Why don't we have a solar eclipse every month during the new moon?

Because the Moon's orbit is tilted by about 5.1 degrees relative to the Earth's orbital plane (the ecliptic). During most new moons, the Moon passes either above or below the Sun in the sky from our perspective. An eclipse only occurs when the new moon phase happens at or very near one of the two points where its orbit crosses the ecliptic plane, called a node.

What determines if an eclipse is total or annular?

It depends on the Moon's distance from Earth. The Moon's orbit is slightly elliptical. If the Moon is closer than average (near perigee), its angular size is larger than the Sun's, causing a total eclipse where the umbra touches Earth. If it is farther (near apogee), its angular size is smaller, creating an annular 'ring of fire' eclipse where the umbra cone falls short of Earth's surface.

Is the Moon's shadow cone always the same length?

No, the length of the Moon's umbral cone varies primarily with the Earth-Moon distance. When the Moon is farther away, the cone is shorter. This variation is why the tip of the umbra sometimes doesn't reach Earth's surface (annular eclipse) and sometimes just barely touches it, creating a very narrow path of totality.

Does the simulator show why the path of totality on Earth is so narrow?

Yes. The geometry of the shadow cones shows that the Moon's umbra is a relatively small, converging cone. By the time it reaches Earth, roughly 235,000 miles from the Moon, the umbra's cross-section is only about 100-170 miles wide, creating the narrow path. The penumbra, in contrast, is much wider, covering a large area for a partial eclipse.

Solar Eclipse Geometry

Sun–Moon–Earth: angular sizes, umbra and penumbra cones, orbit tilt.

About this model

Solar eclipses are dramatic celestial events governed by precise geometric and orbital relationships. This simulator visualizes the core geometry of a total solar eclipse, focusing on the alignment of the Sun, Moon, and Earth. It models the concept of angular size, showing how the Sun's large physical diameter and the Moon's much smaller one can appear nearly identical in our sky due to their vastly different distances. The simulator calculates these angular sizes using the small-angle formula: angular diameter ≈ (physical diameter / distance) in radians. When these angular sizes are comparable, the Moon can completely obscure the Sun. The core of the model is the conical shadow cast by the Moon. It illustrates the umbra—the region of total shadow where the Sun is completely blocked—and the penumbra—the region of partial shadow. The length and width of these cones are determined by the relative sizes and distances of the Sun and Moon. A key simplification is the use of perfectly circular orbits and spherical bodies, ignoring the slight orbital eccentricities and topographic lunar features that affect real eclipses. The model also includes the 5.1-degree tilt of the Moon's orbit relative to the ecliptic plane, explaining why eclipses do not occur every new moon. By adjusting parameters like the Earth-Moon distance, users can see how the umbra's length changes, creating total, annular, or hybrid eclipses. Interacting with this simulation reinforces understanding of scale, perspective, and the celestial mechanics that make total solar eclipses possible on Earth.

Who it's for: High school and introductory undergraduate astronomy or physics students learning about celestial mechanics, scale, and geometry in the solar system.

Key terms

Angular Size
Umbra
Penumbra
Orbital Inclination
Total Solar Eclipse
Annular Eclipse
Ecliptic Plane
Shadow Cone

How it works

A solar eclipse needs the Moon between Earth and the Sun. The umbral cone is where the entire photosphere is blocked; the penumbra is where only part of the Sun is covered. Changing Earth–Moon distance changes whether the umbra reaches the surface (total) or you see a ring (annular).

Key equations

θ ≈ R / d (small-angle) Umbra / penumbra: tangent lines Sun ↔ Moon, extended toward Earth

Frequently asked questions

Why don't we have a solar eclipse every month during the new moon?: Because the Moon's orbit is tilted by about 5.1 degrees relative to the Earth's orbital plane (the ecliptic). During most new moons, the Moon passes either above or below the Sun in the sky from our perspective. An eclipse only occurs when the new moon phase happens at or very near one of the two points where its orbit crosses the ecliptic plane, called a node.
What determines if an eclipse is total or annular?: It depends on the Moon's distance from Earth. The Moon's orbit is slightly elliptical. If the Moon is closer than average (near perigee), its angular size is larger than the Sun's, causing a total eclipse where the umbra touches Earth. If it is farther (near apogee), its angular size is smaller, creating an annular 'ring of fire' eclipse where the umbra cone falls short of Earth's surface.
Is the Moon's shadow cone always the same length?: No, the length of the Moon's umbral cone varies primarily with the Earth-Moon distance. When the Moon is farther away, the cone is shorter. This variation is why the tip of the umbra sometimes doesn't reach Earth's surface (annular eclipse) and sometimes just barely touches it, creating a very narrow path of totality.
Does the simulator show why the path of totality on Earth is so narrow?: Yes. The geometry of the shadow cones shows that the Moon's umbra is a relatively small, converging cone. By the time it reaches Earth, roughly 235,000 miles from the Moon, the umbra's cross-section is only about 100-170 miles wide, creating the narrow path. The penumbra, in contrast, is much wider, covering a large area for a partial eclipse.

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Solar Eclipse Geometry

About this model

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Key equations

Frequently asked questions

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How it works

Key equations

Frequently asked questions