Question

Calculate the parallax of a star (in $\text{sec}$) at the distance of $4.29$ light years when viewed from two locations of earth six months apart in its orbit around the sun. Answer upto 2 places of decimal ( Assume diameter of earths orbit around sun to be $3\times {10}^{11}\text{m}$)

Answer 1

In an orbit around the sun, the distance between six months apart locations is diameter of the Earth orbit itself which is $3\times {10}^{11}\text{m}$.
Now, using parallax method
$\therefore \theta =\frac{d}{D}=\frac{3\times {10}^{11}}{x}$
$=\frac{3\times {10}^{11}}{4.29\times 9.46\times {10}^{15}}\text{rad}$
$=1.512\text{sec}$