Planet and Satellite: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Planet and Satellite. Understanding the underlying formula is key to arriving at the correct answer below:

Gravitational force provides the centripetal force: $$\frac{GMm}{r^2} = m\omega^2r$$.nSince $$g = \frac{GM}{R^2}$$, we can write $$GM = gR^2$$.nSubstituting this gives $$\frac{gR^2}{r^2} = \omega^2r \Rightarrow r^3 = \frac{gR^2}{\omega^2} \Rightarrow r = (\frac{R^2g}{\omega^2})^{\frac{1}{3}}$$.