Solar and lunar eclipses: shadows of a ball and a globe

The idea

An eclipse needs the Sun, Earth and Moon in a straight line; the Moon's tilted orbit keeps its shadow above or below Earth on most months, and the shadow's cone length decides whether a solar eclipse is total or annular.

What you need

• 1 bare lamp with a frosted round bulb about 5 cm across (the Sun)
• 1 globe or 10 cm ball (Earth) on a stand, 1.5 m from the lamp
• 1 bead about 1 cm across on a stiff wire (the Moon), swung around Earth at about 30 cm radius in a plane tilted about 5 degrees to the lamp-Earth line; a 2.5 cm ball would not do, because with a 5 cm bulb its full shadow is as long as the whole bulb-to-ball distance and always reaches Earth
• 1 white card to catch shadows; 1 protractor; 1 tape measure

How to do it

1. Darken the room. Swing the bead around Earth in a plane tilted about 5 degrees and watch its shadow: on most passes the shadow misses Earth above or below.
2. Tilt the plane until the bead passes exactly between the lamp and Earth: a small dark spot (umbra) with a paler ring (penumbra) falls on Earth; measure the spot width.
3. Continue half an orbit to put Earth between lamp and bead: the bead darkens inside Earth's shadow, a lunar eclipse.
4. Move the globe aside and hold the white card on the lamp-bead line 20 cm and then 40 cm behind the bead; note whether a fully dark core shows. Measure the bulb's glowing diameter D, the bead's diameter b and the bulb-to-bead distance d, and compare with the umbra length L = d x b / (D - b).
5. Compute the umbra length for the real Moon from the simulation formula and compare with the Moon's perigee and apogee distances.

What you should see

Solar eclipses form only at new Moon and lunar eclipses only at full Moon, and only when the Moon's orbit plane crosses the lamp-Earth line; at other times the shadow misses. In the model a 1 cm bead 120 cm from a 5 cm bulb casts an umbra L = 120 x 1 / (5 - 1) = 30 cm long: a card 20 cm behind the bead shows a fully dark core about 3 mm across (1 x (1 - 20 / 30) cm) inside a paler penumbra, while at 40 cm there is no dark core, only an evenly grey centre still lit by the ring of bulb around the bead, the annular case. With the real figures from the NASA fact sheets (Sun radius 695,700 km, Moon radius 1737.4 km) and a Sun-Moon distance at new Moon of 149.6 - 0.3844 = 149.2156 million km, the Moon's umbra is 149.2156e6 x 1737.4 / (695,700 - 1737.4) = 373,575 km long. An observer directly beneath the Moon is Earth's radius (6,371 km) nearer to it than Earth's centre is: at the mean distance of 384,400 km that is 378,000 km, beyond the umbra's tip, so a central eclipse is annular; at perigee (363,300 km) it is 356,900 km, inside the umbra, so the eclipse is total. A total eclipse is possible only when the Moon's centre is nearer than about 380,000 km to Earth's centre. The Moon's apparent diameter is 0.518 degrees at mean distance against the Sun's 0.533 degrees, which is why the two discs nearly match. NASA's decade table lists total solar eclipses with totality in Australia on 22 July 2028 and 25 November 2030. The learner knows the model worked when the shadow reaches Earth only near exact alignment and the card shows a dark core when it is nearer than L to the bead and none beyond it.

What changes

What you change

tilt of the bead's orbit plane and distance behind the bead

What you measure

whether a shadow falls on Earth and whether a fully dark core reaches the card

What you keep the same

• lamp size and distance
• ball sizes
• room darkness

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

• There should be an eclipse every month; the 5 degree tilt makes alignment rare.
• A solar eclipse can be seen from the whole day side of Earth; the umbra is a spot a few hundred kilometres wide.
• The Moon's phases are caused by Earth's shadow; a phase is the part of the Moon's sunlit half that faces Earth, and Earth's shadow reaches the Moon only in a lunar eclipse.

Safety card

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

• Science 7-10 Syllabus (2023), NSW Education Standards Authority (implemented from 2026; codes read at curriculum.nsw.edu.au on 22 and 23 September 2026)SC4-OTU-01SC4-WS-01SC4-WS-04
• Australian Curriculum v9AC9S7U03AC9S7I04AC9S7I05

Sources

The pages the author read to write this activity.

1. curriculum.nsw.edu.au/learning-areas/science/science-7-10-2023/outcomes
2. vocabulary.curriculum.edu.au/MRAC/2024/04/LA/SCI/export/MRAC/2024/04/LA/SCI.jsonld
3. science.nasa.gov/eclipses
4. eclipse.gsfc.nasa.gov/SEdecade/SEdecade2021.html
5. nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html
6. nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html
7. science.nasa.gov/moon/moon-phases