Question

The angular diameter for a star is measured to be 1920' ' . The distance of the star is from the earth is $1.5\times {10}^{11}m$. The diameter of the star is (in km) (approximately)

• A. $1.4\times {10}^6$
• B. $1.6\times {10}^5$
• C. $1.8\times {10}^6$
• D. $1.5\times {10}^5$

Answer 1

Answer: (A)

$1.4\times {10}^6$

REF.Image

$\theta ={1920}^{11}$

$=\frac{1920}{3600}\times \frac{\pi }{180}$

$=9.3\times {10}^{-3}$ redian

$d=1.5\times {10}^{11}m$

$=1.5\times {10}^{11}\times {10}^{-3}km$

$=1.5\times {10}^{8}km$

$\theta =\frac{D}{d}$

$D=\theta d$

$=9.3\times {10}^{-3}\times 1.5\times {10}^8$

$=13.95\times {10}^5$

$=1.395\times {10}^{6}km$