Alien artificial gravity

Classical Mechanics Level pending

In your interstellar travels, you have discovered an alien artifact that produces a very strange local gravitational field. You cautiously enter a circular orbit around the device.

As your ship maneuvers into different circular orbits near this device, you notice that the time it takes for you to complete one orbit is entirely independent of your orbital radius from the device!

Intrigued, you want to figure out how the gravitational acceleration caused by this device depends on distance from the device.

What value of \(n\) correctly gives the dependence of the artificial gravitational field strength \(\vec{g}\) on distance from the device \(r\) in the following expression?

\(\vec{g} \propto r^n\)


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