Strong and weak lensing united. II. The cluster mass distribution of the most X-ray luminous cluster RX J1347.5-1145

We have shown that the cluster-mass reconstruction method which combines strong and weak gravitational lensing data, developed in the first paper in the series, successfully reconstructs the mass distribution of a simulated cluster. In this paper we apply the method to the ground-based high-quality multi-colour data of RX J1347.5-1145, the most X-ray luminous cluster to date. A new analysis of the cluster core on very deep, multi-colour data analysis of VLT/FORS data reveals many more arc candidates than previously known for this cluster. The combined strong and weak lensing reconstruction confirms that the cluster is indeed very massive. If the redshift and identification of the multiple-image system as well as the redshift estimates of the source galaxies used for weak lensing are correct, we determine the enclosed cluster mass in a cylinder to M(< 360 h(-1) kpc) = (1.2 +/- 0.3) x 10(15) M-circle dot. In addition the reconstructed mass distribution follows the distribution found with independent methods (X-ray measurements, SZ). With higher resolution (e. g. HST imaging data) more reliable multiple imaging information can be obtained and the reconstruction can be improved to accuracies greater than what is currently possible with weak and strong lensing techniques.