Is this a real galaxy fit?

No — parameters are toy knobs. Real analyses use tilted-ring models, asymmetric drift, and multi-component fits.

Why add velocities in quadrature?

A simple pedagogical split: a central-like Keplerian decline plus an extended halo contribution; the combination is chosen for a smooth, flat outer curve, not from solving Poisson for a specific ρ(r).

Galaxy Rotation Curve

Keplerian decline vs flat v(r); toy halo slider (dark matter motivation).

About this model

For roughly circular motion in the disk plane, the centripetal balance gives v² = G M_enc(r)/r for spherical symmetry as a cartoon. If essentially all mass were concentrated in the inner galaxy, the outer regions would look Keplerian with v decreasing as r^{-1/2}. Observed spiral galaxies often show nearly flat rotation curves to large radii, implying enclosed mass rising approximately linearly with radius in the outer parts — the classic motivation for dark matter halos. This simulator plots a softened Keplerian term plus an isothermal-style halo contribution in quadrature; it is illustrative, not a fit to HI data.

Who it's for: Introductory galactic dynamics; pairs with cosmic distance ladder and black hole shadow pages.

Key terms

rotation curve
Keplerian
flat curve
mass enclosed
dark matter halo

How it works

Rotation curves plot orbital speed v of gas and stars vs galactocentric radius r. If essentially all mass sat in the bright center, the outer disk would be Keplerian: v ∝ r⁻¹/². Many spirals show approximately flat v(r) out to large r, implying mass enclosed grows roughly ∝ r in the outer parts — mass that is not luminous like stars and gas alone. This page does not fit real data; it overlays a softened Keplerian decline with a simple extended-halo contribution so you can see how extra mass at large radius flattens the curve. Dark matter is one explanation; alternatives (MOND, etc.) exist — the point here is the kinematic puzzle.

Key equations

Circular speed: v² = G M_enc(r) / r

Kepler (point-like): v ∝ r^{-1/2} at large r

Flat v ⇒ M_enc ∝ r in outer parts (schematic)

Frequently asked questions

Is this a real galaxy fit?: No — parameters are toy knobs. Real analyses use tilted-ring models, asymmetric drift, and multi-component fits.
Why add velocities in quadrature?: A simple pedagogical split: a central-like Keplerian decline plus an extended halo contribution; the combination is chosen for a smooth, flat outer curve, not from solving Poisson for a specific ρ(r).

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Key equations

Frequently asked questions

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How it works

Key equations

Frequently asked questions