Secular and
Statistical Parallax

The method of parallax is the most reliable one for determining distances to stars but it can only be used for more nearby stars. The primary reason is that the parallax shift angle is very small because the stars are so far away. For stars further and further away, the angle finally becomes too small to measure reliably.

The Baseline for Parallax

This limitation on measuring the parallax angle is ultimately set by the length of the ``baseline'' that we use to measure the angle. This corresponds to the distance across the Earth's orbit, and is 2 astronomical units (2 AU). We could measure parallax for more distant stars if we had a longer baseline.

The discussion of the preceding section indicates that the Sun is moving with respect to the local field of stars in the direction of Vega at a speed of about 20 km/s. This means that over a year, the Sun moves a distance of a little over 4 AU. Thus, this motion of the Sun has the potential to give a longer baseline over which to measure parallax. But, this cannot be used to directly measure the distance to the stars because while the Sun is moving over this distance in a year (taking the Earth with it), all the other stars are in motion too. Thus, the position of any one star changes on the celestial sphere both because of the Sun's motion and because of the motion of the star and we can't disentangle the two without further information.

Measurement of Average Distances using Statistical Arguments

However, this method can still be used to measure the average distance to a set of stars, because for a set of stars their motion with respect to the Sun averages approximately to zero. Methods based upon this argument that measure the distance, not to individual stars, but the average distance to a set of stars are called statistical methods. This particular one is called secular parallax. Another method relying on somewhat different statistical arguments to determine the average distances to a set of stars is called statistical parallax. Although we shall not discuss these statistical methods in detail, they have played an important role in estimating distances to stars that were too large for the standard parallax method.

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