Revised orbital parameters of the accreting millisecond pulsar SAX J1808.4-3658

We present temporal analysis of the three outbursts of the X-ray millisecond pulsar SAX J1808.4-3658 that occurred in 1998, 2000 and 2002. With a technique that uses the chi^2 obtained with an epoch folding search to discriminate between different possible orbital solutions, we find an unique solution valid over the whole five years period for which high temporal resolution data are available. We revise the estimate of the orbital period, P_orb =7249.1569(1) s and reduce the corresponding error by one order of magnitude with respect to that previously reported. Moreover we report the first constraint on the orbital period derivative, -6.6 x 10^-12 < Pdot < +0.8 x 10^-12 s/s. These values allow us to produce, via a folding technique, pulse profiles at any given time. Analysis of these profiles shows that the pulse shape is clearly asymmetric in 2002, occasionally showing a secondary peak at about 145 degrees from the main pulse, which is quite different from the almost sinusoidal shape reported at the beginning of the 1998 outburst.