  For tracking a spacecraft and doing radio science, the transformation between
the proper time $\tau$ given by a clock carried on board a spacecraft and the
barycentric coordinate time (TCB) is investigated under IAU resolutions. In
order to show more clearly physical pictures and improve computational
efficiency, an analytic approach is adopted. After numerical checks, it shows
this method is qualified for a Mars orbiter during one year, especially being
good at describing the influence from perturbing bodies. Further analyses
demonstrate that there are two main effects in the transformation: the
gravitational field of the Sun and the velocity of the spacecraft in the
barycentric coordinate reference system (BCRS). The whole contribution of them
is at the level of a few sub-seconds.
