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HELP! How much orbits will the inner rings of saturn (1.1 Rsaturn) make in the time it takes the outer rings..?

• How much orbits will the inner rings of saturn (1.1 Rsaturn) make in the time it takes the outer rings (8 Rsaturn) to complete one orbit? a) 0.051 orbits b) 0.14 orbits c)1.0 orbits d) 7.2 orbits e) 19.6 orbits

• Answer:

  Kepler's 3rd Law applies here. That is, the cube of the orbital radius is proportional to the square of the orbital period. If we let "k" be the constant of proportionality, we can write the relation as: R³ = kP² So, for the inner rings: (R_inner)³ = k(P_inner)² or, since R_inner = 1.1 Rsaturn: (1.1 Rsaturn)³ = k(P_inner)² And for the outer rings: (R_outer)³ = k(P_outer)² or, since R_outer = 8 Rsaturn: (8 Rsaturn)³ = k(P_outer)² So these are your equations: (1.1 Rsaturn)³ = k(P_inner)² (8 Rsaturn)³ = k(P_outer)² The answer to your query is P_outer / P_inner. So combine the equations above and solve for "P_outer/P_inner" (hint: start by dividing the 2nd equation by the 1st equation). That will give you one of the indicated numbers.