KUNST
SCHÖNHEIT & WELLNESS
HANDWERK
KULTUR & GESCHICHTE
UNTERHALTUNG
UMFELD
ESSEN & GETRÄNKE
GRÜNE ZUKUNFT
REVERSE ENGINEERING
SCHULPROJEKTE
WISSENSCHAFTEN
SPORT
TECHNOLOGIE
WEARABLES
Measuring How Far the Sun Is Compared to the Moon — Aristarchus' Half-Moon Method
Around 270 BC Aristarchus of Samos worked out that the Sun is far more distant than the Moon — and did it with pure geometry. His key idea: when the Moon is exactly half-lit, the Sun, Moon and Earth form a right angle at the Moon. Measure the angle in the sky between the half-Moon and the Sun, and trigonometry gives the ratio of their distances. This blueprint reproduces his method with a simple sighting instrument. It also shows, honestly, why his answer of '19 times' fell short of the true 390 — the geometry is perfect, but the angle is almost impossible to measure by eye. From it Aristarchus argued the Earth goes round the Sun, eighteen centuries before Copernicus.
Fortgeschritten
2
Anweisungen
1
1
Understand the geometry
Understand the geometry
When the Moon shows exactly half its disc lit, the sunlight is hitting it side-on — which means the angle Sun–Moon–Earth is a perfect right angle. The Earth, Moon and Sun then form a right triangle, with the Earth–Moon line and Earth–Sun line as two sides. The angle between them at the Earth unlocks the distance ratio.
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2
Catch a precise half-Moon
Catch a precise half-Moon
Watch for the exact moment of first-quarter or last-quarter Moon, when the terminator (the line between light and dark) is dead straight and half the disc is lit. This is when the right angle at the Moon holds — and judging it precisely is the hardest part.
Benötigte Werkzeuge:
Dowel Rod3
3
Measure the Sun–Moon angle
Measure the Sun–Moon angle
With both the Sun and the half-Moon in the sky, measure the angle between them using a cross-staff or a graduated sighting board. NEVER look at the Sun directly — sight it by the shadow its pinhole or a rod casts on the board while you line the other end up with the Moon.
Benötigte Werkzeuge:
Red Alder Board
Cotton Kitchen String4
4
Note Aristarchus' reading
Note Aristarchus' reading
Aristarchus measured this angle as 87°, just short of a right angle. The true value is about 89.85° — so close to 90° that the naked eye cannot tell the difference. Record your own measured angle for the calculation.
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5
Do the trigonometry
Do the trigonometry
In the right triangle, the ratio of the Sun's distance to the Moon's distance is 1 ÷ cosine(your angle). For 87°, cos 87° ≈ 0.0523, so the Sun works out about 1 ÷ 0.0523 ≈ 19 times farther than the Moon.
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Compare honestly with the truth
Compare honestly with the truth
The real Sun is about 390 times farther than the Moon, not 19. The gap is not a flaw in the reasoning — it is because the true angle (89.85°) is so near 90° that being off by even 3° throws the answer out enormously. The method is exact; only the instrument's precision limits it.
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7
See why it changed history
See why it changed history
Even the modest '19 times' meant the Sun must be vastly bigger than the Earth. Aristarchus reasoned that the small Earth would sooner orbit the giant Sun than the reverse — proposing a Sun-centred cosmos around 270 BC, roughly 1,800 years before Copernicus revived the idea.
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8
Push for better precision
Push for better precision
Repeat on several half-Moons and average your readings, and use the finest angle scale you can build. Every fraction of a degree you gain nearer the true 89.85° pushes your Sun-distance ratio up toward the real value — a direct lesson in how measurement precision drives discovery.
Materialien verbundener Blueprints
You can swap these in
Can't get one of the materials? Swap it for an equivalent — these work just as well.
- Instead of Dowel Rod, try:
Pine Dowel Rod Set (12 Diameters)
Dowel Rod Assortment (12 Sizes) - Instead of Cotton Kitchen String, try:
Guitar String Set (Acoustic, Phosphor Bronze)
Violin String Set (Full Size, Synthetic Core)
Bow String
Recommended for this build
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Chalk LineUsed together and in similar builds
AwlFrequently used with this build's materials
Sloyd Carving KnifeFrequently used with this build's materials
PVA Wood GlueFrequently used with this build's materials
HacksawFrequently used with this build's materials
Dry Softwood BoardFrequently used with this build's materials
Sharp KnifeFrequently used with this build's materials
Stone Mortar and Pestle (large)Frequently used with this build's materialsVerwandte Blueprints
Diese Blueprints teilen Wissen — Techniken, Materialien oder Prinzipien
Related blueprints
Other builds that share materials, tools, or techniques with this one.
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Measuring the Circumference of the Earth — Eratosthenes' Shadow Method
Measuring Pi — Archimedes' Method of Squeezing a Circle Between Polygons
Building Leonardo da Vinci's Armored Car — The Ancestor of the Tank
Casting a Bronze Socketed Spearhead — Bivalve Mould MethodMetalworking
Dyeing Blue with Japanese Indigo — The Fresh-Leaf Salt-Rub Methodtextiles
CC0 Gemeinfrei
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