Nocturna

Nocturna wraps herself in the night sky and asks the oldest question in astronomy: why is it dark?

The Physics

If the universe were infinite, eternal and evenly filled with stars, every line of sight would end on a star and the night sky would blaze. A thin shell of radius r holds a number of stars growing as r², while each star's light falls as 1/r², so every shell adds the same brightness. The way out: the universe has a finite age, t₀ ≈ 13.8 billion years, so light from beyond a certain distance has not reached us, and redshift dims what does arrive.

stars in shell ∝ r² dr, light per star ∝ 1/r² ⇒ each shell adds equal flux

• r: distance to the shell (m)
• dr: shell thickness (m)
• t₀: age of the universe, ≈ 13.8 billion years (≈ 4.35 × 10¹⁷ s)

Heinrich Olbers stated it in 1823 and proposed interstellar dust as the answer, which fails; Edgar Allan Poe guessed the real answer in Eureka (1848). Halley and de Chéseaux had raised the puzzle earlier.

Honest caveat: Dust does not work: over time it would heat up and glow.

On the shirt

Front: Nocturna, the pixel-art character, with the title. Back: the shell argument, why dust fails, the finite-age answer and the Poe, Halley and de Chéseaux history. Printed on a unisex tee.