Stellar Parallax
Hold a finger up and blink between your left and right eye — your finger jumps against the background. Nearby stars do the same tiny jump as the Earth moves from one side of the Sun to the other. Measure that jump and you can measure the distance to a star that’s trillions of kilometres away, all without leaving Earth.
📘 What you need to know
- Astronomical distances use three units: the astronomical unit (AU), the light-year (ly), and the parsec (pc)
- 1 AU = mean Earth–Sun distance ≈ 1.50 × 1011 m
- 1 light-year = distance light travels in one year ≈ 9.46 × 1015 m
- 1 parsec ≈ 3.1 × 1016 m ≈ 3.26 ly
- Stellar parallax is the apparent shift of a nearby star against distant background stars as the Earth orbits the Sun
- The parallax angle p is measured in arcseconds, and distance d in parsecs, linked by p = 1 ÷ d
- Nearer stars have a larger parallax angle; the method works out to about 100 pc
Units for Astronomical Distances
Distances in space are so vast that metres become unwieldy, so astronomers use three larger units. You don’t need to memorise their exact values — they’re in the data booklet — but you do need to know what each one means and how to convert with them.
🧭 The three distance units
- Astronomical unit (AU) — the mean distance from the Earth to the Sun, about 1.50 × 1011 m. Handy for distances within the solar system
- Light-year (ly) — the distance light travels in one year, about 9.46 × 1015 m. Found from d = speed of light × time
- Parsec (pc) — about 3.1 × 1016 m, or 3.26 ly. Defined through parallax (see below). Handy for interstellar distances
What Stellar Parallax Is
As the Earth orbits the Sun, our viewpoint shifts. Observe a nearby star in January and again in July, and the Earth has moved to the opposite side of its orbit — a baseline of 2 AU. From those two positions, the nearby star appears to shift against the fixed backdrop of far-distant stars. That apparent shift is stellar parallax.
Stellar parallax: the apparent shift in position of a nearby star against a background of distant stars, seen from different points in the Earth’s orbit around the Sun.
The distant background stars are so far away that they don’t appear to move at all — they’re the fixed reference. Only the nearby star seems to wander, and the closer it is, the bigger its apparent shift.
The Parallax Equation
The geometry is a very thin right-angled triangle: the short side is 1 AU (Sun to Earth), the long side is the distance d to the star, and the tiny angle at the star is the parallax angle p. Because p is so small, the relationship simplifies beautifully when you use the right units.
The parsec is defined to make this simple: it’s the distance at which a star has a parallax angle of exactly 1 arcsecond (using the Earth–Sun distance as the baseline). With d in parsecs and p in arcseconds, the equation is simply:
So a star at 1 pc has a parallax of 1″, a star at 2 pc has a parallax of 0.5″, and so on. The farther the star, the smaller the parallax angle. Beyond about 100 pc the angle becomes too tiny to measure reliably, which is the method’s limit.
over 6 months
p (arcsec)
d (parsecs)
A star has a measured parallax angle of 0.25 arcseconds. Calculate its distance from Earth in (a) parsecs, (b) light-years. Take 1 pc = 3.26 ly.
A star is 12 light-years from Earth. Calculate its distance in (a) parsecs, (b) astronomical units, and (c) find its parallax angle. Take 1 ly = 9.46 × 1015 m, 1 pc = 3.26 ly, 1 AU = 1.50 × 1011 m.
💡 Top tips
- Units make p = 1 ÷ d work: it only holds with arcseconds and parsecs. Convert into these first, then apply the equation
- Know your symbols: 1 arcminute = 1′, 1 arcsecond = 1″, and there are 3600 arcseconds in a degree
- Nearer = bigger angle. If a question says one star has a larger parallax, it’s the closer one
- Use the data booklet for the conversion factors — you’re not expected to recall 9.46 × 1015 or 3.26 from memory
⚠ Common mistakes
- Using p = 1 ÷ d with the wrong units — it needs arcseconds and parsecs, not degrees and metres
- Getting the relationship backwards — a larger parallax means a nearer star, so smaller distance
- Confusing a light-year with a time — it’s a distance
- Applying parallax beyond ~100 pc — the angles get too small to measure accurately
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