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?

Asked by Abhisek | 1 year ago | 59

1 light year is the distance travelled by light in a year

1 light year = 3 x 108 x 365 x 24 x 60 x 60

= 9.46 x 10^{15} m

Therefore, distance travelled by light in 4.29 light years

= 4.29 x 9.46 x 10^{15} = 4.058 x 10^{16} m

Parsec is also a unit of distance

1 parsec = 3.08 x 10^{16} m

Therefore, the distance travelled by light in parsec is given as

4.29 light years =\( \dfrac{4.508 \times 10^{16}}{3.80 \times 10^{16}}\)

= 1.318 parsec = 1.32 parsec.

Using the relation,

θ = \( \dfrac{d}{D}\)

here,

d is the diameter of Earths orbit, d = 3 × 10^{11} m

D is the distance of the star from the earth,

D = 405868.32 × 10^{11} m

θ = \(
\dfrac{ 3 × 10^{11}}{405868.32 × 10^{11}}\) = 7.39 × 10^{-6} rad

But the angle covered in 1 sec = 4.85 × 10^{–6} rad

7.39 × 10^{-6} rad = \(
\dfrac{ 7.39 \times 10^{-6}}{4.85 \times 10^{-6}}\)^{\(\) }= 1.52″

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