Solar and lunar eclipse simulator: how do eclipses work? • The Science 360

By The Science 360 · Updated October 2026 · 10 min read

How do solar and lunar eclipses work?

An eclipse happens when the Sun, Earth and Moon line up. A solar eclipse is the Moon's shadow falling on Earth at new Moon, and a lunar eclipse is the Moon passing through Earth's shadow at full Moon. We do not get one every month because the Moon's orbit is tilted 5.14° to the plane of Earth's orbit, so most months the Moon passes just above or below the line. Only when new or full Moon happens close to one of the two points where the orbits cross, called the nodes, do the shadows line up.

Whether a solar eclipse is total or annular depends on size. The Sun is 0.53° across, and the Moon is 0.49° when it is far away and 0.56° when it is near, so it sometimes covers the Sun completely and sometimes leaves a ring. In the simulation you can set the Moon's position, how far the node is from the Sun, the Moon's distance, and switch the tilt off to see what a flat orbit would do. For the wider picture see the solar system facts.

Key results from the simulation

The tilt is the whole reason: with the orbit flat, every new Moon gives a central solar eclipse and every full Moon a lunar one. With the real 5.14° tilt the Moon is usually more than a degree above or below the line.
Window for a solar eclipse: the Sun must be within about 16.7° of a node for any solar eclipse, and within about 10.6° for a total or annular one. The Sun moves 0.99° a day, so each eclipse season lasts about 34 days.
Window for a lunar eclipse: within about 16.7° of a node for any lunar eclipse and about 4.7° for a total one, which is why total lunar eclipses are rarer than partial ones.
Total or annular: a Moon near perigee looks 0.56° wide and covers the 0.53° Sun. Near apogee it is 0.49° and leaves a ring of Sun.

Six eclipse set-ups

Each section gives the numbers the simulation shows, explains what you would see, and has a button that sets the Moon position, node offset, tilt and distance. The node offset is how far the Sun is from the Moon’s node at that time, in degrees.

Total solar eclipse: the Moon is close and well aligned

Node offset 1.5°, Moon near perigee (357,500 km)

With the Sun almost on the node, the Moon at new Moon is only 0.13° off the Sun-Earth line, small enough for its shadow to hit Earth. The Moon looks 0.56° across against the Sun's 0.53°, so it covers the whole disc (magnitude 1.04) and the Sun's corona appears around it.

Totality is seen only inside the Moon's umbra, a dark spot that sweeps across Earth along a narrow path, a few hundred kilometres wide at most, for at most about 7.5 minutes. Outside the path the eclipse is only partial. See the telescope buying guide for the safe way to watch the Sun: never without a certified solar filter.

Moon size 0.56° Sun size 0.53° Magnitude 1.04 Moon height 0.13°

Annular solar eclipse: a ring of fire

Node offset 1.5°, Moon near apogee (405,500 km)

The alignment is as good as before, but now the Moon is far away and looks only 0.49° wide, smaller than the Sun's 0.53°. Its shadow cone ends before it reaches Earth, so the observer is in the "antumbra", the region beyond the tip. The Moon covers 92% of the Sun's width and a bright ring is left.

In the side view the umbra's tip (the dashed lines) stops short of Earth. At the average distance of 384,400 km the Moon is 0.52°, still a little too small, which shows that total eclipses need a Moon nearer than average: roughly closer than 373,000 km.

Moon size 0.49° Sun size 0.53° Magnitude 0.92 Distance 405,500 km

Partial solar eclipse: the shadow misses Earth

Node offset 12°, average distance

With the Sun 12.0° from the node, the Moon is 1.07° from the Sun-Earth line at new Moon. That is more than one Earth radius as seen from the Moon (0.95°), so the centre of the shadow passes above or below Earth. People near the poles, on the side where the shadow's penumbra reaches, see the Moon bite the edge of the Sun.

At the best place on Earth the Moon covers about 76% of the Sun's width. Partial eclipses are the most common kind and a large share of them are never visible from populated places. Our cosmic objects post covers other sights that need a clear sky.

