English

Stellar Parallax

High schoolInterdisciplinaryParallax from the Earth orbit: p (arcsec) = 1 / d (parsec); measured positions carry the instrument error

Unlock this lab with a pass

A pass opens every simulation on the site, including Present mode for class. The teaching notes below stay free for everyone.

See passesI already have a pass

One-time payment, no subscription.

About this experiment

Hold a finger up at arm's length and look at it with one eye, then the other: it jumps against the background. Astronomers do the same with the Earth's orbit. A nearby star seen in January and again in July shifts very slightly against much more distant stars, and the size of that shift tells us how far away it is. Even for the nearest star the shift is less than one arcsecond, so measuring it took until 1838. Take photos through different instruments and work out the distances to real stars.

Learning goals

  • Explain parallax as the apparent shift of a nearby object against a distant background
  • Define the parsec and use d = 1 / p to find distances
  • Explain why photos must be taken about six months apart
  • Explain why parallax only works for relatively nearby stars
  • Compare the precision of ground-based telescopes with space missions such as Hipparcos and Gaia

How to use it

  1. 1Watch the telescope view for a whole year. Which stars move and which stay still? Why?
  2. 2With Proxima Centauri and a ground telescope, take a photo, wait six months and take another. Work out the distance and compare with the true value.
  3. 3Take two photos only one month apart. Why is the result less reliable?
  4. 4Switch to Polaris with a ground telescope. Can you measure its parallax? Now try Hipparcos and Gaia.
  5. 5Try the naked eye. Why could astronomers before telescopes not detect stellar parallax?
  6. 6Compare Vega and Proxima Centauri. Why does Vega trace a rounder ellipse?

The model

Distance in parsecs from the parallax angle in arcseconds
One parsec: the distance at which 1 AU subtends one arcsecond
Small-angle approximation, with p in radians
The Earth moves across a whole diameter of its orbit

Assumptions

  • The Earth orbit is a circle of 1 AU. The star traces an ellipse of semi-axes p and p·sin β, where β is its angle above the plane of the orbit.
  • Distances are rounded Gaia and Hipparcos values. The motion of the star across the sky (proper motion) is left out.
  • Each photo adds a random error of the size typical for the instrument: 60″ by eye, 0.05″ for a ground telescope, 0.001″ for Hipparcos and 0.00002″ for Gaia.
  • The distance from your photos divides the measured shift by the shift a star at 1 pc would show between the same two dates.

Try this in class

  1. Q1A star has a parallax of 0.25″. How far away is it in parsecs and in light years?
  2. Q2Why do astronomers measure parallax using the orbit of the Earth rather than two places on the Earth?
  3. Q3Gaia can measure 20 microarcseconds. What is the furthest distance it can reach with 10 % accuracy?
  4. Q4Why does the error in the distance grow so quickly for distant stars?
  5. Q5If astronomers observed from Mars, which orbits at 1.52 AU, how would the parallax of a star change?

Frequently asked questions

Why is the unit called a parsec?

It is short for parallax second: the distance at which a star shows a parallax of exactly one arcsecond. It is about 31 trillion kilometres.

Who first measured a stellar parallax?

Friedrich Bessel in 1838, for the star 61 Cygni, at about 0.3 arcseconds. The fact that no parallax could be seen for so long was once used as an argument that the Earth did not move.

How are more distant stars measured?

Parallax calibrates other methods, such as the brightness of Cepheid variable stars and type Ia supernovae, which reach much further. This chain of methods is called the cosmic distance ladder.