Calculating Orbital Velocity Ratios for Planets A and B

[mariners02]

Planet A and planet B are in circular orbits around a distant star. Planet A is 8.5 times farther from the star than is planet B. What is the ratio of their speeds Va/Vb

This problem seems very simple, thought i could just use F=1/r^2, find the difference in forces, which would also be the difference in velocity. Can anyone explain the error in my thinking?

 

[qraal]

Planet A and planet B are in circular orbits around a distant star. Planet A is 8.5 times farther from the star than is planet B. What is the ratio of their speeds Va/Vb

This problem seems very simple, thought i could just use F=1/r^2, find the difference in forces, which would also be the difference in velocity. Can anyone explain the error in my thinking?

The problem is that the force is proportional to the velocity squared divided by the radius. Thus the velocity squared is proportional to the inverse of the radius.

 

[mariners02]

So i could just do V=Sqrt(1/8.5)=.35?