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.

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

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aristeus aristeus · Answer 2 · 2019-10-22T08:10:57+02:00

Answer:

The ratio of speed will be 0.408

Explanation:

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

So [tex]R_A=6R_B[/tex]

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

As [tex]R_A=6R_B[/tex]

So [tex]v_A=\sqrt{\frac{GM}{6R_B}}[/tex]-----EQN 1

Speed of planet B [tex]v_B=\sqrt{\frac{GM}{R_B}}[/tex]------RQN 2

Dividing equation 1 by equation 2

[tex]\frac{v_A}{V_B}=\sqrt{\frac{1}{6}}[/tex]

[tex]\frac{v_A}{V_B}=0.408[/tex]

So the ratio of speed will be 0.408