Find 1 parsec in millions of km

Question

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

Hint given: the arc length (s) spanned by an angle of θ radians in a circle of radius r is given by s=rθ 



-Find 1 parsec in millions of km.

1 parsec= ___ millions of km

Answer 1

First change 1/3600 degrees to radians.

radians = degrees(pi/180) = (1/3600)(pi/180) = 4.85 x 10^(-6) radians

Now radius = arc length / radians = 150,000/0.00000485 = 3.09 x 10^13 or 30.9 trillion kilometers.