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Accurate and radially extended stellar kinematic data reaching R=97'' fromthe center are presented for the cD galaxy of Fornax, NGC 1399. The stellarrotation is small (<= 30 km/s); the stellar velocity dispersion remainsconstant at 250-270 km/s. The deviations from Gaussian line of sight velocitydistributions are small, at the percent level. We construct dynamical models ofthe galaxy, deprojecting its nearly round (E0-E1) surface brightnessdistribution, and determining the spherical distribution function that bestfits (at the 4 percent level) the kinematic data on a grid of parametrizedpotentials. We find that the stellar orbital structure is moderately radial,with beta=0.3 +- 0.1 for R<=60'', similar to results found for some normalgiant ellipticals. The gravitational potential is dominated by the luminouscomponent out to the last data point, with a mass-to-light ratio M/L_B=10 solarunits, although the presence of a central black hole of M approx 5 x 10^8 solarmasses is compatible with the data in the inner 5 arcsec. The influence of thedark component is marginally detected starting from R approx 60''. Using theradial velocities of the globular clusters and planetary nebulae of the galaxywe constrain the potential more strongly, ruling out the self-consistent caseand finding that the best fit solution agrees with X-ray determinations. Theresulting total mass and mass-to-light ratio are M=1.2-2.5 x 10^12 solar massesand M/L_B=22-48 M solar units inside R=417'' or 35 kpc for D=17.6 Mpc.Comment: 14 pages, Latex File, 7 Postscript figures, to appear in A

The Orbital Structure and Potential of NGC 1399