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.