We study the projected radial distribution of satellite galaxies around more than 28,000 Luminous Red Galaxies (LRGs) at 0.28<z<0.40 and trace the gravitational potential of LRG groups in the range 15<r/kpc<700. We show that at large radii the satellite number density profile is well fitted by a projected NFW profile with r_s~270 kpc and that at small radii this model underestimates the number of satellite galaxies. Utilizing the previously measured stellar light distribution of LRGs from deep imaging stacks we demonstrate that this small scale excess is consistent with a non-negligible baryonic mass contribution to the gravitational potential of massive groups and clusters. The combined NFW+scaled stellar profile provides an excellent fit to the satellite number density profile all the way from 15 kpc to 700 kpc. Dark matter dominates the total mass profile of LRG halos at r>25 kpc whereas baryons account for more than 50% of the mass at smaller radii. We calculate the total dark-to-baryonic mass ratio and show that it is consistent with measurements from weak lensing for environments dominated by massive early type galaxies. Finally, we divide the satellite galaxies in our sample into three luminosity bins and show that the satellite light profiles of all brightness levels are consistent with each other outside of roughly 25 kpc. At smaller radii we find evidence for a mild mass segregation with an increasing fraction of bright satellites close to the central LRG.
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