Conversion : We know that
1 light year = 9.46 × 1015 m
∴ 4.29 light years = 4.29 × 9.46 × 1015
= 4.058 × 1016 m
Also, 1 parsec = 3.08 × 1016 m
∴ 4.29 light year = \(\frac{4.058\times10^{16}}{3.08\times10^{16}}\)
= 1.318 parsec
= 1.32 parsec
(b) Parallax− In six months, the distance between two observations will be equal to the diameter of the orbit, i.e.
2 × radius of orbit
2 AU = 2 × 1.496 × 1011 m
Using, θ = \(\frac{b}{D}\)
where b = 2 × 1.496 × 1011 m
and D = 4.058 × 1016
we get, θ = \(\frac{2\times1.496\times10^{11}}{4.058\times10^{16}}\)
= 7.37 × 10-6 rad
= 7.37 × 10-6 × \(\frac{180\times60\times60}{\pi}\)
= 1.52 second of arc.