Question

Saturn has a number of rings around it. Assume each ring is due to particles following their own circular orbits around saturn. The radius of the inner most and outer most ring is nearly 7 x 10⁴ km and 1.35 x 10⁵ km respectively. What is the ratio of the time period of particles in the inner most and outer most ring?

(1) ~ 0.373

(2) ~ 2.68

(3) ~ 3.72

(4) ~ 0.27

Answer 1

(1) ~ 0.373

Let T₀ and T_i be the time period of the particle in the outer most and inner most ring respectively. Let R₀ and R_i be the corresponding radii of the orbit. Using Kepler’s third law.