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Qmechanic
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What is wrong with this reasoning about angular velocity $\omega$?

Satellite $X$ orbits a planet with orbital radius R. Satellite Y orbits the same planet with orbital radius 2R. Satellites X and Y have the same mass.

What is $\frac{\text{centripetal acceleration of X}}{\text{centripetal acceleration of Y}}?$

My reasoning is that both satellites orbit the same planet, they have the same angular velocity $\omega$.

As such, $a_{c_x} = \frac{v_{x}^{2}}{r}$ where $v = \omega \cdot r$. Thus,

$$a_{c_x} = \frac{\omega^2 \cdot r^2}{r} \implies = \omega^2 \cdot r$$.

Doing the same thing for $a_{c_y} = \omega^2 \cdot 2r$.

Then, $$a_{c_x}/ a_{c_y} = \frac{1}{2}$$