  The objective of this paper is to study the tidally locked 3:2 spin-orbit
resonance of Mercury around the Sun. In order to achieve this goal, the
effective potential energy that determines the spinning motion of an
ellipsoidal planet around its axis is considered. By studying the rotational
potential energy of an ellipsoidal planet orbiting a spherical star on an
elliptic orbit with fixed eccentricity and semi-major axis, it is shown that
the system presents an infinite number of metastable equilibrium
configurations. These states correspond to local minima of the rotational
potential energy averaged over an orbit, where the ratio between the rotational
period of the planet around its axis and the revolution period around the star
is fixed. The configurations in which this ratio is an integer or an half
integer are of particular interest. Among these configurations, the deepest
minimum in the average potential energy corresponds to a situation where the
rotational and orbital motion of the planet are synchronous, and the system is
tidally locked. The next-to-the deepest minimum corresponds to the case in
which the planet rotates three times around its axis in the time that it needs
to complete two orbits around the Sun. The latter is indeed the case that
describes Mercury's motion. The method discussed in this work allows one to
identify the integer and half-integer ratios that correspond to spin-orbit
resonances and to describe the motion of the planet in the resonant orbit.
