the other half is dark. As the Moon goes round the Earth, we see different amounts of its lit half (Figure 2.1):
The phases are not caused by the Earth's shadow; that happens only in an eclipse. From Rwanda, close to the equator, the Moon's path across the sky is steep, so a thin evening crescent often looks like a bowl: its lit side faces down towards the Sun, which has just set below the western horizon.
Figure 2.1: The phases of the Moon. The lit half always faces the Sun; the phase depends on how much of that half faces the Earth.
Definition
The phases of the Moon are the changing shapes of its lit part as seen from Earth, caused by the changing angle between the Sun, the Earth and the Moon. The sidereal month, 27.32 days, is the time the Moon takes to go once round the Earth relative to the stars; the synodic month, 29.53 days, is the time from one new moon to the next (NASA). Example: a first-quarter Moon is half lit and appears 90° east of the Sun, so it is highest in the sky at about sunset.
Worked example 1: why a lunar month is longer than an orbit
While the Moon goes round the Earth once (27.32 days), the Earth moves about a twelfth of the way round the Sun, so the Moon must travel a little further to line up with the Sun again. Show that the synodic month satisfies , where days and days, and find .
The Moon gains on the Sun's direction at a rate equal to the difference of the two angular speeds, . It must gain a full to return to the same phase, so
The same idea gives the daily delay of moonrise: the Moon falls behind the Sun by one full day in 29.53 days, so it rises on average minutes later each day.
An eclipse happens when the Sun, the Earth and the Moon lie in a straight line, so that one body's shadow falls on another. Because the Sun is not a point, each shadow has two parts: a dark central cone, the umbra, from which the Sun is completely hidden, and a lighter penumbra around it, from which it is partly hidden (Figure 2.2).
A solar eclipse happens at new moon, when the Moon passes between the Sun and the Earth. Where the Moon's umbra touches the Earth, a path usually less than a few hundred kilometres wide, the eclipse is total: the sky darkens and the Sun's faint outer atmosphere, the corona, appears. In the much wider penumbra the eclipse is partial. If the Moon is near the far point of its orbit, it looks slightly smaller than the Sun and its umbra does not reach the Earth; a ring of Sun stays visible round it, an annular eclipse.
A lunar eclipse happens at full moon, when the Moon passes into the Earth's shadow. It can be seen from the whole night side of the Earth at once. In a total lunar eclipse the Moon does not vanish but turns a coppery red: sunlight passing through the Earth's atmosphere is bent into the shadow, and the blue part is scattered away on the way, as at sunset.
Figure 2.2: The geometry of solar and lunar eclipses, with the umbra and penumbra of each shadow.
Why is there not an eclipse every month? The Moon's orbit is tilted by about to the plane of the Earth's orbit (NASA). Usually the new moon passes a little above or below the Sun and the full moon a little above or below the Earth's shadow. Eclipses happen only when a new or full moon falls near one of the two points where the Moon's orbit crosses the Earth's orbital plane, which occurs in "eclipse seasons" about six months apart.
Definition
The umbra is the region of total shadow, where the whole of the light source is hidden; the penumbra is the region of partial shadow, where only part of it is hidden. A solar eclipse occurs when the Moon's shadow falls on the Earth (only at new moon); a lunar eclipse occurs when the Moon enters the Earth's shadow (only at full moon). Example: an observer in the Moon's umbra sees a total solar eclipse; an observer in its penumbra, a few hundred kilometres away, sees a partial one.
Worked example 2: total or annular?
The Moon (diameter 3475 km) ranges between 363 300 km and 405 500 km from the Earth (NASA), and the Sun (diameter km) between and km. Compare their angular sizes and decide when a central eclipse is total.
When the Moon is near its closest, it looks larger than the Sun and can cover it completely: a total eclipse. When it is near its farthest, it is always smaller than the Sun, and a central eclipse is annular.
Worked example 3: how long is the Moon's shadow?
By similar triangles, the umbra of a sphere of radius lit by a Sun of radius at distance has length . Using , (Moon) and (Sun), find and compare it with the Earth–Moon distance.
The umbra is about 375 000 km long, almost exactly the Earth–Moon distance. Sometimes its tip just reaches the Earth's surface, giving a narrow path of totality; sometimes it falls short, giving an annular eclipse. That is why total solar eclipses are rare at any one place.
Warning
Safety and common mistakes. (1) Never look at the Sun directly or through binoculars, a camera or a telescope, even during a partial eclipse: it can permanently damage the eyes. Ordinary sunglasses, however dark, are not safe. Use eclipse glasses meeting the ISO 12312-2 standard, or project an image of the Sun through a pinhole in a card onto a surface, with your back to the Sun (NASA). Only during totality itself is it safe to look without protection. (2) The phases are not caused by the Earth's shadow. (3) A lunar eclipse needs a full moon and a solar eclipse a new moon, but most full and new moons give no eclipse, because of the tilt.
Tip
Ask where the Sun is. The lit side of the Moon always points to the Sun. Full moon: Sun behind you, Moon opposite, rising at sunset. New moon: Moon next to the Sun. Eclipses: everything in a straight line, solar at new moon, lunar at full moon.
Eclipses: Crash Course Astronomy #5, presented by Phil Plait. Watch how the umbra and penumbra of the Moon and the Earth produce total, partial and annular solar eclipses and lunar eclipses, and why the Moon's tilted orbit makes them rare.
Practice
Key points
Sources and credits
Written by Ganzaa: the lesson text, derivations, diagrams, worked examples and practice exercises.
Quick check
Put the phases in the order they appear after a new moon.
Tap the cards in the right order.
