evidence for dark matter
Imagine spinning a merry-go-round: the riders on the outer edge have to hold on tighter than those near the middle, because the outside moves faster. Galaxies behave the same way — except that the stars far out at the edges of a spinning galaxy whirl around far too fast for the gravity of the visible stars and gas to hold them in. By all rights they should fly off into space. The fact that they do not means something invisible is there, gripping them with extra gravity. That unseen something is called dark matter, and the evidence that it exists is now overwhelming, even though no one has ever held a piece of it.
The evidence does not come from one observation but from many independent ones that all point the same way. The rotation speeds of galaxies are one. Another is the way whole clusters of galaxies bend the light of objects behind them, an effect called gravitational lensing — the bending is far stronger than the visible matter could produce. The cosmic microwave background, the leftover glow of the early universe, carries a precise fingerprint that only fits if most of the matter in the cosmos is dark. And in the famous Bullet Cluster, two galaxy clusters collided: the ordinary gas piled up in the middle, but the gravity (mapped by lensing) sailed on ahead with the stars, showing the dark matter passed straight through, just as a barely-interacting substance should.
Adding it all up, ordinary matter — everything made of atoms, all the stars, planets, gas, and people — is only about a sixth of the total matter in the universe. The rest, roughly five times as much, is dark matter, and we know it is there only by its gravity. What it actually is remains one of the biggest open questions in all of physics, and it sits squarely on the boundary between particle physics and cosmology, because the leading explanation is that it is some new kind of particle the Standard Model does not contain.
In the outer reaches of our own Milky Way, stars orbit at roughly the same speed no matter how far out they are — a flat 'rotation curve' that visible matter alone cannot explain, but that a surrounding halo of dark matter accounts for neatly.
Galaxies spin as if held by unseen extra mass.
Dark matter is inferred only from its gravity; we have never detected it any other way. A minority of physicists argue the real fix might instead be a change to the law of gravity itself, though that idea struggles to explain the full set of observations, especially the Bullet Cluster.