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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.
NCERT Solutions for Class 11 Physics Part 1 Chapter 2 Exercise 24



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Angular diameter is the angle subtended by the diameter of the planet at the eye..
let the angular diameter be Ф.

Let the eye be at A,  the center of the planet be O, and the diameter of the planet perpendicular to the line AO be BOC.

   Ф = angular diameter = angle CAB = 2 * angle OAC
     OB = OC = radius of the planet.
       AO = 824.7 million km

   tan (Ф/2) =   OB / OA

  Diameter of Jupiter = 2 * OB = 2 * 824.7 * 10⁶ * tan [ 35.72 / (2 * 60 *  60) ]⁰
                     =   142, 817.8 km

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