Question

The Earth has a radius of RE 6371 km and an average density of E 5:514 g cm 3 . Jupiter is much bigger and heavier with a radius of RJ 70000 km and an average density of J 1326 kg m 3 . Use these values to answer following questions (write down your steps): (a). Approximately how many Earths fit into Jupiter (by volume)? (b). How many times heavier is Jupiter compared to Earth?

Answer 1

(a) volume of Jupiter = N × volume of earth

or, 4/3πR³ = N × 4/3πr³

or ,R³ = N × r³

or, N = (R/r)³ = (70000/6371)= 1326.39

hence, there are 1326 earths fit into Jupiter .

(b) mass of Jupiter /mass of earth = (volume of Jupiter × density of Jupiter)/(volume of earth × density of earth)

= (4/3πR³ × 1.326 )/(4/3πr³ × 5.51)

= R³ × 1.326/r³ × 5.51

= (7000/6371)³ × (1.326/5.51)

= 319.2 ≈ 319

hence, mass of Jupiter = 319 × mass of earth