Question

A star is located a light year away from us.what is its distance in parsec .what is the parallax shown by this star when viewed from to locations 3×10^11m

Answer 1

Hey.

Here is the answer.

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Distance of the star from us = 1 ly

1 light year is the distance travelled by light in one year.

So, 1 light year = Speed of light × 1 year

= 3 × 10^8 × 365 × 24 × 60 × 60

= 94608 × 10^11 m

∵ 1 parsec = 3.08 × 10^16 m

∴ 1 ly = 94608 × 10^11 / 3.08×10^16 parsec

= 0.30716883 parsec

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Now, Using the relation,

θ = d / D

where,
Star is viewed from , d = 3 × 10^11 m

Distance of the star from the earth,

D = 94608 × 10^11 m

∴ θ = 3 × 10^11 / 94608 × 10^11 rad

= 3.17 × 10^-6 rad

But, 1 sec = 4.85 × 10^–6 rad

∴ 3.17 × 10^-6 rad = 3.17 × 10^-6 / 4.85 × 10^-6 sec

= 0.653 sec

Hence, the parallax shown by the star is of 0.653 sec when viewed from the given distance.

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Thanks.