What causes stellar parallax?

We observe that when a nearby star is seen from earth, from two different observation points in time, against the background of a distant star or a cluster of stars; there is apparent movement of the star. We term this apparent movement of star as Stellar parallax.

and line joining the point of observation on earth and the star. Stellar parallax angle #p# is the angle, in seconds, in the triangle at the star vertex.

Application

The Stellar parallax is used to measure the distance to those stars which are close to the Sun and have measurable stellar parallax angle. For very distant stars the angle will be extremely small.

In the right triangle
#sinp=(1"AU")/d#
Using small-angle approximations that if #angle x# be expressed in radian and is very small: #sinxapproxx#,
#=>p'' approx \frac {1 \text{AU}} {d} \cdot 180 \cdot \frac{3600} {\pi}#
where #p# is measured in seconds of arc.

This also gives the definition of parsec, (pc), the distance for 1 second of arc of stellar parallax.

#d = 1 \text{AU}cdot 180 \cdot \frac{3600} {\pi}-=1"parsec"#