Revised Orbital Parameters of the Accreting Millisecond Pulsar SAX J1808.4-3658

We present a 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 \u3c72 obtained with an epoch-folding search to discriminate between different possible orbital solutions, we find an unique solution valid over the whole 5 yr period for which high temporal resolution data are available. We revise the estimate of the orbital period, Porb=7249.1569(1) s, and reduce the corresponding error by 1 order of magnitude with respect to that previously reported. Moreover, we report the first constraint on the orbital period derivative, -6.6 710-12<P\u2d9orb<+0.8 710-12 s s-1. 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\ub0 from the main pulse, which is quite different from the almost sinusoidal shape reported at the beginning of the 1998 outburst