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
the Jupiter.
1051ml​

Answer 1

Answer: 1.435 × 10⁵ km

Explanation:

Distance of Jupiter from Earth,

D = 824.7 × 10⁶ km

= 824.7 × 10⁹ m

Angular diameter = 35.72" = 35.72 × 4.874 ×

10⁶ rad

Diameter of Jupiter = d

Using the relation

¤ = d/D

d= ¤D = 824.7 × 10⁹ × 35.72 × 872 × 10-⁶

= 143520.76 × 10³ m

= 1.435 × 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