Galaxy schematic with slit
Face-on pedagogical view. Published curves are inclination-corrected intrinsic $V(R)$.
Face-on pedagogical view. Published curves are inclination-corrected intrinsic $V(R)$.
Compare total, visible-only Keplerian, components, and optional MOND prediction.
Rotation curve showing velocity versus radius for the currently selected galaxy preset.
Dark matter evidence appears when observed $V(R)$ stays flat where visible-mass-only Keplerian prediction declines.
$$V_{\rm total}(R)=\sqrt{V_{\rm bulge}^2+V_{\rm disk}^2+V_{\rm halo}^2}$$
$$M_{\rm dark}(<R)=\frac{V_{\rm obs}^2R}{G}-M_{\rm vis}(<R)$$
$$V_{\rm Kep}(R)\propto R^{-1/2} \quad (R\gg R_d)$$
$$V_{\rm MOND}\approx\left(G\,M_{\rm vis}\,a_0\right)^{1/4}$$
Dark matter is non-luminous mass that clumps in galaxy halos and clusters. Dark energy is a separate phenomenon — it drives the accelerating expansion of the universe. They share the word "dark" but are unrelated physics.