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प्रश्न
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?
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उत्तर
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`
संबंधित प्रश्न
The principle of ‘parallax’ in section 2.3.1 is used in the determination of distances of very distant stars. The baseline AB is the line joining the Earth’s two locations six months apart in its orbit around the Sun. That is, the baseline is about the diameter of the Earth’s orbit ≈ 3 × 1011m. However, even the nearest stars are so distant that with such a long baseline, they show parallax only of the order of 1” (second) of arc or so. A parsec is a convenient unit of length on the astronomical scale. It is the distance of an object that will show a parallax of 1” (second) of arc from opposite ends of a baseline equal to the distance from the Earth to the Sun. How much is a parsec in terms of meters?
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