Question

The Earth has a radius of RE ≈ 6371 km and an average density of ρE ≈ 5.514 g/
cm3
. Jupiter is
much bigger and heavier with a radius ofRJ ≈ 70000 kmand an average density of ρJ ≈ 1326 kg/
m3
.
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

Answer:

a) Approximately 1326 number of earths can fit into jupiter

b) jupiter is 318.9 times heavier than earth.

Explanation:

a) Volume of jupiter = 4πR³/3

Volume of Earth = 4πr³/3

If n number of earth can fit into jupiter, then the volume of n number of earths combine will be equal to volume of jupiter,

=> n x Volume of Earth = Volume of jupiter

=> n x 4πr³/3 = 4πR³/3

=> n = (R/r)³ = (70000/6371)³ = 1326.4 ≈ 1326

Hence Approximately 1326 number of earths can fit into jupiter

b) density of earth = 5.514 g/cm³ = 5514 kg/m³

we know that mass is defined as the product of density and volume

i.e. mass = density x volume

=> Mass of jupiter/mass of earth = [(density of jupiter)/ (density of earth)] x [(volume of jupiter)/ (volume of earth)]

=> Mj/Me = (1326/5514) x 1326 = 318.9

hence jupiter is 318.9 times heavier than earth.