• Black Einstein Ring physics hoodie, pixel-art gravitational lensing design, worn by a model, front close-up
  • Black Einstein Ring physics hoodie, pixel-art gravitational lensing design, worn by a model, back close-up
  • Black Einstein Ring physics hoodie, pixel-art gravitational lensing design, front view
  • Black Einstein Ring physics hoodie, pixel-art gravitational lensing design, back view
  • Black Einstein Ring physics hoodie, pixel-art gravitational lensing design, turning on a model
  • Black Einstein Ring physics hoodie, ΨP Pixelated Physics neck label
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Einstein Ring HoodieONE GALAXY, SEEN AS A RING | Pixelated Physics

Einstein Ring Hoodie – ONE GALAXY, SEEN AS A RING | Pixelated Physics

$54.99 USD
$54.99 USD
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Shipping calculated at checkout. Free US shipping · $10 flat shipping outside the US.
Color
Black
Size
S–5XL
Made
To order · shipping times

Mass bends light. Line a distant galaxy up behind a nearer one and the light arrives from several directions at once. A background galaxy lensed by a point mass into arcs and a ring, from the exact lens equation β = θ − θE²/θ. Mass is the lens. Pixel-art unisex hoodie in black; equation, symbols and sources in the physics panel below.

Color
Size

Size guideS–5XL · inches

Details

Size & fitS–5XL

Unisex Heavy Blend hoodie (Gildan 18500), classic fit.

SizeWidthLengthSleeve
S202733.5
M222834.5
L242935.5
XL263036.5
2XL283137.5
3XL303238.5
4XL323339.5
5XL343440.5

Measurements in inches. Width and length ±1 in, sleeve (from center back) ±0.75 in.

ShippingFree US

Free US shipping. $10 flat shipping outside the US.

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

Mass bends light. Line a distant galaxy up behind a nearer one and the light arrives from several directions at once.

For a point mass the mapping is exact and short: β = θ − θE²/θ. A source exactly behind the lens becomes a ring of radius θE. Move it slightly off axis and the ring breaks into two bright arcs, one on each side.

Lensing keeps surface brightness, so the art was made by tracing each pixel back through the lens equation to the source galaxy and copying its brightness. The amber dot is the lens.

Einstein worked out the ring in 1936 and thought it would never be seen. The first ring was found in radio data in 1988, and a complete infrared ring in 1998.

One galaxy, seen as a ring.

Equations

\[\beta = \theta - \frac{\theta_E^2}{\theta}\]
\[\theta_E^2 = \frac{4GM}{c^2}\,\frac{D_{ls}}{D_l\,D_s}\]
SymbolMeaningUnit
\(\beta\) true angular position of the source \(\mathrm{rad}\)
\(\theta\) apparent angular position of the image \(\mathrm{rad}\)
\(\theta_E\) Einstein radius \(\mathrm{rad}\)
\(G\) gravitational constant \(\mathrm{m^3·kg^{-1}·s^{-2}}\)
\(M\) lens mass \(\mathrm{kg}\)
\(c\) speed of light \(\mathrm{m/s}\)
\(D_l, D_s, D_{ls}\) distances to the lens, to the source, and from lens to source \(\mathrm{m}\)

Sources

  1. Einstein (1936) Lens-Like Action of a Star by the Deviation of Light in the Gravitational Field, Science 84, 506
  2. Schneider, Ehlers & Falco, Gravitational Lenses (1992)
  3. King et al. (1998) A complete infrared Einstein ring in the gravitational lens system B1938+666, MNRAS 295, L41
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