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S2 Weighed Sagittarius A* Four Times and Got Four Answers

September 13, 2026 · Runtime 12:17 · Watch on YouTube

The mass of the Milky Way's black hole is quoted to a quarter of one per cent, from one star's sixteen-year orbit. The same team has published it four times since 2018, each to under one per cent, and the first and last differ by five. The instrument never changed its answer; what changed is what the answer was multiplied by.

Chapters

Transcript

May 2018: a star at 7,650 km/s 0:00

In May two thousand eighteen, a star went past the black hole at the centre of our galaxy at seven thousand six hundred and fifty kilometres per second. Two and a half per cent of the speed of light. It passed one hundred and twenty times farther out than the Earth sits from the Sun, and four telescopes in Chile, working as one, watched it go by to twenty millionths of a second of arc.

The number the instrument returned 0:24

That pass is how the black hole was weighed. Four point three million suns, to a quarter of one per cent. This episode ends on the number the instrument actually returned for that orbit, and on what a quarter of one per cent leaves out.

Last episode leaned on that mass. The ring the Event Horizon Telescope measured was tested against it, and the test was only as sharp as the mass allowed. Tonight, where the mass comes from, and why it keeps changing.

S2, a sixteen-year orbit 0:56

The star is called S two. It is a young, hot star, a main sequence B star, and it happens to sit on a sixteen year orbit that comes closer to the black hole than anything else astronomers had found when the watch began. It is not the only one. Dozens of stars loop around that point. S two is simply the one with the best combination of brightness and speed.

Thirty years of watching one star 1:22

The watch began in nineteen ninety two, with a speckle camera on a three and a half metre telescope in Chile, and a second team at the Keck telescopes in Hawaii from nineteen ninety five. In two thousand two the star swung through its closest point, and for the first time the orbit could be drawn as an ellipse.

Kepler: size cubed over period squared 1:42

A closed orbit is a scale. Kepler wrote the rule four hundred years ago. The mass at the centre is the size of the orbit, cubed, divided by the period, squared. Nothing about the black hole has to be seen. The star does the weighing, and the telescope only has to keep watching.

But look at what the telescope actually hands over. The period is a clock, and clocks are honest: sixteen point zero five years. The size of the orbit is not a length. It is an angle. One hundred and twenty five thousandths of a second of arc, from the centre of the ellipse to its edge.

One per cent of distance is three per cent of mass 2:24

To turn that angle into kilometres, you multiply by the distance to the galactic centre. And to turn kilometres into a mass, you cube it. Which means every one per cent you are wrong about the distance becomes three per cent of black hole. The mass is not a separate measurement. It is the distance, cubed.

3.7, then 4.31 million suns 2:47

So the first weighing, in two thousand two, came out at three point seven million suns, give or take one and a half million. By two thousand nine, with twenty eight stars and one complete orbit of S two, the fit gave four point three one. And that paper split the error in two. Statistical, one and a half per cent. From the distance, eight.

Where the distance comes from 3:13

Which raises the obvious question. If the mass needs the distance, where does the distance come from? The answer is the same orbit, read a second way, and it is the part of this story that makes the whole thing possible at all.

A spectrograph measures how fast the star moves toward or away from us, in kilometres per second, with no distance involved anywhere. The camera measures how fast it moves across the sky, in angle per year. A physical speed set against an angular one is a distance. The orbit measures its own.

8,277 parsecs, no ladder underneath 3:50

That makes the orbit of S two one of the very few places where the distance to the galactic centre is measured geometrically, with no rung of the ladder from episode two underneath it. Eight thousand two hundred and seventy seven parsecs, plus or minus nine. About twenty seven thousand light years, known to a tenth of a per cent.

Mass and distance are one number 4:12

But it also ties the two numbers together. Fit them jointly and the mass rides on the distance to a power of about two. Quote the mass without the distance it was fitted at, and you have quoted half a number.

Keck 3.975, VLT 4.297: 8% apart, 0.05% apart 4:26

Here is what that looks like in practice. In two thousand nineteen the Keck team published three point nine seven five million suns. The European team, four point three. Eight per cent apart. Put both at the same distance and they agree to five parts in ten thousand. Neither was wrong. They were fitted at different distances, and the mass followed.

GRAVITY: four telescopes, 130 metres 4:53

Now the instrument that pushed the error down. In two thousand seventeen the four eight metre telescopes of the Very Large Telescope were joined by GRAVITY, which combines their light as if they were one mirror a hundred and thirty metres across. The same trick as the last two episodes, at a shorter wavelength.

Pairs of telescopes, interference fringes, and a phase. What the phase gives is the separation between the star and the black hole, to about fifty millionths of a second of arc. Twenty, on the best nights. Not a picture. A vector, from one point to another.

