Theory — Galaxies and Cosmology: Black Holes, the Milky Way, and the Expanding Universe
Parts A and B treat the Galactic centre; Parts C and D treat galaxies and the expanding universe.
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:
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:
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.
Galaxies are vast systems of stars, gas, dust, and dark matter. Studying how they are built and how they move reveals the history of the whole universe.
4. Types of galaxies
Galaxies come in three broad kinds: spirals with a disk and arms like our own; ellipticals, smooth round balls of mostly old stars; and irregulars with no clear shape. Some galaxies have blazing centres powered by supermassive black holes; the most extreme are quasars.
5. Hubble’s law
In the 1920s it was found that a galaxy’s recession speed is proportional to its distance:
v in km/s, d in megaparsecs (Mpc), H0 in km/s per Mpc
So H0 = v / d, and the more distant a galaxy, the faster it recedes.
The recession is measured from the redshift of the galaxy’s spectral lines. The relation is not because we are at a special centre; space itself is expanding, carrying the galaxies apart.
6. The age of the universe
Running the expansion backward, all galaxies were together at one moment. The time since then is roughly the inverse of the Hubble constant:
(with H0 in km/s per Mpc)
For H0 ≈ 70, the age is about 14 billion years.
7. The expanding universe
This expansion began in the hot, dense Big Bang about 13.8 billion years ago, whose afterglow we still detect as the cosmic microwave background. The universe also contains dark matter and dark energy, which together shape its expansion and fate.
8. The search for life
The Big Bang made hydrogen and helium; every heavier element in a living cell was forged in stars and scattered by stellar death. That is why the search for life beyond Earth begins with the chemistry traced in this lab. Astronomers look for planets in a star’s habitable zone, where liquid water can exist, and for biosignatures such as oxygen or methane in a planet’s spectrum. The Drake equation organises the question by multiplying the rate of star formation by the fractions of stars with planets, habitable planets with life, and civilisations able to communicate. No life beyond Earth has yet been found, so every factor after the first two remains an estimate.
Apparatus
Studying the Galactic centre and distant galaxies uses tools for infrared and radio imaging, timing orbits, and measuring redshifts. In the simulation these are modelled, but the readings match what each instrument would give.
Instructions
Work through all four tabs. Calculate first by hand, then press the button to compare.
Part A — Weigh the black hole
- Read the star’s orbital semi-major axis a (AU) and period P (years).
- Compute the enclosed mass M = a3 / P2 in solar masses by hand.
- Enter your value and press Check; it compares within 8 percent.
Part B — Size of the event horizon
- Set a black hole’s mass in solar masses.
- Compute the Schwarzschild radius Rs = 2.95 km × M by hand.
- Enter your value and press Check.
Part C — Hubble’s law and the age of the universe
- Read a galaxy’s recession velocity v (km/s) and distance d (Mpc).
- Compute the Hubble constant H0 = v / d by hand.
- Enter your value and press Check; the panel also shows the implied age ≈ 978 / H0 billion years.
Part D — Classify galaxies
- View a galaxy’s shape.
- Predict whether it is spiral, elliptical, or irregular, then press Check.
Simulation
A star on an elliptical orbit around an unseen point at the Galactic centre; the semi-major axis and period of the orbit are shown and the enclosed mass is computed from them.
A black hole drawn as a dark disc whose radius, the Schwarzschild radius, grows in proportion to the mass entered.
A Hubble diagram of recession velocity against distance for several galaxies; the points fall on a straight line whose slope is the Hubble constant.
An image of a galaxy whose shape, spiral, elliptical, or irregular, is to be classified.
Team Questions
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.
Worked example: the Hubble constant and the age of the universe
A galaxy recedes at v = 7000 km/s at a distance d = 100 Mpc.
H0 = v / d = 7000 / 100 = 70 km/s per Mpc.
The implied age is 978 / H0 = 978 / 70 ≈ 14 billion years, close to the accepted 13.8 billion years. Measuring the slope of the velocity-distance relation and inverting it is the calculate-then-compare core of the lab.