## Stellar Parallax

To determine the distance to a star, astronomers measure the apparent change in its position over one year. As the Earth orbits the Sun during this period, the observer (taking measurements at the opposite sides of the Earth's orbit) notices an apparent movement of the star compared to more distant stars. The closer a star is to the Earth the greater the observed parallax.

Figure 3.1: Astronomers measure the apparent shift in the star's position at different times of the year.

As in the diagram, the lines of sight and the line connecting the observer's position form a triangle, with the star at the apex. The parallax of the star is equal to the angular radius of the Earth's orbit as seen from the star. The distance d to the star (measured in parsecs) is equal to the reciprocal of the parallax angle p (in arc-seconds):

 d(parsec) = 1/ p(arcsecond)

### Limits on Parallax

The greater the distance to the star, the wider the baseline required for obtaining a discernible parallax. The baseline for observations from the Earth is limited to our planet's orbit around the Sun. Parallax angles smaller than about 0.01 arcsecond are very difficult to measure accurately from Earth, therefore stellar distances for stars further than around 100 parsecs cannot be measured from Earth.

However, ESA's Hipparcos satellite, unrestricted by the Earth's orbit or its atmosphere, spent three and a half years measuring star positions with unprecedented accuracy. Hipparcos allowed astronomers to measure the parallaxes of 120 000 stars, up to 500 light years (about 150 parsecs) from the Sun. Another experiment on the Hipparcos satellite, called Tycho, measured parallaxes for more than 1 million stars in the Galaxy, although to lesser accuracy.

 The parsec Distances using parallax

Last Update: 14 May 2013