  The purpose of this work is to study the phenomenon of tidal locking in a
pedagogical framework by analyzing the effective gravitational potential of a
two-body system with two spinning objects. It is shown that the effective
potential of such a system is an example of a fold catastrophe. In fact, the
existence of a local minimum and saddle point, corresponding to tidally-locked
circular orbits, is regulated by a single dimensionless control parameter which
depends on the properties of the two bodies and on the total angular momentum
of the system. The method described in this work results in compact expressions
for the radius of the circular orbit and the tidally-locked spin/orbital
frequency. The limiting case in which one of the two orbiting objects is
point-like is studied in detail. An analysis of the effective potential, which
in this limit depends on only two parameters, allows one to clearly visualize
the properties of the system. The notorious case of the Mars' moon Phobos is
presented as an example of a satellite that is past the no return point and,
therefore, will not reach a stable or unstable tidally-locked orbit.
