Convert 4.29 light years into parsecs. Calculate the parallax of a sta

1.	Convert 4.29 light years into parsecs. Calculate the parallax of a star at the distance when viewed from two locations of earth six months apart in its orbit around sun.
Answer» 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 × 10¹¹m 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.

Convert 4.29 light years into parsecs. Calculate the parallax of a star at the distance when viewed from two locations of earth six months apart in its orbit around sun.

Answer»

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 × 10¹¹m

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.