Moon height 1.07° Magnitude 0.76 Covered 76% Node offset 12°

Total lunar eclipse: the blood Moon

Full Moon, node offset 1.5°

At full Moon on the node the Moon is only 0.13° from the centre of Earth's shadow. The umbra there has an angular radius of 0.69° and the Moon's is 0.26°, so the Moon fits entirely inside with room to spare (magnitude 1.57). The edge of the umbra is blurred by Earth's atmosphere, which the simulation does not draw.

The Moon does not vanish, it turns copper red, because red light is bent through Earth's atmosphere into the shadow: you would see every sunrise and sunset on Earth at once. A lunar eclipse can be seen from everywhere the Moon is above the horizon, so far more people see one than a given solar eclipse.

Umbra radius 0.69° Moon radius 0.26° Magnitude 1.57 Moon height 0.13°

Switch the tilt off: an eclipse every month

Flat orbit (5.14° tilt removed)

If the Moon's orbit were in the same plane as Earth's, the Moon would be exactly on the Sun-Earth line at every new Moon (height 0.00°) and every full Moon. The simulation shows that even with the node offset at 25°, which normally gives nothing, you get a central solar eclipse: annular solar eclipse at the average distance, magnitude 0.97.

There would be about 12 solar and 12 lunar eclipses a year, instead of the real two to five solar eclipses and up to three lunar. This is the clearest way to see that the tilt is the explanation. In real life eclipses recur in a pattern: eclipse seasons are about 346.62 ÷ 2 = 173 days apart.

Moon height 0.00° Result Annular solar Magnitude 0.97 Tilt off

Far from the node: the shadows miss

Node offset 25°, tilt on

With the Sun 25.0° from the node, the Moon at new Moon is 2.17° above or below the Sun-Earth line, far more than it takes. Its shadow passes well clear of Earth and nothing happens. Two weeks later at full Moon (set the slider to 180°) the Moon is 2.17° from the middle of Earth's shadow, while the umbra reaches out only 0.69° and the penumbra 1.22°, so it passes by in clear sunlight.

This is what happens in most months. The Moon's height above or below the ecliptic reaches 5.14° at most, which is many Moon-widths, so the shadows miss. Only when the Sun is within about 16.7° of a node, for about 34 days twice a year, is an eclipse possible.

Moon height 2.17° Shadow limit 1.48° Result None Node offset 25°

The sizes that decide the eclipse type

Moon distance	Moon size	Sun size	Solar eclipse if centred	Umbra radius at Moon	Penumbra radius at Moon
Near (357,500 km)	0.56°	0.53°	Total	0.76°	1.29°
Average (384,400 km)	0.52°	0.53°	Annular	0.69°	1.22°
Far (405,500 km)	0.49°	0.53°	Annular	0.64°	1.17°

Values come from the formulas the simulation uses, with the Sun taken as 0.533° across (it varies from about 0.524° to 0.542° through the year). The middle row is annular because 384,400 km is the average distance, while the Moon looks as large as the Sun at about 373,000 km.

How the simulation works

The Moon is placed by its elongation D, the angle from the Sun as seen from Earth (0° at new Moon, 180° at full Moon). Its orbit is inclined 5.14° to the ecliptic, the plane of Earth's orbit. If S is how far the Sun is from the ascending node, the Moon's distance from the node is u = S + D, and its height above the ecliptic is β = asin(sin 5.14° × sin u). That height is zero at the two nodes and largest, 5.14°, a quarter turn from them.

For a solar eclipse the Moon-Sun separation comes from cos(sep) = cos β cos D. The Moon's angular radius is asin(1,737 km ÷ distance), and the Sun's is 0.27°. The Moon's shadow axis reaches Earth when sep is below about one Earth radius as seen from the Moon (the parallax, asin(6,378 km ÷ distance), about 0.95° at the average distance). If sep is within that, a total or annular eclipse is seen along a path; if sep is up to that plus the two radii, a partial one is seen somewhere.

