We present an update of the orbital ephemeris of the binary X-ray pulsar Her X-1 and determine an improved value for the rate of orbital decay .
In addition , we report the first measurement of the orbital eccentricity .
We have analyzed pulse timing data of Her X-1 from X-ray observations by RXTE ( Rossi X-Ray Timing Explorer ) and INTEGRAL over the period 1996 – 2007 .
Accurate pulse arrival times were determined from solar system bary-centered photon arrival times by generating pulse profiles averaged over appropriately short integration times .
Applying pulse phase connection techniques , it was possible to determine sufficiently accurate local ephemeris data for seven observation periods distributed over 12 years .
Combining the new local T _ { \pi / 2 } values with historical values from the literature we update the orbital ephemeris of Her X-1 to T _ { \pi / 2 } = MJD 46359.871940 ( 6 ) and P _ { orb } = 1.700167590 ( 2 ) d and measure a continuous change of the orbital period of dP _ { orb } / dt = - ( 4.85 \pm 0.13 ) \times 10 ^ { -11 } { ss ^ { -1 } } .
For the first time , a value for the eccentricity of the orbit of Her X-1 is measured to be \epsilon = ( 4.2 \pm 0.8 ) \times 10 ^ { -4 } .