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Question
The nearest star to our solar system is 4.29 light years away. How much is this distance in terms of parsecs? How much parallax would this star (named Alpha Centauri) show when viewed from two locations of the Earth six months apart in its orbit around the Sun?
Solution
Distance of the star from the solar system = 4.29 ly
1 light year is the distance travelled by light in one year.
1 light year = Speed of light × 1 year
= 3 × 108 × 365 × 24 × 60 × 60 = 94608 × 1011 m
∴4.29 ly = 405868.32 × 1011 m
∵1 parsec = 3.08 × 1016 m
:. 4.29 ly = `(405868.32 xx 10^(11))/(3.08xx 10^(16))`
Using the relation.
`theta = d/D`
where
Diameter of Earth's orbit, `d = 3 xx 10^(11) m`
Distance of the star from the Earth, D = `405868.32 xx 10^(11) m`
`:. theta = (3 xx 10^(11))/(405868.32xx 10^(11)) = 7.39 xx 10^(-6) rad`
But, 1 sec = 4.85 × 10–6 rad
`:. 7.39 xx 10^(-6) rad = (7.39 xx 10^(-6))/(4.85xx10^(-6)) = 1.52`
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