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Black holes in the classroom: resources for teachers

Five ready-to-use activities, from secondary school to university, with answer keys: weigh Sgr A* with Kepler, read the M87* image, listen to a black hole merger.

Updated 8 October 2026

The activities below use the site's tools and real data. They are free, with no sign-up. Levels are given for upper secondary school (ages 15 to 18) and the first year of university.

1. Weigh the Milky Way's black hole with Kepler

Ages 17 to 181 h

Apply Kepler's third law to the star S2, which orbits Sgr A*.

The star S2 completes its orbit in about 16.0 years. Seen from Earth, the semi-major axis of its orbit is 0.125 arcseconds, and the Galactic Centre is about 8,280 parsecs away.

  1. Convert the semi-major axis to astronomical units (at 1 parsec, 1 arcsecond corresponds to 1 AU).
  2. Write Kepler's third law in AU, years and solar masses.
  3. Deduce the mass of Sgr A* and compare it with the published value.
Go deeperAnswer key

a ≈ 0.125 × 8,280 ≈ 1,035 AU.

M = a³ / T² ≈ 1035³ / 16.0² ≈ 4.3 × 10⁶ M☉
With a in AU, T in years and M in solar masses (S2's own mass is negligible).

The GRAVITY collaboration finds 4.30 million solar masses with far finer measurements. This work was recognised by the 2020 Nobel Prize in Physics.

2. Orders of magnitude: squeezing Earth into a black hole

Ages 15 to 1730 min

Work with powers of ten and a formula, then check with the calculator.

  1. Compute r = 2GM/c² for Earth (M = 5.97 × 10²⁴ kg), then for the Sun (M = 1.99 × 10³⁰ kg).
  2. Compare each result with an everyday object.
  3. What happens to the radius if the mass is multiplied by 10? Check with the calculator.
Go deeperAnswer key

Earth: r ≈ 8.9 mm, a marble 1.8 cm across. Sun: r ≈ 2.95 km. The radius is proportional to the mass, so it is also multiplied by 10.

3. Reading the M87* image

Ages 17 to 18 and first-year university45 min

Relate an angular size to a real size, then test an observation against a prediction of general relativity.

The M87* ring is 42 microarcseconds across. The galaxy is 16.8 megaparsecs away and the black hole weighs 6.5 billion solar masses.

  1. Convert the angle to radians (1 arcsecond ≈ 4.85 × 10⁻⁶ rad) and deduce the ring's real diameter.
  2. Compute the horizon radius rs = 2GM/c².
  3. General relativity predicts a ring about 5.2 rs across. Conclude.
Go deeperAnswer key

θ ≈ 2.0 × 10⁻¹⁰ rad and d ≈ 5.2 × 10²³ m, so D = θ·d ≈ 1.1 × 10¹⁴ m, about 700 AU. With rs ≈ 1.9 × 10¹³ m, the ring is about 5.5 rs across, consistent with the prediction given the uncertainty on the mass (± 0.7 billion solar masses).

4. Listening to a black hole merger

Ages 15 to 1830 min

Link frequency, period and pitch on a real signal turned into sound.

On the gravitational waves page, play the slowed-down chirp, then look at the waveform.

  1. Describe how the pitch and loudness change.
  2. The signal goes from 35 Hz to 150 Hz: compute the matching periods.
  3. Why does the frequency rise as the two black holes get closer?
Go deeperAnswer key

The sound gets higher and louder. T = 1/f: about 29 ms at 35 Hz and 6.7 ms at 150 Hz. The black holes orbit faster and faster as they get closer (Kepler's third law), and the emitted wave follows that rhythm.

5. Debate: can information disappear?

Ages 17 to 18 and university1 h

Build an argument from a real, open scientific debate.

Using the information paradox page and its interactive Page curve, students defend one of the historical positions: Hawking in 1976, then those who argued information is preserved.

Prompts: what is a reversible law? What would settle the question? Why did Hawking change his mind in 2004?

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