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Umbrar

Dark Matter Physics

\[v(r) = \sqrt{\frac{G\,M(r)}{r}}\]
$21.99 USD
$21.99 USD
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Why don’t spinning galaxies fly apart? Umbrar is the unseen answer. For a circular orbit, v(r) = √(GM(r)/r), so speeds should fall far from the centre. Vera Rubin and others measured flat rotation curves instead, implying extra mass we cannot see: dark matter. What it is remains unknown. Pixel-art black ceramic mug in 11 or 15 oz; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in ~10 days

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

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Made to order: about 10 days of production and handling before it ships.

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.

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The physics

For a star in a circular orbit, the speed tells you how much mass lies inside the orbit. Measured speeds stay roughly constant far out in galaxies, so the enclosed mass keeps growing with radius: dark matter.

Umbrar cannot be seen. You can only see what Umbrar holds together.

For something in a circular orbit, gravity supplies the pull, and the speed depends on how much mass lies inside the orbit, the first line. Out past most of a galaxy's stars and gas, the enclosed mass should stop growing, so orbital speeds should fall off with distance, the way outer planets move more slowly than inner ones.

They do not. In the 1970s Vera Rubin, Kent Ford and colleagues measured the rotation of spiral galaxies, Andromeda first, and found the speeds stay roughly flat far out. Flat speed means the enclosed mass keeps growing in proportion to radius, the second line, well beyond the visible light. Fritz Zwicky had seen a similar shortfall in galaxy clusters in the 1930s.

Most astronomers take this, with other evidence, as the signature of dark matter: mass that pulls but does not shine. It is inferred from gravity, not detected directly, and what it is remains unknown. A minority of researchers instead try modified gravity.

UNSEEN. STILL HOLDING IT TOGETHER. That is the whole case for Umbrar so far.

Equations

\[v(r) = \sqrt{\frac{G\,M(r)}{r}}\]
\[v \approx \text{const} \;\Rightarrow\; M(r) \propto r\]
SymbolMeaningUnit
\(v(r)\) circular orbital speed at radius r \(\mathrm{m/s}\)
\(G\) Newtonian constant of gravitation \(\mathrm{m³·kg⁻¹·s⁻²}\)
\(M(r)\) total mass enclosed within radius r \(\mathrm{kg}\)
\(r\) distance from the galaxy's centre \(\mathrm{m}\)

Sources

  1. Rubin & Ford (1970) Rotation of the Andromeda Nebula, ApJ 159, 379
  2. Rubin, Ford & Thonnard (1980) Rotational properties of 21 Sc galaxies, ApJ 238, 471
  3. Zwicky (1937) On the Masses of Nebulae and of Clusters of Nebulae, ApJ 86, 217
  4. NASA Science — Dark Matter
  5. Encyclopaedia Britannica — Dark matter

Source Rubin, V. C.; Ford, W. K., Jr. (1970). Rotation of the Andromeda Nebula from a Spectroscopic Survey of Emission Regions. The Astrophysical Journal 159, 379.doi.org/10.1086/150317

Field notes

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