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Fritz ZwickyToo Fast To Be LitSticker

Fritz Zwicky Sticker – Too Fast To Be Lit | Physics Sticker

$6.99 USD
$6.99 USD
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3" × 3"
Surface
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What holds a galaxy cluster together? In 1933 Fritz Zwicky found galaxies in the Coma cluster moving far too fast for the visible matter to hold. By the virial theorem, σ² ~ GM/R, so fast motions need much more mass than shines. He called the missing mass dunkle Materie and refined the case in 1937. A 3" pixel-art physicist sticker; equation, symbols and sources in the physics panel below.

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Free US shipping$10 flat shipping outside the USMade to order, ships in 2–5 business days

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Size3″ × 3″

3″ × 3″ kiss-cut sticker.

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Free US shipping · $10 flat shipping outside the US, whatever's in your order.

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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.

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The physics

In 1933 Fritz Zwicky timed the Coma cluster and found the galaxies moving too fast for the glowing mass alone.

The virial estimate is σ² ~ GM/R. Invert it: M_vir ≈ σ² R / G. If the observed dispersion exceeds what luminous mass can bind, you need dark mass.

On the sticker Coma appears as dots with velocity arrows too long for the lit matter, stamped MISSING MASS.

Zwicky called it dunkle Materie. Decades later the name stuck, and the mass budget of the universe still does not add up without it.

Too fast to be lit.

Equations

\[\sigma^2 \sim \frac{GM}{R}\]
\[M_{\mathrm{vir}} \approx \frac{\sigma^2 R}{G}\]
SymbolMeaningUnit
\(\sigma\) line-of-sight velocity dispersion of galaxies \(\mathrm{km/s}\)
\(G\) gravitational constant \(\mathrm{pc M_\odot^{-1} (km/s)^2}\)
\(M\) gravitating mass within radius R \(\mathrm{M_\odot}\)
\(R\) characteristic cluster radius \(\mathrm{pc}\)
\(M_{vir}\) virial mass implied by \sigma and R \(\mathrm{M_\odot}\)

Sources

  1. Zwicky (1933) Die Rotverschiebung von extragalaktischen Nebeln, Helvetica Physica Acta 6, 110
  2. Binney & Tremaine, Galactic Dynamics, Ch. on clusters and the virial theorem
  3. Wikipedia, Dark matter / Fritz Zwicky
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