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

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

Step-by-step explanation:

Given,

The distance between Jupiter and earth is 630 million km = D
`630*10^6` 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 * (d)/(D)`

Substituting all the values in the equation;

46 =
`206265 * (d)/(630 * 10^(6))`

Calculating for d;

d =
`630^(*) 10^(6) * (46)/(206265)`

d = 140,498.8728092502 km

The diameter of Jupiter is 140498.87 km

`\frac{\text {Jupiter}}{\text {Earth}}=(140498.87)/(12742)=11`

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