• Pixel-art sticker of Dimmia, personifying Transit Depth, with the caption “I Cross, You Dim.”

IndexRelativity & CosmosSticker

Dimmia

Transit Depth Physics

\[\frac{\Delta F}{F} = \left(\frac{R_p}{R_\star}\right)^2\]
$4.99 USD
$4.99 USD
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Meet Dimmia, a small dark planet who dims a whole star each time she passes in front. The dip is the square of the planet-to-star radius ratio: Jupiter crossing a Sun-like star gives about 1%. Her third-of-a-star size blocks about 11%, possible around a red dwarf. 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 Dimmia, a small dark planet who makes a whole star dim a little each time she passes in front.

Most exoplanets are far too faint to see directly. But if a planet's orbit is lined up edge-on from our point of view, it crosses the face of its star once every orbit. For a few hours it blocks a small disc of starlight, and telescopes watching the star see its brightness dip.

The fractional dip is ΔF/F = (Rₚ/R⋆)², the ratio of the planet's disc area to the star's. A Jupiter-sized planet crossing a Sun-like star has Rₚ/R⋆ ≈ 0.10, so the star dims by about 1%. An Earth-sized planet gives only about 0.008%.

The planet in the art is a third of the star's width, which would block about 11% of its light. That is possible for a giant planet around a small red dwarf.

NASA's Kepler and TESS missions have found thousands of planets this way.

Equations

\[\frac{\Delta F}{F} = \left(\frac{R_p}{R_\star}\right)^2\]
SymbolMeaningUnit
\(\Delta F/F\) fractional drop in the star's brightness \(\mathrm{dimensionless}\)
\(R_p\) radius of the planet \(\mathrm{m}\)
\(R_\star\) radius of the star \(\mathrm{m}\)

Sources

  1. NASA — What's a transit?
  2. Wikipedia — Methods of detecting exoplanets
  3. OpenStax Astronomy 2e — Planets beyond the Solar System: Search and Discovery

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