1. Stability for celestial objects is defined in terms of whether the
planet or other object will oscillate about a circular orbit after
being disturbed. It does not resume a circular orbit after
disturbance removed. The criteria for oscillation is f(a) +
(a/3)df/dr < 0 where a is radius and f is force. The radius will vary
repeatedly between r(max) and r(min) for inverse square type force.
See Fowles Jr/Sr level mechanics book.
2. Over a long time planets and stars cannot be considered as point
particles. The tidal interaction can change the separation and period
( Earth & Moon).