  It is usually assumed that the "$t$" parameter in the equations of dynamics
can be identified with the indication of the pointer of a clock. Things are not
so easy, however. In fact, since the equations of motion can be written in
terms of $t$ but also of $t'=f(t)$, $f$ being any well behaved function, each
one of those infinite parametric times $t'$ is as good as the Newtonian one to
study classical dynamics. Here we show that the relation between the
mathematical parametric time $t$ in the equations of dynamics and the physical
dynamical time $\sigma$ that is measured with clocks is more complex and subtle
than usually assumed. These two times, therefore, must be carefully
distinguished since their difference may have significant consequences.
Furthermore, we show that not all the dynamical clock-times are necessarily
equivalent and that the observational fingerprint of this non-equivalence has
the same form as that of the Pioneer anomaly.
