Question

The sun's angular diameter is measured to be 1920".
The distance D of the sun from the earth is 1.496*10^11.Find the diameter of the sun.[hint d is directly proportional to D]

Answer 1

angular diameter is the angle subtended by the diameter of the Sun planet at the eyes of a viewer.

     δ = angular diameter in radians
     d = actual diameter of Sun planet
    D = distance between the surface of Earth and Sun. = 1.496 * 10^11 meters

    tan δ/2 =  (d/2) / D 
  
  δ in radians = δ in arcseconds / 3600  * π/180  = 1920/3600* π/180 radians

   d = 2 D  tan δ/2 = 1.39 *10^9 meters
           = 1.390 &10^6  km

Earth's diameter = 12,742 km
Sun's diameter is around 109 times Earth's.  so it is 1388872 km
       = 1.388 * 10^6 km

So the calculated figure and the diameter from the book are matching nearly.