Solar Eclipse
A solar eclipse occurs when the Moon passes directly between Earth and the Sun, casting a shadow on Earth's surface. Because the Moon's apparent angular size is remarkably close to the Sun's, the Moon can either completely (total), partially, or annularly cover the solar disc — producing one of nature's most spectacular phenomena.
How a Solar Eclipse Occurs
The Moon orbits Earth at an average distance of 384,400 km. The Sun is about 400× farther away but also 400× larger, making their apparent angular diameters nearly identical (~0.5°). A solar eclipse can only happen at New Moon — when the Moon is between Earth and the Sun — but the Moon's orbital plane is tilted 5.1° relative to the ecliptic, so eclipses only happen when the Moon is near one of its orbital nodes.
The Shadow System
| Shadow Region | Description | Eclipse Seen | Area on Earth |
|---|---|---|---|
| Umbra | Full shadow cone — no direct sunlight | Total solar eclipse | ~100–270 km wide |
| Penumbra | Partial shadow — some sunlight blocked | Partial solar eclipse | Thousands of km |
| Antumbra | Beyond the umbra tip — Moon appears smaller | Annular solar eclipse | ~150 km path |
Types of Solar Eclipse
Moon's umbra reaches Earth. Sun is completely covered. The solar corona becomes visible. Totality lasts up to 7 min 32 s. Path of totality is narrow (~100–270 km).
Only the penumbra falls on an observer. The Sun appears as a crescent. Seen across a wide region around the totality path. No corona is visible.
Moon is near apogee — too small to cover Sun fully. A bright "ring of fire" surrounds the Moon. Occurs when Moon's angular diameter < Sun's.
Transitions between total and annular along the path. Rare — happens because Earth's curvature changes the observer's distance to the Moon's shadow tip.
Key Formulas
Solved Examples
Example 1 — Angular Diameter of the Moon
The Moon has radius r = 1,737 km and is at distance d = 384,400 km. Calculate its angular diameter.
Solution:
θ = 2 × arctan(1737 / 384400) = 2 × arctan(0.004519)
= 2 × 0.2590° = 0.518°
The Sun's angular diameter: 2 × arctan(696,000 / 149,600,000) = 2 × 0.2666° = 0.533°
Both are very close — this remarkable coincidence enables total eclipses.
Example 2 — Length of the Moon's Umbra
Given rSun = 696,000 km, rMoon = 1,737 km, Sun–Moon distance = 149,216,000 km at a given time.
Solution:
L = rMoon × dSun–Moon / (rSun − rMoon)
L = 1737 × 149,216,000 / (696,000 − 1737)
L = 1737 × 149,216,000 / 694,263
L ≈ 373,200 km
Since the Earth–Moon distance is ≈384,400 km > 373,200 km, the umbra does NOT reach Earth → annular eclipse!
Example 3 — Duration of Totality
The path width of totality is 150 km. The Moon's shadow moves at ~0.5 km/s relative to Earth's surface. Find the duration of totality for a stationary observer in the center of the path.
Solution:
Duration = path width / shadow speed
= 150 km / 0.5 km·s⁻¹ = 300 s = 5 minutes
Maximum theoretical totality is ~7 min 32 s (at minimum Moon distance, maximum Sun distance, at equator).
Practice Questions
- Why do solar eclipses not occur every New Moon? Explain using orbital inclination.
- The Moon is at perigee (356,500 km). Calculate its angular diameter and determine whether a total or annular eclipse would result.
- A total solar eclipse has a path width of 200 km. If the shadow speed is 0.48 km/s, how long does totality last?
- Explain why the Saros cycle (18 yr 11 d) allows eclipse prediction, using the synodic and draconic months.
- During an annular eclipse, the Moon's angular diameter is 0.493°. Compare this to the Sun's 0.533° and calculate the fraction of solar disc that is blocked.
- Why does the solar corona become visible only during totality and not during partial or annular eclipses?
Frequently Asked Questions
What is a solar eclipse?
A solar eclipse occurs when the Moon passes between Earth and the Sun, casting a shadow on Earth's surface. Depending on the alignment and the Moon's distance, observers may see a total, partial, or annular eclipse. Solar eclipses can only happen at New Moon when the Moon is near one of its orbital nodes.
Why don't solar eclipses happen every month?
The Moon's orbital plane is tilted 5.1° relative to Earth's orbital plane (the ecliptic). This means that at most New Moons, the Moon passes either above or below the Sun as seen from Earth and no eclipse occurs. Eclipses only happen when New Moon coincides with the Moon being near an orbital node — the intersection of the two planes — which happens roughly twice per year.
What is the difference between a total and annular eclipse?
In a total eclipse, the Moon is close enough (near perigee) that its apparent angular diameter exceeds the Sun's, so it completely covers the solar disc and the umbra reaches Earth's surface. In an annular eclipse, the Moon is near apogee and appears smaller than the Sun, so a ring (annulus) of sunlight remains visible — the umbra's tip falls short of Earth and only the antumbra reaches the surface.
What is the umbra and penumbra?
The umbra is the darkest, central part of the Moon's shadow where all direct sunlight is blocked. Observers in the umbra experience totality. The penumbra is the outer, partial shadow region where only part of the Sun's disc is blocked by the Moon. Observers in the penumbra see a partial eclipse. The antumbra is the region beyond the umbra's tip where the Moon appears smaller than the Sun — observers here see an annular eclipse.
Why can we see the solar corona during a total eclipse?
The solar corona is the Sun's outer atmosphere, extending millions of kilometres into space. It emits only about one-millionth of the photospheric brightness, so it is invisible in normal daylight. During totality, when the photosphere is completely blocked by the Moon, the sky darkens enough for the faint corona to become visible to the naked eye — appearing as a pearly white halo around the Moon's silhouette.
What is the Saros cycle?
The Saros cycle is a period of approximately 18 years, 11 days, and 8 hours (6,585.3 days) after which the Sun, Earth, and Moon return to nearly the same geometric configuration. This means that eclipses repeat in families — each eclipse in a Saros series is followed 18+ years later by a very similar eclipse. The cycle was known to ancient Babylonian astronomers and allowed eclipse prediction centuries in advance.
Is it safe to look at a solar eclipse?
It is never safe to look directly at the Sun except during the brief period of complete totality in a total solar eclipse. Partial and annular eclipses must always be viewed through certified eclipse glasses (ISO 12312-2) or a proper solar filter. Even when 99% of the Sun is covered, the remaining 1% is still intense enough to cause permanent retinal damage (solar retinopathy) within seconds.
How long can totality last?
Totality can last anywhere from a fraction of a second (at the edges of the path) to a maximum of about 7 minutes 32 seconds. The maximum occurs when the Moon is at perigee (closest to Earth, largest angular diameter), Earth is at aphelion (farthest from Sun, smallest solar angular diameter), and the observer is near the equator where Earth's rotation speed is greatest, extending the shadow's passage.
What is the path of totality?
The path of totality is the narrow strip on Earth's surface swept by the Moon's umbra. It is typically 100–270 km wide and traces a curved path across thousands of kilometres. Only observers within this path experience totality; everyone else sees at most a partial eclipse. The path moves from west to east at about 1,700 km/h (faster than most aircraft).
What are Baily's Beads and the Diamond Ring effect?
Baily's Beads are small, bright points of sunlight that appear just before or after totality as sunlight streams through the valleys and gaps on the Moon's rugged limb (edge). When only a single bead remains, it creates the spectacular Diamond Ring effect — a brilliant point of light with the corona forming the "ring" — which lasts only a second or two at the start and end of totality.