Theory — Black Holes and the Milky Way Galaxy

The Milky Way is our home galaxy, a vast rotating disk of a few hundred billion stars, and at its centre lies a supermassive black hole.

1. Structure of the Milky Way

The galaxy has a flat disk wound into spiral arms, a central bulge, and a surrounding spherical halo of old stars and globular clusters. The Sun sits in the disk about 27,000 light-years from the centre. Much of the galaxy’s mass is unseen dark matter, inferred from how fast the disk rotates.

2. Black holes

A black hole is a region where gravity is so strong that not even light can escape. Its boundary is the event horizon, whose radius (the Schwarzschild radius) grows in proportion to mass:

Schwarzschild radius Rs = 2.95 km × (M / MSun)
A one-solar-mass black hole is just 3 km across; a supermassive one is far larger.

3. Weighing the central black hole

We cannot see the black hole, but we can watch stars orbit it. A star’s orbit obeys Kepler’s third law in Newton’s form, which gives the enclosed mass:

Mass from a star’s orbit M = a3 / P2
  M in solar masses, a in AU, P in years
Timing one star’s orbit weighs the unseen black hole.

Stars near the Galactic centre, tracked for decades, orbit an invisible point known as Sagittarius A*, giving a mass of about four million Suns packed into a region smaller than our solar system: a supermassive black hole.

Apparatus

Studying the galactic centre uses tools for infrared imaging, timing orbits, and mapping the galaxy. In the simulation these are modelled, but the readings match what each instrument would give.

Black hole and disk
A black hole surrounded by a glowing accretion disk of infalling matter.
Event horizon
The boundary from within which nothing, not even light, can escape.
Milky Way, top view
The galaxy seen face-on, showing the spiral arms winding out from the centre.
Milky Way, edge view
The galaxy seen edge-on, showing the thin disk and central bulge.
Star orbit
A star’s elliptical orbit around the unseen central mass, timed to weigh it.
Radio telescope
Observes the radio source at the Galactic centre through the obscuring dust.

Instructions

Work through both tabs. Calculate first by hand, then press the button to compare.

Part A — Weigh the black hole

Part B — Size of the event horizon

Simulation

Galactic-Centre BenchCalculate first, then check against the simulation.

Team Questions

1. The mass of the Milky Way’s central black hole is measured from:
2. The event horizon of a black hole is:
3. The Sun sits in which part of the Milky Way?

Example Report

Worked example: the mass of Sagittarius A*

Star S2 orbits the Galactic centre with a = 1000 AU and P = 16 years.

M = a3 / P2 = 10003 / 162 = 109 / 256 ≈ 3.9 × 106 solar masses.

The central object holds about four million solar masses in a tiny region, which can only be a supermassive black hole. Weighing it from a single star’s orbit is the calculate-then-compare core of the lab.

Practice Questions

1. The Schwarzschild radius of a 10 solar-mass black hole is about:
2. Most of the Milky Way’s mass is thought to be:
3. Using M = a^3 / P^2, a star with a = 3300 AU and P = 94 yr encloses about: