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?

Given,

Distance of the nearest star, d = 4.29 ly

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

∴ 1 ly = Speed of light × 1 yr

⇒ 1 ly = 3 × 10⁸ m s^-1 × (365 × 24 × 60 × 60 s)

⇒ 1 ly = 9.46 × 10¹⁵ m

So, d = 4.29 × 9.46 × 10¹⁵ m

⇒ d = 4.058 × 10¹⁶ m

We know, 1 parsec = 3.09 × 10¹⁶ m

So,

⇒ d = 1.313 parsec

We know,

where, θ is the parallax angle

l is the diameter of the Earth’s orbit = 3 × 10¹¹ m

d is the distance of the star from Earth

∴

⇒ θ = 7.39 × 10^-6 rad

⇒

∴ θ = (7.39 × 10^-6 rad)/(π/648000 rad)

⇒ θ = 1.52”

NOTE: It is to be noted that a lightyear is a unit of distance and not time.

Parallax is a difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines of sight.