Data for two major moons of Jupiter are given below: • Io: orbital period

PHYSICS · Multi-part · CBSE · Physics · Gravitation · Gravitation

Problem

T_1 = 1.77\,\text{d}

, mean orbital radius

r_1 = 4.22\times10^{8}\,\text{m}

• Europa: orbital period

T_2 = 3.55\,\text{d}

, mean orbital radius

r_2 = 6.71\times10^{8}\,\text{m}

(i) Calculate

T^2

and

r^3

for each moon and tabulate the results. (ii) Show that the ratio

\dfrac{T^2}{r^3}

is nearly the same for both moons and state what this reveals about their motion. (iii) Using the common value of

\dfrac{T^2}{r^3}

obtained above, estimate the mean orbital radius of Ganymede, another Jovian moon whose orbital period is

7.15\,\text{d}