Problem 8 on Units & Dimensions

Description:

Problem

The nearest star to our solar system is 4.29 light years away. How much parallax would this star show when viewed from two locations of the Earth six months apart in its orbit around Sun?

(Given: Diameter of Earth’s orbit: 3 × 10¹¹m)

Solution

Visualizing the problem −

Converting light years to meters,

4.29 ly = 4.29 × 3 × 10⁸ × 365 × 24 × 3600 = 4.06 × 10¹⁶ m

Now,

θ(in radians) = b/d = 3 × 10¹¹/4.06 × 10¹⁶

θ = 7.39 × 10^-6rad = 1.52"