Adaptive optics imaging on a single one of those telescopes had placed the star to a few hundred millionths. GRAVITY improved that by an order of magnitude, and it did so right at the point of the orbit where the improvement matters most.

Pericentre: 120 AU, 1,400 horizon radii 5:48

May two thousand eighteen. Pericentre. One hundred and twenty astronomical units from the black hole, fourteen hundred times the radius of its horizon, at seven thousand six hundred and fifty kilometres per second. For comparison, Neptune sits thirty astronomical units from the Sun and moves at five and a half kilometres per second.

And the star's light came back redder than Newton allows. About two hundred kilometres per second of extra redshift at closest approach, in equal parts from the star's speed and from its light climbing out of the black hole's gravity. Out at the far end of the orbit, the same effect is six kilometres per second.

The collaboration wrote the result the way this channel likes results written. Not confirmed, but a number: zero point nine, plus or minus zero point one seven, on a scale where Newton is zero and Einstein is one. The Keck team, independently, got zero point eight eight.

Twelve arcminutes per orbit 6:52

Two years later, with the star back on the far side of its orbit, a second effect. The ellipse itself turns, by twelve minutes of arc per orbit, in the direction Einstein predicted for Mercury a century earlier. By two thousand twenty two that was a seven sigma detection.

The precession does one more job, and it is the one that matters tonight. Any spread out mass inside the orbit, stars, remnants, dark matter, would drag the ellipse the other way. The data leave room for at most about three thousand suns inside the orbit. One part in a thousand of the black hole.

Four tests of relativity, four numbers 7:33

So by now the orbit has been used four times as a test of relativity, and all four came back as a number rather than a verdict. Zero point nine. One point zero four. One point one. Zero point nine nine seven. Einstein is one, and every error bar covers it.

4.297 million suns, a quarter of a per cent 7:56

Which brings us to the published mass, from four stars fitted together in two thousand twenty two. Four point two nine seven million suns, plus or minus zero point zero one two. A quarter of one per cent, and the best constrained black hole mass this channel has ever used.

Where the quarter of a per cent lives 8:16

And this is where the quarter of a per cent actually lives. The angle is known to three hundredths of a per cent. The period, to less than a hundredth. The distance, to eleven hundredths. Cube the distance and you have nearly the whole error bar. The mass inherits the distance, and almost nothing else.

The systematic error is three times larger 8:38

That is the first thing the quarter of a per cent hides. It is the statistical error. The systematic one, the same team wrote in a companion paper, is about forty thousand suns. Three times larger. It comes from where the reference frame sits, and from stars that pass in front of each other, and it does not shrink by watching longer.

Four papers, four masses 9:02

The second is in the record. GRAVITY has published this mass four times. Two thousand eighteen, four point one zero. Nineteen, four point one five. Twenty, four point two six. Twenty two, four point two nine seven. Each one quoted to under one per cent. The first and the last are five per cent apart.

Now look at what moved and what did not. The angle of the orbit went from one hundred twenty five point four to one hundred twenty four point nine five. A third of a per cent. The distance went from eight thousand one hundred and twenty two parsecs to eight thousand two hundred and seventy seven. Two per cent. Cubed, that is the whole five.

The black hole did not get heavier 9:53

So the black hole did not get heavier. The galactic centre got farther away, in the fit, as the reference frame improved and more stars were added, and the mass rode along, because it was never a separate number. The instrument kept returning the same angle. What changed is what the angle was multiplied by.

The third thing it hides is scope. S two never gets closer than a hundred and twenty astronomical units. Everything inside that, the black hole and whatever else is there, is weighed together. The orbit says the extra is under a tenth of a per cent. It cannot say zero.

What S2 cannot feel: the spin 10:36

And there is one property of the black hole that S two cannot feel at all. Its spin. A spinning mass drags space around with it, and at a hundred and twenty astronomical units the drag on S two's orbit is far below anything the instrument can see. The mass has a quarter of a per cent. The spin has no number from this orbit at all.

S301: twelve AU at 8% of c 10:59

In August two thousand twenty six the same instrument found a star that passes ten times closer. Twelve astronomical units, closer than Uranus is to the Sun, at eight per cent of the speed of light, once every eight point seven years. That star's orbit will move with the spin.

So the practical version. When a mass is quoted to a fraction of a per cent, ask at what distance, and ask what that distance was measured with. If the answer is the same orbit, the two numbers are one number, and the error bar is the distance, cubed.

