The sun's angular diameter is measured to be 1920'' ( 1920 seconds) . The distance D of sun from the earth is 1.496 × 10^11m . Find the diameter of the sum.

Asked by arunavamitra50 | 17th Apr, 2018, 09:33: AM

Expert Answer:

 
Given:
D = 1.496 × 1011 m
theta = 1920 seconds
 
Solution:
 
The distance D from the Earth to the Sun is very large.
This makes the diameter of the Sun 'd' almost like a straight line.
Also, the value of theta also gets reduced due to the the very large distance of 'D'.
Such an orientation makes it a right angled triangle.
 
Using the definition of trigonometric ratios we get,
 
tan (theta) = d / D ... (1)
As theta is negligible, tan (theta) is also redundant.
 
Thus 
tan (theta) = theta ...(2)
Applying (2) in (1)
 
(theta) = d / D ...(3)
 
converting theta from seconds to degrees,
theta in degrees = 1920 seconds / (60 x 60) = 0.53
 
converting theta in degrees to radians for calculation,
theta in radians = 0.53 x π/180 = 0.0093 
 
Using (3)
d = D x theta in radians
d= 1.496 × 1011 m x 0.0093 radians
d= 1.39 x 109 m 
 
 

Answered by Abhijeet Mishra | 17th Apr, 2018, 02:59: PM