Short and step by step — from the orbits of single stars to neighboring galaxies.
Where do spiral arms come from?
The arms aren't rigid “spokes” made of stars — a galaxy would wind those up like thread on a spool after just a few turns (the so-called winding problem). According to density wave theory (B. Lindblad; C.C. Lin and F. Shu, 1964), stars move on slightly elongated orbits whose orientation turns gradually with distance from the center:
r = a · [1 + e · cos(mu)], θ = u + φ(a) + Ωpt, φ(a) = φ0 − ka
Where neighboring orbits come close, the stars — like cars in a traffic jam — bunch up and we see an arm (m is the number of arms, k the twist, e the eccentricity). Stars flow through the arm, while the pattern itself turns more slowly, at the speed Ωp. Turn on “Show orbits” to see it.
Gas falling into an arm gets compressed: dark dust lanes lie along the inner edge of the arms, and just behind them young, hot, blue stars are born. Their radiation ionizes hydrogen, which glows pink (the Hα line, 656 nm) — these are H II regions.
A simplification: this is a kinematic model — the orbits are set in advance, and the stars don't attract one another.
Rotation curve and dark matter
On a circular orbit, the gravity of the mass M(<r) enclosed within the orbit sets the speed:
v = √G · M(<r)r ⇒ v ∝ r−1/2 (mass concentrated at the center)
If nearly all the mass sat in the bright center, stars farther out would slow down like the planets of the Solar System (Kepler). Yet in the 1970s Vera Rubin and Kent Ford measured that in spiral galaxies, the stars and gas at the edges orbit almost as fast as those closer in — the curve is flat. From v ≈ const it follows that M(<r) = v²r/G ∝ r: mass keeps growing even though there's hardly any light left. We call this invisible mass dark matter. Back in 1933, Fritz Zwicky noticed a similar problem in the Coma Cluster of galaxies.
Example: the Sun, r ≈ 26,000 ly, v ≈ 224 km/s → M(<r) ≈ 9·1010 solar masses, and the orbital period T = 2πr/v ≈ 220 million years.
Model: a bulge (Plummer), an exponential disk (Freeman's formula), an HI gas disk and an isothermal dark matter halo. The data points are schematic — they have the shape typical of real rotation curves.
Galaxy collisions
In 1972 the brothers Alar and Juri Toomre showed with a simple calculation that the long tails and bridges around some galaxies are caused by tidal forces during a close pass. Their method — the restricted N-body problem — works here too: two massive cores attract each other, while thousands of light star particles feel only the cores, not each other:
a = −Σi GMi (r − ri)(|r − ri|² + ε²)3/2
The tidal force is the difference between the pull on the near and far sides of a galaxy, Δa ≈ 2GMd/D³ — which is why it grows sharply during a close approach. A bridge forms on the near side, a tail on the far side. We compute the motion with the “leapfrog” method: v ← v + a·Δt/2, x ← x + v·Δt, v ← v + a·Δt/2 — it conserves energy well.
Simplifications: the cores are “softened” point masses (a Plummer potential), and the effect of the dark halos is replaced by simple drag (dynamical friction) — without it the galaxies couldn't merge. Times and distances are approximate.
Our place in the Universe
The Sun lies about 26,000 light-years from the center of the Milky Way, in the small Orion Arm, between the large Sagittarius and Perseus Arms. The Galaxy's disk is about 100,000 light-years across and holds 100 to 400 billion stars, and at its very center hides the black hole Sagittarius A*, with a mass of about 4 million Suns.
The Milky Way, Andromeda and the Triangulum Galaxy are the three largest of the more than 80 galaxies in the Local Group, which is about 10 million light-years across.
1 light-year ≈ 9.46 · 1012 km (9.46 trillion km)
The light from Andromeda that you can see today with the naked eye set out about 2.5 million years ago — roughly when the first members of the genus Homo lived in Africa.
The map is schematic: from inside the disk it's hard to see the shape of the arms, so their course is still being studied. The Local Group galaxies are projected onto the plane of the Milky Way.
Hubble's tuning fork
In 1926 Edwin Hubble sorted galaxies by their appearance, and in 1936 he drew a diagram shaped like a tuning fork. Ellipticals are labeled En, where
n = 10 · (1 − b/a)
(b/a is the axis ratio of the visible ellipse). Next come the lenticulars S0, the spirals Sa–Sc (from tightly to loosely wound arms and from a large to a small bulge), and the barred spirals SBa–SBc. Galaxies with no clear shape are irregulars (Irr). How flattened an elliptical galaxy looks also depends on the angle we view it from — rotate E6 in mode 1 and see.
Did you know…?
- The Sun speeds around the center of the Galaxy at about 230 km/s (over 800,000 km/h), and one lap takes about 220 million years. The last time we were at this point of our orbit was in the Late Triassic, when the first dinosaurs lived.
- When galaxies collide, the stars themselves almost never hit each other. If the Sun were a grain of sand 1 mm across, the nearest star — Proxima Centauri — would be about 29 km away.
- A collision with Andromeda isn't a done deal: an analysis of measurements from the Gaia and Hubble telescopes published in 2025 gives about a 50% chance that the two galaxies will merge within the next 10 billion years.