Question

(a) One of the moons of Jupiter, named Io, has an orbital radius of 4.22 ✕ 108 m and a period of 1.77 days. Assuming the orbit is circular, calculate the mass of Jupiter. _____kg

(b) The largest moon of Jupiter, named Ganymede, has an orbital radius of 1.07 ✕ 109 m and a period of 7.16 days. Calculate the mass of Jupiter from this data. _____kg

(c) Are your results to parts (a) and (b) consistent? Yes?/No?

Explain.

Answer 1

here,

a)

the radius of lo , r1 = 4.22 * 10^8 m

the period , T1 = 1.77 days = 1.77 * 24 * 3600 s

let the mass of jupiter be M

T1 = 2*pi*sqrt(r1^3 /(G * M))

1.77 * 24 * 3600 = 2 *pi * sqrt((4.22 * 10^8 )^3 /(6.67 * 10^-11 * M))

solving for M

M = 1.9 * 10^27 kg

the mass of Jupiter is 1.9 * 10^27 kg

b)

the radius of Ganymede , r2 = 1.07 * 10^9 m

the period , T1 = 7.16 days = 7.16 * 24 * 3600 s

let the mass of jupiter be M

T1 = 2*pi*sqrt(r1^3 /(G * M))

7.16 * 24 * 3600 = 2 *pi * sqrt((1.07 * 10^9 )^3 /(6.67 * 10^-11 * M))

solving for M

M = 1.9 * 10^27 kg

the mass of Jupiter is 1.9 * 10^27 kg

c)

YES , the answer of part A and part B is consistent