Question

when the planet Jupiter is at a distance of 824.7 million kilometer from the earth, it's angular diameter is measured to be 35.72" of arc. calculate the diameter of Jupiter ​

Answer 1

Answer:

Distance of Jupiter from the Earth, D=824.7×10

6

km

Angular diameter 35.72

′′

=35.72×4.874×10

−6

rad

Diameter of Jupiter = d

Using the relation,

θ = d/ D

d=θ 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

Answer 2

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