Newtonian gravity applied to only the visible stars and gas predicts orbital speed falling off as v ∝ 1/√r at large radius. Real galaxies instead show a flat rotation curve — the signature of an unseen dark-matter halo.
Dark Matter Halo (NFW)
Show visible-only comparison
Legend
Visible matter only (Keplerian)
Dark matter halo contribution
Total (real, observed ≈ flat)
Observed data points
Live Readout
Cursor radius
— kpc
v (visible only)
— km/s
v (with halo)
— km/s
Discrepancy factor
—×
Halo mass
— M☉
v_disk²+v_bulge² gives the Keplerian visible-only prediction (falls as 1/√r at large r).
NFW halo: ρ(r)=ρ₀/[(r/r_s)(1+r/r_s)²], v_halo²=GM_halo(r)/r.
v_total²=v_disk²+v_bulge²+v_halo² — matches the observed flat curve. Vera Rubin's 1970s
measurements of 200+ spiral galaxies established this as the strongest evidence for dark matter.