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You cannot see a black hole directly, because no light escapes from it. You can, however, watch what it does to the stars around it. For almost thirty years Andrea Ghez and her team did exactly that at the centre of our galaxy. This post explains how, works through the calculation that turns one star's orbit into a mass, and ends with what her way of working can teach you.
Who is Andrea Ghez?
Ghez was born in New York City on 16 June 1965, according to her Nobel Prize facts page. The 2020 press release notes that she earned her PhD at Caltech in 1992 and is a professor at the University of California, Los Angeles. She shared half of the 2020 Nobel Prize in Physics with Reinhard Genzel "for the discovery of a supermassive compact object at the centre of our galaxy". The other half went to Roger Penrose for showing that black hole formation follows from general relativity.
Why is the galactic centre so hard to observe?
The centre of the Milky Way lies behind thick clouds of gas and dust, and Earth's turbulent atmosphere blurs every image. The Nobel Committee's popular science background explains that Ghez's team uses the Keck Observatory in Hawaii, whose mirrors are almost 10 metres across and made of 36 hexagonal segments. The breakthrough was adaptive optics: a thin extra mirror that changes shape to cancel the atmosphere's distortion. Infrared telescopes are what first let astronomers see through the dust to the stars at the centre.
What did the stars reveal?
In 1998 Ghez and colleagues reported in The Astrophysical Journal on 90 stars near the radio source Sagittarius A*, with speeds as high as 1400 km/s. The way the speeds rose closer to the centre matched motion around a central dark mass of about 2.6 million Suns packed into a tiny volume.
Over the following years the team followed one star, S0-2 (Genzel's group calls it S2), through a complete orbit. The Nobel Committee notes that it goes round the centre in less than 16 years, while the Sun takes more than 200 million years to orbit the galaxy. The press release summarises the conclusion of both teams: around four million solar masses packed into a region no larger than our solar system. A supermassive black hole is the only explanation currently known.
Worked example: weighing a black hole with Kepler's third law
For a small body orbiting a much larger mass, Kepler's third law can be written in convenient units:
M = a³ / P²
where M is in solar masses, a (the semi-major axis) is in astronomical units and P is in years. You can check it on the Earth: a = 1 AU, P = 1 year, M = 1 Sun.
Ghez's team published S0-2's orbit in The Astrophysical Journal in 2008. In their fit with no extra assumptions, the values are:
Distance to the galactic centre: R₀ = 7.96 kiloparsecs = 7960 pc
Period: P = 15.86 years
Semi-major axis as seen from Earth: 126.5 milliarcseconds = 0.1265 arcseconds
Step 1: convert the angle to AU. By the definition of the parsec, an angle of 1 arcsecond at a distance of 1 parsec spans 1 AU. So a = 0.1265 × 7960 ≈ 1007 AU.
Step 2: apply Kepler's law. a³ = 1007³ ≈ 1.021 × 10⁹. P² = 15.86² ≈ 251.5. M = 1.021 × 10⁹ / 251.5 ≈ 4.06 × 10⁶ solar masses.
That matches the paper's result of 4.1 ± 0.6 million solar masses. The star sits about a thousand times farther from the centre than Earth is from the Sun, yet it completes an orbit in 16 years, so the mass inside its orbit must be enormous.
Common mistakes:
Mixing up milliarcseconds and arcseconds. 126.5 mas is 0.1265 arcseconds, not 126.5.
Using kiloparsecs directly. The small-angle rule needs parsecs.
Squaring instead of cubing. It is a³ over P², and an error here changes the answer by a factor of a thousand.
The arcsecond-parsec trick in step 1 is the same one behind Friedrich Bessel's measurement of a star's distance. For the law itself, see our post on Kepler's laws of planetary motion.
What came next?
S0-2 swings very close to the black hole. In 2019 the team reported in Science that during its closest approach, the star's light was stretched to longer wavelengths by gravity. This gravitational redshift does not exist in Newton's theory, and the measurements fitted Einstein's general relativity better than Newtonian gravity.
What can a student take from Andrea Ghez?
Fix the tool, then ask the question. Much of her early work went into getting sharp images through the atmosphere.
Check against a rival team. The Nobel press release stresses that Ghez's and Genzel's independent groups reached the same answer, which made it convincing.
Simple laws go a long way. The same Kepler's law you use for satellites weighs a black hole.
To practise orbital questions like this, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning, so you can see why each conversion is needed.
Try it now: use M = a³/P² for Jupiter (a = 5.2 AU, P = 11.86 years) and check that you get close to one solar mass.
