I'm Not Sure How to Solve This Physics Problem

Question

Two planets in circular orbits around a star have speeds of v and 7v. (a) What is the ratio of the orbital radii of the planets? (b) What is the ratio of their periods?

Answer 1

Recall that orbital velocities/speeds depend on the mass of the host star only:

v = √(GM/r)

where G is the gravitational constant, M is the mass, and r is the orbital radius.

(a) Solve this for radius, substitute their speeds respectively, and take the ratio of the two radii for each planet.

(b) Do the same using the orbital period formula: T = 2πr/v