Is central motion stable with criteria for force function f(r)?

[LagrangeEuler]

In central motion we have criteria for stability. For function of force $$f(r)$$
we have stability if
$$f'(r)+\frac{3}{r}>0$$

This is stability in what sence? Do I have then periodic orbits or what? Is it in some connection with calculations of Lyapunov exponent? Thanks for the answer.

 

[ShayanJ]

Stability in the sense that if you give the satellite a little push, it doesn't escape the orbit, rather it oscillates in the radial direction, while orbiting!(Just imagine a sinusoid with a circle as the x axis!)