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Galileo Galilei Sticker

Telescope. Tea. Trouble with the Church. | Physics

\[d = \tfrac{1}{2}g t^{2}\]
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Point a new instrument at the sky and the old cosmos starts to crack. In 1610 Galileo’s telescope revealed Jupiter’s four largest moons and the phases of Venus, evidence against an Earth-centred cosmos. A pixel-art portrait on a 3" × 3" sticker; the physics panel below has the equation, every symbol and the sources.

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Size3″ × 3″

3″ × 3″ kiss-cut sticker.

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The physics

Galileo found that a falling body's distance grows with the square of the time. In equal time intervals the distances covered go in the ratio of the odd numbers 1, 3, 5 and so on, which is the signature of constant acceleration.

The sticker says Telescope. Tea. Trouble with the Church. The physics is in the gap between the telescope and the trouble.

In 1610 Galileo turned an improved telescope on Jupiter and found four points of light that travelled with it, night after night: moons circling something other than the Earth. He published them that year in The Sidereal Messenger. It did not prove that the Earth moves, but it removed the argument that everything must circle us. In 1633 the Church tried him for defending the Sun-centred system in his Dialogue and sentenced him to imprisonment, which he served under house arrest.

He kept working. His last great book, Two New Sciences, published in 1638, set out the mathematics of motion. Galileo slowed falling down by rolling balls along gentle ramps, where the motion was slow enough to time. His result is the first formula on this page: distance from rest grows as the square of the time. The second line is the same law in a form you can check with a ruler. In equal successive intervals, a falling body covers distances in the ratio 1 : 3 : 5 : 7, the odd numbers. Add them up and you get 1, 4, 9, 16, the squares. The odd numbers are what make it a square.

The same book argues that without air, heavy and light bodies would fall together. At the end of the last Apollo 15 moonwalk in 1971, commander David Scott dropped a 1.32-kilogram hammer and a falcon feather side by side on the Moon. They hit the ground together.

Galileo was not the first to look up, nor the first to doubt Aristotle. He rolled the balls, timed them, and wrote the numbers down.

Telescope, tea, trouble. The odd numbers came first.

Equations

\[d = \tfrac{1}{2}g t^{2}\]
\[d_1 : d_2 : d_3 : \dots = 1 : 3 : 5 : \dots\]
SymbolMeaningUnit
\(d\) distance fallen from rest \(\mathrm{m}\)
\(g\) gravitational acceleration \(\mathrm{m/s²}\)
\(t\) time \(\mathrm{s}\)
\(d_n\) distance covered in the n-th equal time interval \(\mathrm{m}\)

Sources

  1. Encyclopaedia Britannica — Galileo
  2. NASA NSSDCA — The Apollo 15 Hammer-Feather Drop

Source Galilei, G. (1638). Discorsi e dimostrazioni matematiche intorno a due nuove scienze, Third Day (naturally accelerated motion). Leiden: Elzevir.

Field notes

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