Question

Prob. 1. The angular diameter of Jupiter is 36 second of arc. If the distance of Jupiter from the
earth is 8.25 x 108 km, find the diameter of the Jupiter.​

Answer 1

Given:

The angular diameter of Jupiter is 36 second of arc. The distance of Jupiter from the

earth is 8.25 x 10^8 km.

To find:

Diameter of Jupiter

Calculation:

First, we need to convert angular diameter from arc second unit to radians:

$\therefore \: 36 \: arc \: sec$

$= \: \dfrac{36 \times 2\pi}{360 \times 60 \times 60}$

$= \: 36 \times 4.874 \times {10}^{ - 6} \: rad$

$= \: 175.46 \times {10}^{ - 6} \: rad$

Let diameter of Jupiter be d ;

$\therefore \: \theta = \dfrac{d}{D}$

$= > \: d = \theta \times D$

$= > \: d = 176.46 \times {10}^{ - 6} \times 8.25 \times {10}^{8}$

$= > \: d = 1447.578 \times {10}^{2} \: km$

$= > d = 144757.8 \: km$

So, final answer is

$\boxed{ \sf{ \large{d = 144757.8 \: km}}}$