Question

Jupiter’s moon, Ganymede takes 7.15 Earth days to orbit Jupiter. Ganymede is measured to be 7.1 X 10-3 AU from Jupiter’s center. A second moon of Jupiter, Callisto, takes 16.69 Earth days to orbit Jupiter. How far away is Callisto from the center of Jupiter?

Answer 1

0.0124 AU

Step-by-step explanation:

Ganymede takes 7.15 Earth days to orbit Jupiter. Ganymede is measured to be 7.1 X 10⁻³ AU from Jupiter’s center.

We need to find how far away is Callisto from the center of Jupiter if a second moon of Jupiter, Callisto, takes 16.69 Earth days to orbit Jupiter. Let it is r₂. Using third law of Kepler.

`T^2\propto r^3`

i.e.

`((T_1)/(T_2))^2=((r_1)/(r_2))^3\\\\(r_1)/(r_2)=((T_1)/(T_2))^(2/3)\\\\r_2=(r_1)/(((T_1)/(T_2))^(2/3))\\\\r_2=(7.1* 10^(-3))/(((7.15)/(16.69))^(2/3))\\\\r_2=0.0124\ \text{AU}`

So, Callisto is 0.0124 AU from the center of the Jupiter.