Planet a and planet b are in circular orbits around a distant star. planet a is 4.5 times farther from the star than is planet b.
what is the ratio of their speeds va/vb?

If we base this on Kepler's Third Law, then t^2 = r^3
So, if we increase the distance (r) by a factor of 4.5 then the time (t) will be increased by a factor of (4.5) ^ (3/2) or (4.5) ^ (1.5)
4.5 ^ 1.5 = 9.55
So their velocity (and their orbital time) would be in the ratio of 9.55 : 1

The answer it dorneo dodneurekd r egg rorne