  We consider the geometric Titius-Bode rule for the semimajor axes of
planetary orbits. We derive an equivalent rule for the midpoints of the
segments between consecutive orbits along the radial direction and we interpret
it physically in terms of the work done in the gravitational field of the Sun
by particles whose orbits are perturbed around each planetary orbit. On such
energetic grounds, it is not surprising that some exoplanets in multiple-planet
extrasolar systems obey the same relation. But it is surprising that this
simple interpretation of the Titius-Bode rule also reveals new properties of
the bound closed orbits predicted by Bertrand's theorem and known since 1873.
