• Pixel-art sticker of Collapso, personifying Gravitational Free-Fall Time, with the caption “Denser Cloud, Faster Collapse.”

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Collapso

Gravitational Free-Fall Time Physics

\[t_{\text{ff}} = \sqrt{\frac{3\pi}{32 G \rho}}\]
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Meet Collapso, a cloud of gas in space slowly falling in on herself to make a star. Her free-fall time depends only on density, not size. A dense core near 4 × 10⁻¹⁶ kg/m³ would collapse in about 100 000 years, quick by galactic standards. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Meet Collapso, a cloud of gas in space who is slowly falling in on herself to make a star.

Stars form inside cold clouds of gas and dust. If a clump becomes dense enough, its own gravity overwhelms the pressure that holds it up, and it starts to collapse. With nothing to stop it, the clump would fall to a point in a time called the free-fall time.

That time depends only on the density ρ: t_ff = √(3π/(32Gρ)). Denser clouds collapse faster. Surprisingly, the size of the cloud does not matter at all.

A typical dense core in a molecular cloud has about 10¹¹ molecules per cubic metre, a density near 4 × 10⁻¹⁶ kg/m³. Its free-fall time works out to about 100 000 years, which is quick by the standards of the galaxy.

In practice rotation, magnetic fields and heating slow things down, and a new star takes a few times longer to settle. The free-fall time is still the starting estimate astronomers use.

Equations

\[t_{\text{ff}} = \sqrt{\frac{3\pi}{32 G \rho}}\]
Symbols
SymbolMeaningUnit
\(t_{\text{ff}}\) free-fall time \(\mathrm{s}\)
\(G\) gravitational constant \(\mathrm{N·m²/kg²}\)
\(\rho\) density \(\mathrm{kg/m³}\)