Question

Suppose you measure the parallax angle for a particular star to be 0.1 arcsecond. The distance to this star is

Answer 1

Answer: 10 parsecs

Parallax is the angle formed by the observation lines to a very distant object from two separated points.

The procedure to measure this distance in the case of a star, is based on observing it from two different places far away from each other, and then through trigonometry reach to the following relationship:

$d=\frac{r}{sin(p)}$    (1)

Where:

$d$ is the distance from Earth to the observed star (in Parsecs $1pc=206265AU$)

$r$ is the earth-sun distance that is equivalent to an astronomical unit (1AU=150000000km)

$p$ is the angle of the parallax (in arc seconds $''$)

Now, the distance to an object (measured in parsecs) is the reciprocal of the parallax (measured in arcseconds).

Then, in its simplified mode, the stellar parallax is given by the following equation:

$d=\frac{1}{p}$ (2)

$d=\frac{1}{0.1''}$

Finally we have the distance to the star:

$d=10pc$