Deriving stellar distances using the method of stellar parallax.

Figure 1.3 Schematic Representation of stellar Parallax. Distant stars act as a fixed reference coordinate system. Nearby stars, when observed 6 months apart, will show a small movement with respect to the background of fixed stars. At position 1, the nearby star would be viewed against a background that contained star B while 6 months later, at position 2, the nearby star would be viewed against a background that contained star A.

The angle which we measure with respect to the baseline of the earth's orbit about the sun is called the parallactic or parallax angle.

This angle would have a size of 1 arc second (1/3600 of a degree) for a star that had a distance of 1 parsec from the earth. 1 parsec is equal to 3.26 light years.

The nearest star to us has a distance of 4.1 light years so that all parallactic angles are less than 1 arc second for all stars. This means its impossible to measure this effect with the naked eye.

The observational problem in measuring accurate stellar distances is then that atmospheric motions/smearing make positional measurements of stars, at levels of accuracy less than 1 arc second difficult.

Therefore, many measurements of the star are needed to record an accurate parallax. In practice, one usually requires 20 years of measurements of a single star.

If we measure the parallactic angle, then we can directly know the distance to the star. The distance in parsecs is simply

1/p

where p is the angle measured in arcseconds. Thus a star that has p = 0.1 would have distance of 1/p = 10 parsecs = 32.6 light years.