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Satellites A and B orbit the Earth in circles, and B's radius is 9 times A's…

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Satellites A and B orbit the Earth in circles, and B's radius is $9$ times A's. Find the ratios $\dfrac{v_B}{v_A}$ , $\dfrac{T_B}{T_A}$ and $\dfrac{\omega_B}{\omega_A}$ , and, for equal masses, $\dfrac{K_B}{K_A}$ .

Need a reminder? The key ideaShow

In a circular orbit of radius $r$ : $v = \sqrt{\dfrac{GM}{r}}$ , $T = 2\pi\sqrt{\dfrac{r^3}{GM}}$ , independent of the satellite's mass. Its energies: $K = \dfrac{GMm}{2r}$ , $U = -2K$ , $E = -K$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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