Question 2.24
NCERT Class XI Physics
When the planet Jupiter is at a distance of 824.7 million kilometers from the Earth, its angular diameter is measured to be 35.72" of arc. Calculate the diameter of Jupiter.
Solution in Brief
(detailed solution given after the video below)
Parallax angle is small so parallax formula b = D θ is applicable. Substituting, b = (824.7 x 10^6 km) x 35.72" and using 1" = 4.85 x 10^-6 radians, we get b = 1.429 x 10^8 meters (Answer).
Video Explanation
Please watch this youtube video for a quick explanation of the solution:
Solution in Detail
$ \begin{aligned} &\text{Given, }\\ &\text{(i) parallax angle } \theta = 35.72\rq\rq\\ &\text{(ii) distance } D = 824.7 \times 10^6 \text{ km}\\ &\text{SF in D} =4 \text{, and SF in } \theta = 4\\\\ &\text{by parallax equation } b = D \times \theta\\\\ &\therefore b = 824.7 \times 10^6 \text{ km} \times 35.72\rq\rq\\\\ &\text{but } 1\rq\rq = 4.85 \times 10^{-6} \text{ rad}\\ &\text{and } 1\text{ km} = 1000 \text{ m}\\\\ &\therefore b = 824.7 \times 10^9 \times 35.72 \times 4.85 \times 10^{-6}\\ &b = 1.42872 \times 10^8 \text{ m}\\\\ &\text{due to multiplication, SF in } b \\ &\text{will be min(D, } \theta \text{), i.e., } 4\\\\ &\text{rounding, } b = 1.429 \times 10^8 \text{ m} \:\underline{Ans} \end{aligned} $
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