Question

when jupiter is a distance of 630 million kilometres from earth (4.2 astronomical units), it has an apparent angular diameter of 46 arcseconds (46/3600 of degree). Calculate jupiter's diameter in kilometers, and state how many times larger this is than diameter of earth

Answer 1

Answer:

Jupiter's diameter is 11 times greater than that of Earth

Explanation:

Given,

The distance between Jupiter and earth is 630 million km = D  $630\times10^6$ km

Let, the angular diameter be  a = 46 arcseconds

Diameter of Jupiter be d

We know that Earth’s diameter = 12,742 km

According to the formula;

a (in arcseconds) =   $206265 * \frac{d}{D}$

Substituting all the values in the equation;

46 = $206265 * \frac{d}{630 * 10^{6}}$

Calculating for d;

d =  $630^{*} 10^{6} * \frac{46}{206265}$

d = 140,498.8728092502 km

The diameter of Jupiter is 140498.87 km

$\frac{\text {Jupiter}}{\text {Earth}}=\frac{140498.87}{12742}=11$

Therefore, Jupiter’s diameter is 11 times greater than Earth’s diameter.