Question

A star has a parallax angle $p$ of 0.723 arcseconds. What is the distance of the star?
(a) 1.38 parsecs
(b) 2.38 parsecs
(c) 3.38 parsecs
(d) 4.38 parsecs

Answer 1

In this solution we are going to use the relationship between star’s distance and its parallax angle.
In the relation , we put the value of distance in parsec and value of parallax angle in arcseconds.

Complete Step by Step Answer: Given:
Parallax angle $p = 0.723\;{\mathop{\rm arcsec}\nolimits} onds$
The formula used to calculate distance of star is given as:
Distance $d = \dfrac{1}{p}\;\;\;........(1)$
Where $d$is distance of star (in parsec) and$p$is parallax angle
Substituting the value of $p$ in equation (1), we get,
$\begin{array}{l} d = \dfrac{1}{{0.723\;{\rm{arcseceond}}}}\\\ d = 1.38\;{\rm{parsec}} \end{array}$
Therefore, the distance of star is $1.38\;{\rm{parsec}}$
Additional Information:
Parallax is an effective method to find the distance of a star by measuring the angle it subtends. Parallax is the apparent change in the position of an object because of change in the position of the observer.
The distance calculated using parallax method is generally given in the units of parsecs (or parallax seconds). One parsec is the distance from where any object (star or planet) has a parallax angle of one arcseconds.
Keep in mind that parallax methods have limitations like, it is only applicable to objects or stars closer to the earth because farther the star smaller will be the parallax and lesser will be the accuracy. We generally avoid using parallax method to measure the distance if parallax angle is less than 0.01 arcseconds.

Note: Remember that, in the formula $d = \dfrac{1}{p}$; the value of $d$must be in parsecs only. Many-a-times,the distance of the star is given in units of light-years and parallax angle is asked. In such questions, first change the units of distance from light-years to parsecs ( $1\;ly = 0.31\;par\sec s$) and then substitute it in the formula.