Your own "Orbit"

You are huge fanboy of physics experiment and love to play with gravity (No, not that movie). Your next mission is to orbit the a custom planet of specified density, and radius, manually, as efficient as possible.

What is the minimum height (in metre) you have to reach in order to have a stable orbit with a velocity $5 \text {ms}^{-1}$ above the planet surface ?

Details and Assumptions

• Radius of the planet ( $R_p$ ) = 4km
• Density of the planet is same as that of earth, $\rho_p = 5.5 \text{g cm}^{-3}$
• The planet is assumed to be spherical in shape with uniform density
• No atmosphere, drag, friction or any kind of resisting force