For a lunar eclipse the same separation is measured from the centre of Earth's shadow. The umbra's angular radius at the Moon is the parallax plus the Sun's parallax minus the Sun's radius, and the penumbra's is the parallax plus the Sun's parallax plus the Sun's radius. The Moon is totally eclipsed if it is wholly inside the umbra, partially if it overlaps it, and penumbral if it only touches the outer shadow. The magnitude is the fraction of the Moon's (or Sun's) diameter covered.

In the side view horizontal distances are true. Earth, the Moon, the shadows and the tilt are enlarged by the same factor (about 6), so the Moon touches a shadow in the picture exactly when it does in the numbers. The play button runs the Moon round its orbit at about one day per second, with the node offset held fixed, which a real month does not do: the Sun moves about 29° along its path in a month.

What the model leaves out

Orbit shape: the Moon moves faster at perigee than at apogee and its distance really changes as it goes round. Here the distance is a control you set, and the orbit is drawn as a circle.
Which place on Earth: the solar view shows the best place on Earth. The path, its length and the duration of totality, up to about 7.5 minutes, are not modelled. A real observer must be inside the path.
The Moon's motion over a month: the node offset is fixed while the Moon goes round. In reality the Sun shifts about 29° along the ecliptic and the node moves about 1.5° backward.
Atmosphere and shadow edges: Earth's air makes the umbra about 2 percent larger and fuzzy, and the Sun's edge is not sharp. Contacts here are geometric.
Sun size: the Sun is fixed at 0.533° across. It varies by about 3 percent through the year as Earth's distance changes.
Hybrid eclipses: when the Moon and Sun look almost exactly the same size, an eclipse can be annular at the edges of the path and total in the middle. This model switches at one value.

Common misconceptions

“There should be an eclipse every month.” Only if the orbits were in the same plane. Switch the tilt off in the simulation and every new and full Moon becomes an eclipse. With the real tilt the Moon is usually well above or below the line.

“A total lunar eclipse is dangerous to watch.” No. A lunar eclipse is just the Moon in shadow and is safe to view with the naked eye or a telescope. Only the Sun, including a partial or annular eclipse of it, needs certified filters.

Frequently asked questions

How do eclipses work?

A solar eclipse happens when the new Moon passes in front of the Sun and its shadow falls on Earth. A lunar eclipse happens when the full Moon passes through Earth's shadow. Both need the Sun, Earth and Moon to line up, which happens only when the Moon is near one of the two points where its orbit crosses Earth's orbital plane.

Why is there not an eclipse every month?

The Moon's orbit is tilted 5.14° to the plane of Earth's orbit. At most new Moons it passes above or below the Sun and at most full Moons above or below Earth's shadow. An eclipse needs the Sun within about 16.7° of a node for a solar eclipse, which happens in two windows of about 34 days a year.

What is the difference between total, annular and partial solar eclipses?

In a total eclipse the Moon looks bigger than the Sun and covers it completely. In an annular eclipse the Moon is farther away, looks smaller than the Sun and leaves a ring. In a partial eclipse the shadow's axis misses Earth, or the observer is outside the central path, and the Moon covers only part of the Sun.

Why does the Moon turn red in a total lunar eclipse?

Earth’s atmosphere bends sunlight round the planet into its shadow, and scatters out the blue light, so what reaches the Moon is red and orange. How dark or bright it looks depends on dust and clouds in the air at the time.

Can I look at a solar eclipse?

Only through eclipse glasses or a solar filter that meets the ISO 12312-2 standard, or by projection. Never look at a partial or annular eclipse with the naked eye or an unfiltered telescope or camera, since it can damage the eye. Only during the few minutes of totality, when the Sun is completely covered, is it safe without a filter. A telescope needs a front-mounted solar filter, as discussed in the telescope guide.

How often do eclipses happen?

There are at least two solar eclipses a year and up to five, plus up to three lunar ones, and up to seven eclipses of both kinds in a year. The eclipse seasons are about 347 ÷ 2 = 173 days apart, and the whole pattern repeats after about 18 years, the Saros cycle. A total solar eclipse is visible from any given place only once every few hundred years on average.