Astronomers don't need to know a distance before using parallax to determine a star's distance. In fact, parallax is the primary method used to determine the distance to nearby stars.

Here's how it works:

1. Observation: Astronomers observe a star from two different points in Earth's orbit, typically six months apart when Earth is on opposite sides of the Sun.

2. Angle Measurement: They measure the apparent shift in the star's position against the background of more distant stars. This shift is called the parallax angle.

3. Distance Calculation: The distance to the star is calculated using the formula: distance = 1 / parallax angle (where the parallax angle is measured in arcseconds).

The smaller the parallax angle, the farther away the star. This is why parallax is only useful for relatively nearby stars. For stars beyond about 10,000 light-years, the parallax angle becomes too small to measure accurately.