  The long-term dynamical evolution is a crucial point in recent planetary
research. Although the amount of observational data is continuously growing and
the precision allows us to obtain accurate planetary orbits, the canonical
stability analysis still requires N-body simulations and phase space trajectory
investigations. We propose a method for stability analysis of planetary motion
based on the generalized R\'enyi entropy obtained from a scalar measurement.
The radial velocity data of the central body in the gravitational three-body
problem is used as the basis of a phase space reconstruction procedure. Then,
Poincar\'e's recurrence theorem contributes to finding a natural partitioning
in the reconstructed phase space to obtain the R\'enyi entropy. It turns out
that the entropy-based stability analysis is in good agreement with other chaos
detection methods, and it requires only a few tens of thousands of orbital
period integration time.