124.95 milliarcseconds. Next: the star that feels the spin 11:36

One hundred and twenty four point nine five thousandths of a second of arc. The size of one star's orbit around the black hole at the centre of the Milky Way, measured as an angle by an interferometer that never saw the black hole at all. Cube it, multiply by a distance, divide by a period, and you have a mass quoted to a quarter of a per cent, and the reason it keeps changing. Next time: the star that feels the spin. S three oh one, at eight per cent of the speed of light. Absolute Magnitude Space. Every episode ends in a measured number.

Description and sources

S2 has been followed around Sagittarius A* since 1992, and since 2017 by GRAVITY, which combines four 8 m telescopes into a 130 m baseline and returns the star's separation from the black hole to about 50 microarcseconds. Kepler turns a closed orbit into a mass: size cubed over period squared. But the telescope hands over the size as an ANGLE, 124.95 milliarcseconds, and turning it into kilometres needs the distance to the galactic centre, which enters cubed. That distance comes from the same orbit, read a second way (km/s from the spectrograph against milliarcseconds per year from the camera), so mass and distance are fitted together and the mass rides on the distance to a power near two. That is why Keck's 3.975 million suns and the VLT's 4.297, eight per cent apart, agree to 0.05 per cent once put at the same distance; and why GRAVITY's 4.100, 4.154, 4.261 and 4.297 walk upward while the angle held to a third of a per cent: the fitted distance moved two per cent, and two per cent cubed is the whole five. The quarter of a per cent is the statistical error; the systematic one is three times larger. The episode ends on the number the instrument returned: 124.95 +/- 0.04 milliarcseconds.

PRINT-READY, FROM THIS CHANNEL

The Conversion Chain, Vol. 01 — the method, and four numbers taken apart with it

https://therepository.gumroad.com/l/the-conversion-chain

PRIMARY SOURCES

GRAVITY Collaboration (2022). A&A 657, L12. arXiv:2112.07478 -- M = 4.297 +/- 0.012 million suns (stat), R0 = 8,277 +/- 9 pc; a(S2) = 0.12495 arcsec; systematics ~40,000 suns; extended mass < 3,000 suns; Table B.1.
GRAVITY Collaboration (2020). A&A 636, L5. arXiv:2004.07187 -- Schwarzschild precession, 12 arcmin per orbit, f_SP = 1.10 +/- 0.19; M = 4.261, R0 = 8,246.7 pc, P = 16.0455 yr.
GRAVITY Collaboration (2019). A&A 625, L10. arXiv:1904.05721 -- R0 = 8,178 +/- 13 +/- 22 pc; M = 4.154; f_redshift = 1.04 +/- 0.05; separation to 20 microarcseconds.
GRAVITY Collaboration (2018). A&A 615, L15. arXiv:1807.09409 -- pericentre May 2018: 120 AU, ~1,400 R_S, ~7,650 km/s; ~200 km/s redshift, f = 0.90 +/- 0.17; M = 4.100, R0 = 8,122 pc, a = 125.40 mas.
Gillessen et al. (2009). ApJ 692, 1075. arXiv:0810.4674 -- 4.31 +/- 0.06 (stat) +/- 0.36 (R0); 28 stars; M scales as R0^2.19.
Ghez et al. (2008). ApJ 689, 1044. arXiv:0808.2870 -- 4.1 +/- 0.6 million suns, R0 = 8.0 +/- 0.6 kpc, Keck.
Do et al. (2019). Science 365, 664. arXiv:1907.10731 -- redshift 0.88 +/- 0.17; 3.975 million suns at 7,959 pc.
Schodel et al. (2002). Nature 419, 694 -- 3.7 +/- 1.5 million suns; SHARP at the NTT since 1992.
GRAVITY Collaboration (2017). A&A 602, A94. arXiv:1705.02345 -- 130 m baseline; ~50 microarcsecond astrometry.
ESO eso2612 (19 Aug 2026) -- S301: 25,000 km/s, 8.7 yr, 12 AU. Mang et al., Nature.
Reid et al. (2019). ApJ 885, 131. arXiv:1910.03357 -- R0 = 8.15 +/- 0.15 kpc from maser parallaxes.
Arithmetic redone here: (0.12495 arcsec x 8,277 pc)^3 / 16.0455^2 = 4.2965 million suns; (8,277/8,122)^3 - 1 = 5.8%.

ARCHIVE PLATES: all 17 are credited on screen in the video and listed in this project's manifest.

Absolute Magnitude takes one number the internet repeats and asks what an instrument actually returned. Every episode ends on a measured figure with its source on screen, and says plainly which part of it was converted afterwards.

No AI-generated imagery is used on this channel. Every frame of archive footage is real, publicly released material, credited on screen with its licence; every diagram is drawn in code from the numbers in the cited papers.

Corrections are pinned, not quietly edited.

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