Galaxy Rotation Curve
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
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).
More from Astronomy & The Sky
Other simulators in this category — or see all 28.
Stellar Life Cycle
Cloud → MS → giant/SN → WD / NS / BH vs initial mass (schematic).
Exoplanet Radial Velocity
K from masses & P; sinusoidal V_r(t); M sin i.
Exoplanet Transit (light curve)
Uniform disk overlap; R_p/R_*; impact b; F(t) vs period.
Sphere of Influence (Hill)
r_H ≈ a (m/3M)^(1/3): schematic secondary orbit and Hill radius vs masses and a.
Measuring c (ToF toy)
c ≈ 2D/Δt round-trip; schematic path + Fizeau/Foucault context.
GPS & Relativity
Weak-field + SR clock drift estimates vs altitude and orbital speed.