We present a detailed study of the ${0}_{g}^{\ensuremath{-}}{(P}_{3/2})$ pure long-range electronic state of the
87Rb2 molecule. The high-resolution spectral data provided by photoassociative spectroscopy of
87Rb2 is analyzed by using the generalized simulated annealing method. The dipole matrix element of the
5p 87Rb atomic state and other effective asymptotic parameters for the ${0}_{g}^{\ensuremath{-}}{(P}_{3/2})$ long-range state are determined and a complete analytical description of the potential well is obtained. We extract a radiative lifetime of the
5P3/2 and
5P1/2 states equal to 26.25(8) ns and 27.75(8) ns, respectively, with a precision (0.3%) comparable to atomic physics experiment.