Question

when the planet Jupiter is at a distance of a 24.7 million kilometres from the Earth its angular diameter is measured to be 35.72" of 1 arc. Calculate the diameter of Jupiter ​

Answer 1

Given information:-

r = 824.7*10^6 km , Θ = 35.72" arc

To find

l = ?

Solution:-

First convert Θ value in kilometres.

$\frac{35.72}{3600} \times \frac{22}{ 7 \times 180} rad \\ \\ 824.7 \times 10 ^{6} km$

Note:- here, we divided by 3600 that is to convert in kilometres and then π\180 to convert in radian.

Now, Θ = l / r , r*Θ = l

$324.7 \times 10 ^{6} \times \frac{35.72}{3600} \times \frac{22}{7 \times 180} = l$

$= \frac{142.87 \times 10 ^{6} }{10 ^{3} }$

$= 142.87 \times 10 ^{3}$

So, when we convert in scientific notation then,

$= 1.42 \times 10 ^{5} km$

Therefore , Diameter of Jupiter = 1.42*10^5km