• Cosmic Weights & Measures sticker sheet: pixel-art Rømer, Payne-Gaposchkin, du Châtelet, Chandrasekhar on a white A5 sheet
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Cosmic Weights & Measures SheetRømer, Payne-Gaposchkin, du Châtelet & Chandrasekhar | 9 Pixel Art Stickers

Cosmic Weights & Measures Sticker Sheet – Rømer, Payne-Gaposchkin, du Châtelet & Chandrasekhar | 9 Pixel Art Stickers

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5.83″ × 8.27″
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What you getA5 sheet · 9 stickers

One A5 kiss-cut sheet (5.83″ × 8.27″) on white sticker paper with 9 stickers, made to order.

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The physics

Nine stickers on one sheet: the Department of the Sky, staffed by four inspectors.

Rømer's line is Io Isn’t Late. Light Is. In 1676 Ole Rømer predicted that Jupiter's moon Io would come out of eclipse about ten minutes late, because Earth had moved farther away and the light needed longer to arrive. He put light's trip across Earth's orbit at about 22 minutes. Today's figure is 16.6. That is the +10 on Io's slip.

Payne-Gaposchkin's line is Almost Certainly Real. Her 1925 thesis showed that stellar spectra differ mainly by temperature, and her numbers made hydrogen and helium vastly abundant, a result she called almost certainly not real. It was real. The barcode is built from four genuine hydrogen absorption lines, at 410.2, 434.0, 486.1 and 656.3 nanometres.

Du Châtelet's line is 2× The Speed. 4× The Dent. Willem 's Gravesande's clay experiments showed impact growing with mass times speed squared, and in 1740 Émilie du Châtelet made them the centre of her case for vis viva. Kinetic energy is half of it.

Chandrasekhar's line is No Seconds. In 1931 he showed that a white dwarf has a maximum mass, about 1.44 solar masses in the idealised model for carbon and oxygen. Wilhelm Anderson and Edmund Stoner had found simpler limits first. The tag rounds it to 1.4 MAX.

Four inspectors. One universe. Inspected.

Equations

\[\begin{gathered} \Delta t = \frac{\Delta d}{c} \\ \frac{2\,\text{AU}}{c} \approx 16.6\ \text{min} \end{gathered}\]
\[\begin{gathered} X + Y + Z = 1 \\ (\text{Sun's surface today:} \\ X\approx0.74,\ Y\approx0.25, \\ Z\approx0.013) \end{gathered}\]
\[\begin{gathered} \frac{1}{\lambda_{\text{vac}}} = R_{\text{H}}\left(\frac{1}{2^{2}} - \frac{1}{n^{2}}\right) \\ n = 3,\ldots,6 \\ \Rightarrow\; \lambda_{\text{air}} \approx 656.3,\ 486.1, \\ 434.0,\ 410.2\ \text{nm} \end{gathered}\]
\[\begin{gathered} E_k = \tfrac{1}{2} m v^{2} \\ v = \sqrt{2 g h}\;\Rightarrow\; h \propto v^{2} \end{gathered}\]
\[\begin{gathered} M_{\text{Ch}} \approx \frac{5.73}{\mu_e^{2}}\,M_\odot \approx 1.4\,M_\odot \\ (\mu_e = 2) \end{gathered}\]
SymbolMeaningUnit
\(\Delta t\) extra light travel time \(\mathrm{s}\)
\(\Delta d\) extra distance light must travel \(\mathrm{m}\)
\(c\) speed of light in vacuum \(\mathrm{m/s}\)
\(\text{AU}\) astronomical unit, about the mean Earth–Sun distance \(\mathrm{m}\)
\(X, Y, Z\) mass fractions of hydrogen, helium, everything heavier \(\mathrm{1}\)
\(\lambda_{\text{vac}}, \lambda_{\text{air}}\) Balmer line wavelengths in vacuum and in air \(\mathrm{m}\)
\(R_{\text{H}}\) Rydberg constant for hydrogen \(\mathrm{m⁻¹}\)
\(n\) upper energy level of the transition \(\mathrm{1}\)
\(E_k\) kinetic energy \(\mathrm{J}\)
\(m\) mass \(\mathrm{kg}\)
\(v\) impact speed \(\mathrm{m/s}\)
\(g\) gravitational acceleration \(\mathrm{m/s²}\)
\(h\) drop height \(\mathrm{m}\)
\(M_{\text{Ch}}\) Chandrasekhar mass limit (idealised) \(\mathrm{kg}\)
\(\mu_e\) mean molecular weight per electron \(\mathrm{1}\)
\(M_\odot\) solar mass \(\mathrm{kg}\)

Sources

  1. Rømer (1677) A Demonstration concerning the Motion of Light, Phil. Trans. 12, 893
  2. Bobis & Lequeux (2008) Cassini, Rømer and the velocity of light, JAHH 11, 97
  3. Payne (1925) Stellar Atmospheres, Harvard Observatory Monographs No. 1, p. 188 — scan via ADS
  4. DeVorkin (2010) C. H. Payne, H. N. Russell and standards of evidence, JAHH 13, 139
  5. Asplund, Grevesse, Sauval & Scott (2009) The Chemical Composition of the Sun, ARA&A 47, 481
  6. NIST Handbook of Basic Atomic Spectroscopic Data — hydrogen strong lines (air wavelengths)
  7. Du Châtelet, Institutions de physique (1740), ch. 21 'Of the Force of Bodies' — English translation
  8. Wikipedia — Willem 's Gravesande (clay experiments)
  9. Stanford Encyclopedia of Philosophy — Émilie du Châtelet
  10. Chandrasekhar (1931) The Maximum Mass of Ideal White Dwarfs, ApJ 74, 81
  11. Chandrasekhar, Nobel Lecture (1983) On Stars, Their Evolution and Their Stability
  12. Blackman — Anderson and Stoner published white dwarf mass limits before Chandrasekhar, arXiv:1103.1342
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