Find to one decimal place to Proxima Centauri distance in parsecs.

Question

Astronomers measure large distances in parsecs. (One parsec is the radius of a circle for which an arc of angle 1/3600° has length equal to the distance from Earth to the sun, about 150 million kilometers.)

Proxima Centauri, our nearest star except for the sun, is about 4·10¹³ km from Earth. Find to one decimal place its distance in parsecs.

Answer 1

(1/3600) of a degree is equivalent to 4.84813x10^-6 radians.

Arc length = angle (in radians) x radius

150,000,000 = 4.84813x10^-6 x radius

radius = 3.093976 x 10¹³ km (= 1 parsec)

Distance = 4x10¹³ km ÷ 3.093976 x 10¹³ km = 1.3 parsecs