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A star is 1.45 parsec light years away. How much parallax would this star show when viewed from two locations of the earth six months apart in its orbit around the sun?

A
2 Parsec
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B
0.725 Parsec
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C
1.45 Parsec
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D
2.9 Parsec
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Solution

The correct option is A 2 Parsec
One light year = speed of light × one year
or 1ly=3×108×(24×3600)=94608×1011m
So, 4.29ly=4.29×(94608×1011)=4.058×1016m
As 1 parsec =3.08×1016m
(Parsec is a unit of length used to measure large distances to objects outside our Solar System)
Thus, 4.29ly=4.058×10163.08×1016=1.32 parsec
Now angular displacement , θ=dD
where d= diameter of earth's orbit =3×1011m and
D= distance of star from the earth =4.058×1016m
So, θ=3×10114.058×1016=7.39×106 rad
As 1sec=4.85×106rad so, 7.39×106rad=7.39×1064.85×106=1.52sec

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