Question

Planet A and Planet B are in circular orbits around a distant star. Planet A is 6.0 times farther from the star than Planet B. Find the ratio of their speeds. Va/Vb.

Answer 1

The answer is easy if you know the physics. 



a/a' = (r/R)^2 = (r/9r)^2 = 1/81; so that a = a'/81.
A's radial acceleration must be 1/81 of B's. And each acceleration is a = v^2/R and a' = V^2/r, where v and V are the tangential speeds you want the ratio for. 

a = v^2/R = v^2/9r = V^2/81r = a'/81 In which case v^2/V^2 = 9/81 = 1/9; so that 1/3 = Va/Vb ANS

Answer 2

Answer:

The ratio of speed will be 0.408

Explanation:

We have given that Planet A is 6 times farther than planet B

So $R_A=6R_B$

We know that speed is given by $v_A=\sqrt{\frac{GM}{R_A}}$, here G is gravitational constant and $R_A$ is distance from star to planet A

As $R_A=6R_B$

So $v_A=\sqrt{\frac{GM}{6R_B}}$-----EQN 1

Speed of planet B $v_B=\sqrt{\frac{GM}{R_B}}$------RQN 2

Dividing equation 1 by equation 2

$\frac{v_A}{V_B}=\sqrt{\frac{1}{6}}$

$\frac{v_A}{V_B}=0.408$

So the ratio of speed will be 0.408