Question

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.

Answer 1

Distance of Jupiter from the Earth, $D=824.7\times {10}^{6}km$

Angular diameter ${35.72}^{\prime \prime }=35.72\times 4.874\times {10}^{-6}rad$

Diameter of Jupiter = d

Using the relation,

$\theta$ = d/ D

$d=\theta$ D = 824.7 x ${10}^9$ x 35.72 x 4.872 x ${10}^{-6}$ = 143520.76 x ${10}^3$ = 1.435 x ${10}^5$ Km