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?

#### Solution

Distance of the star from the solar system = 4.29 ly

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

1 light year = Speed of light × 1 year

= 3 × 10^{8} × 365 × 24 × 60 × 60 = 94608 × 10^{11} m

∴4.29 ly = 405868.32 × 10^{11} m

∵1 parsec = 3.08 × 10^{16} m

:. 4.29 ly = `(405868.32 xx 10^(11))/(3.08xx 10^(16))`

Using the relation.

`theta = d/D`

where

Diameter of Earth's orbit, `d = 3 xx 10^(11) m`

Distance of the star from the Earth, D = `405868.32 xx 10^(11) m`

`:. theta = (3 xx 10^(11))/(405868.32xx 10^(11)) = 7.39 xx 10^(-6) rad`

But, 1 sec = 4.85 × 10^{–6} rad

`:. 7.39 xx 10^(-6) rad = (7.39 xx 10^(-6))/(4.85xx10^(-6)) = 1.52`