How measuring angles lets us find the distance

We do this by using the apparent motion of an object, resulting from looking at it from different positions. Over the course of the year as the Earth moves round the Sun, nearby stars appear to move with respect to more distant stars (these still move but this movement is much smaller - Gaia uses Quasars (the extremely bright centres found in some galaxies) to define what is not moving). The angle through which the star appears to move is related to how far away it is.

As the stars are a long way away these angles are really small. The get an idea of the size of these angles the full moon, covers about half a degree. If we take a degree and divide it into 60 pieces, 1 of those pieces would be 1 arc minute, and this would be the angle covered by a regular (22cm diameter) football if it was 756 metres away. If you were to take 1 arc minutes and divide it into 60 pieces, 1 of those pieces would be 1 arc second , this would be the angle covered by a football 45.4 kilometres away.

If we measure the parallax of a star and found that is was 1 arc second we would known that the star was 1 parsec away. (1 parsec is 3.26 light years or 30,856,778,570,831 kilometres) However, the closest stars are further away than this so we need to be able to measure really small angles. Gaia can do this, and by the end of the mission will be able to find the distances to stars up to half-a-millon light years away.