Using the Sloan Digital Sky Survey (SDSS), we probe the halo mass distribution by studying the velocities of satellites orbiting isolated galaxies. In a subsample that covers 2500 deg2 on the sky, we detect about 3000 satellites with absolute blue magnitudes going down to MB=-14; most of the satellites have MB=-16 to -18, comparable to the magnitudes of M32 and the Magellanic Clouds. After a careful, model-independent removal of interlopers, we find that the line-of-sight velocity dispersion of satellites declines with distance to the primary. For an L* galaxy the rms line-of-sight velocity changes from ~120 km s-1 at 20 kpc to ~60 km s-1 at 350 kpc. This decline agrees remarkably well with theoretical expectations, as all modern cosmological models predict that the density of dark matter in the peripheral parts of galaxies declines as ρDM~r-3. Thus, for the first time we find direct observational evidence of the density decline predicted by cosmological models; we also note that this result contradicts alternative theories of gravity such as modified Newtonian dynamics (MOND). We also find that the velocity dispersion of satellites within 100 kpc scales with the absolute magnitude of the central galaxy as σ~L0.3 this is very close to the Tully-Fisher relation for normal spiral galaxies.