Galaxy rotation curves and dark matter
If a galaxy’s mass were where its light is, stars far from the centre would orbit slowly, the way outer planets do. Measurements show they don’t: rotation speeds stay roughly flat far beyond the visible disc. That gap is one of the strongest pieces of evidence for dark matter.
Interactive, free and runs in your browser. Part of the Frontier Physics simulations.
What you will see
A living spiral galaxy of thousands of stars rotating differentially, with density-wave spiral arms. Beside it, two curves: the speed predicted from visible mass, falling off with radius, and the observed speed, staying flat. Pick a radius and the card shows how much of the enclosed mass must be unseen.
Try this
- Move the radius outward and watch the predicted and observed speeds separate.
- Find the radius where most of the enclosed mass is invisible.
- Watch inner stars lap outer stars: the galaxy does not rotate like a solid disc.
Common misconception
Flat rotation curves do not mean the stars are not obeying gravity. They obey it, but the gravity is coming from much more mass than we can see, spread well beyond the visible galaxy.
Exam-style question
The Sun orbits the galaxy at about 220 km/s, 8 kpc (2.5 × 10²⁰ m) from the centre. Estimate the mass enclosed by its orbit.
For a circular orbit M = v²r/G = (2.2 × 10⁵)² × 2.5 × 10²⁰ / 6.67 × 10⁻¹¹ ≈ 1.8 × 10⁴¹ kg, about 9 × 10¹⁰ solar masses.
Key equations
v = √(GM(r) / r)M(r) = v² r / G
Curriculum
IB Physics E.5, enrichment: astrophysics and cosmology.