• Pixel-art sticker of Parallaxa, personifying Stellar Parallax, with the caption “Near Stars Shift More.”

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Parallaxa

Stellar Parallax Physics

\[d\,[\mathrm{pc}] = \frac{1}{p\,[\mathrm{arcsec}]}\]
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Meet Parallaxa, who measures how nearby stars seem to shift against much more distant ones as Earth orbits the Sun. The distance in parsecs is one over the parallax in arcseconds, so a star with a parallax of one arcsecond is one parsec away, by definition. 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 Parallaxa, a nearby star who seems to shift a little against the background as Earth goes round the Sun.

Hold a finger at arm's length and look at it with one eye, then the other: it jumps against the background. Stars do the same as Earth moves around its orbit. Half the total shift, measured using a baseline of one astronomical unit, is the parallax angle p. A star with a parallax of one arcsecond is, by definition, one parsec away, about 3.26 light-years. So distance in parsecs is just one over parallax in arcseconds.

Every star's parallax is smaller than one arcsecond. The nearest, Proxima Centauri, has about 0.77 arcseconds, placing it about 1.3 parsecs away. Friedrich Bessel made the first successful measurement, of the star 61 Cygni, in 1838.

Parallax is the first rung of the cosmic distance ladder: it calibrates the brighter yardsticks used farther out. The European Space Agency's Gaia mission has measured parallaxes for over a billion stars.

Tiny angles mean large errors for distant stars, so parallax works only within our galaxy.

Equations

\[d\,[\mathrm{pc}] = \frac{1}{p\,[\mathrm{arcsec}]}\]
SymbolMeaningUnit
\(d\) distance to the star \(\mathrm{pc}\)
\(p\) parallax angle \(\mathrm{arcsec}\)

Sources

  1. OpenStax Astronomy 2e — Surveying the Stars
  2. OpenStax Astronomy 2e — Fundamental Units of Distance
  3. Wikipedia — Stellar parallax

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