This is the second in a series of papers dedicated to unveil the mass structure and orbital content of a sample of flattened early-type galaxies in the Coma cluster. The ability of our orbit libraries to reconstruct internal stellar motions and the mass composition of a typical elliptical in the sample is investigated by means of Monte-Carlo simulations of isotropic rotator models. The simulations allow a determination of the optimal amount of regularization needed in the orbit superpositions. It is shown that under realistic observational conditions and with the appropriate regularization internal velocity moments can be reconstructed to an accuracy of about 15 per cent; the same accuracy can be achieved for the circular velocity and dark matter fraction. In contrast, the flattening of the halo remains unconstrained. Regularized orbit superpositions are applied to a first galaxy in our sample, NGC 4807, for which stellar kinematical observations extend to 3 Reff. The galaxy seems dark matter dominated outside 2 Reff. Logarithmic dark matter potentials are consistent with the data, as well as NFW-profiles, mimicking logarithmic potentials over the observationally sampled radial range. In both cases, the derived stellar mass-to-light ratio agrees well with independently obtained mass-to-light ratios from stellar population analysis. Kinematically, NGC 4807 is characterized by mild radial anisotropy outside r>0.5 Reff, becoming isotropic towards the center. Our orbit models hint at either a distinct stellar component or weak triaxiality in the outer parts of the galaxy.
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