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प्रश्न
Consider a sunlike star at a distance of 2 parsecs. When it is seen through a telescope with 100 magnification, what should be the angular size of the star? Sun appears to be (1/2)° from the earth. Due to atmospheric fluctuations, eye can’t resolve objects smaller than 1 arc minute.
उत्तर
The angle of the sun's diameter `(1/2)^circ` is subtended by 1 A.U. since the distance from the sun increases angle subtended in the same ratio.
Now, 2 x 105 A.U. will from an angle of θ = `(1/(4 xx 10^5))^circ`, since the diameter is the same angle subtended on earth by 1 parsec will be same.
If the sunlike star is at 2 parsec the angle becomes half = (1.25 × 10–6)°
Thus, angle = 75 × 10–6 min
When it is seen with a telescope that has a magnification of 100, the angle formed will be 7.5 × 10–3 min, viz., less than a minute.
Hence, it can't be observed by a telescope.
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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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