Question

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 x 10''m. 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 metres ?
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Answer 1

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Answer 2

Answer:

1 parsec = 3.086 × 10¹⁶metres

Explanation:

Parsec is basically a version of parallax with larger numbers.

Here we take, the mean radius of Earth's Orbit, i.e, one Astronomical Unit (AU) as the base and 1" as angle (in radian, the same would be 4.848×10-⁶ rad)

I AU = 149597871 km, roughly equal to 150 million km.

So, the equation will be

θ = Arclength/ Radius

4.848 × 10-⁶ = 1 parsec / 1 AU

⇒ 4.848 × 10-⁶ × 149597871 = 1 parsec

⇒ 1 parsec = 3.086 × 10¹⁶metres