Question

Define Parallex method on the basis of this solve, the nearest star to our solar system is 4.29 light years away. how much is this distance in terms of par sec? How much parallex would this star show when viewed from two locations of the earth six months apart in its orbit around the sun.

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Answer 1

$$\begin{gathered} Dis\tan ceofthestarfromsolarsystemis4.29lightyear \\ weknow \\ 3.26lightyear=1parsec \\ 4.29lightyear=\frac{1\times 4.29}{3.26}=1.31parsec. \\ dis\tan ceofthestarisr=1.31parsec \\ in6months,earthcoversthedis\tan ce470\times {10}^{9}maroundthesun. \\ arclengthl=470\times {10}^{9}m \\ 1.5\times {10}^{11}m=1A.U. \\ 470\times {10}^{9}m=\frac{1}{1.5\times {10}^{11}}\times 470\times {10}^{9}AU=3.13AU \\ l=3.13AU \\ parallex\left(\theta \right)=\frac{l}{r} \\ \theta =\frac{3.13}{1.31} \\ \theta =2.3" \\ \theta =2.3second \end{gathered}$$