Updating the orbital ephemeris of Hercules X-1; rate of decay and eccentricity of the orbit

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Table 3:

Orbital elements of Her X-1.
$T_{\pi/2}(0)$ [MJD (TDB)]	=	46 359.871940(6)¹
$P_{\rm orb}(0)$ [d]	=	1.700167590(2)
$\dot P_{\rm orb}(0)$ [d/d]	=	$(-4.85\pm0.13)\times 10^{-11}$
$a~{\rm sin}~i$ [lt-s]	=	13.1831(4)²
eccentricity $\epsilon$	=	$(4.2\pm0.8) \times 10^{-4}$
omega [deg]	=	$96.0 \pm 10.0$

¹ The uncertainties in parentheses (68%) refer to the last digit(s).
² Note that Deeter et al. (1981) had measured $a ~{\rm sin} ~i = 13.1831(3)$ lt-s (with a slightly smaller uncertainty). All other values are updated or new.

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