Around 129 BC, an astronomer working on the island of Rhodes finished a list of the positions and brightnesses of roughly 850 stars. It was the first systematic star catalogue in the Greek tradition, and it made possible a discovery that requires comparing the sky across centuries.
Almost nothing Hipparchus wrote has survived. A single minor commentary remains. Everything else is known through later authors, above all Ptolemy’s Almagest, written nearly three hundred years afterwards, which incorporates his data and credits him repeatedly.
Why He Made It
Pliny the Elder gives a reason for the catalogue that may or may not be accurate but is at least memorable. A new star appeared in the sky, probably a nova, around 134 BC. Hipparchus, struck by the fact that the heavens could change at all, decided to record the stars so that future observers would be able to tell whether anything had moved, brightened, or vanished.
Whatever prompted it, the catalogue is an instrument aimed at the future. A single observation of the sky tells you where things are. A catalogue tells the next generation where things used to be.
The Magnitude Scale
Hipparchus needed a way to record brightness, and the system he devised is still in use.
He sorted the stars into six classes. The brightest were of the first magnitude, the faintest visible to the naked eye were of the sixth, and the rest were distributed between. The scale runs backwards from the modern instinct, since a larger number means a fainter star, which is a persistent source of confusion for anyone learning astronomy today.
In 1856 Norman Pogson formalised it by noting that a first magnitude star is roughly a hundred times brighter than a sixth magnitude one, and defined each magnitude step as a fixed ratio of about 2.512, the fifth root of a hundred. That definition preserved Hipparchus’s classes almost exactly while making the scale continuous and extensible. Modern catalogues give magnitudes to two decimal places on a system anchored to an eye judgement made in the second century BC.
Precession
The catalogue’s most important use came from comparison rather than observation.
Hipparchus measured the position of the bright star Spica relative to the autumn equinox point, and compared his figure with a measurement made by Timocharis in Alexandria about a hundred and fifty years earlier. The two did not agree. Spica had shifted by around two degrees.
Checking other stars, he found the same effect. The whole celestial sphere appeared to be drifting slowly relative to the equinoxes, at a rate he estimated at not less than one degree per century. The modern value is about one degree every seventy two years.
This is the precession of the equinoxes, and the cause is that the Earth’s axis wobbles like a spinning top, tracing a full circle roughly every twenty six thousand years. Hipparchus had no way to know the mechanism, which requires Newtonian gravity and the equatorial bulge of the Earth to explain, and which Newton addressed in the Principia. What he could do was detect the effect and measure its rate.
Finding it at all is the achievement. The shift is far too slow to notice within a lifetime. It only becomes visible if someone recorded the positions carefully long ago, someone else records them carefully now, and the two records are compared. Hipparchus had Timocharis’s numbers, and Babylonian records of eclipses and lunar positions going back centuries, which he used extensively.
The Distance to the Moon
Hipparchus also produced the first reliable measurement of the distance to another celestial body, and the method is a model of ancient ingenuity.
He used a solar eclipse that was total at one location and partial at another, with the two locations a known distance apart. The difference in how much of the Sun was covered gives the parallax of the Moon, the angle by which its apparent position shifts when viewed from two places, and from the parallax the distance follows by triangulation.
His answer was that the Moon lies between fifty nine and sixty seven Earth radii away. The true mean distance is about sixty. Given a value for the size of the Earth of the kind Eratosthenes had established a century earlier, this converts directly into a distance in stadia.
It is the second rung of what would become the cosmic distance ladder: measure the Earth, then use the Earth as a baseline to measure the Moon, then use larger baselines to reach further. Every subsequent step in astronomy repeats the pattern.
The Rest of the Work
Hipparchus’s contributions across astronomy are extensive, and much of what Ptolemy systematised was built on them:
- He computed the length of the tropical year as 365 days, 5 hours and 55 minutes, about six and a half minutes too long
- He constructed a table of chords, effectively the first trigonometric table, which made it possible to calculate the sides of triangles from angles. Trigonometry as a computational tool begins with him
- He built a geometric model of the Sun’s motion using an eccentric circle, which accounts for the unequal lengths of the seasons
- He worked on the motion of the Moon, determining the periods of its various cycles with impressive accuracy
- He is credited with improving or introducing instruments including the dioptra and possibly an early astrolabe
The Catalogue’s Fate
The star catalogue was lost, and its contents have been the subject of a long argument.
Ptolemy’s catalogue in Books VII and VIII of the Almagest lists 1,022 stars. Since Ptolemy worked nearly three centuries later, precession should have shifted every position by around four degrees, and Ptolemy states that he adjusted for this. Historians from Delambre onwards have noticed that certain systematic errors in Ptolemy’s positions are consistent with taking Hipparchus’s numbers and applying a slightly incorrect precession correction, rather than observing afresh.
This has been read as a serious accusation and also, more moderately, as ordinary ancient practice, since reworking inherited data was normal and Ptolemy credits Hipparchus openly throughout. What is not disputed is that a large part of Hipparchus’s work survives inside Ptolemy’s.
In 2022, researchers using multispectral imaging on a medieval manuscript from St Catherine’s Monastery, a palimpsest whose original text had been scraped off and overwritten, recovered passages giving stellar coordinates in a form that appears to come directly from Hipparchus’s catalogue. The recovered positions are accurate to within about one degree and, notably, are more accurate than the corresponding figures in Ptolemy.
The Line He Started
The practice Hipparchus established, recording positions precisely so that later observers can detect change, is the backbone of observational astronomy.
Tycho Brahe rebuilt the enterprise in the sixteenth century with far better instruments, cataloguing around a thousand stars to an accuracy of one or two arcminutes, and it was that catalogue which gave Kepler the raw material for the elliptical orbits. Edmond Halley in 1718 compared his own positions with Ptolemy’s, discovered that several bright stars had moved, and established that the fixed stars have proper motion of their own.
Each of those results is a comparison across time, and each depends on someone earlier having written the numbers down carefully enough to be worth checking.
Our six book pack on the history of astronomy collects the works where that tradition reached its modern form, including Tycho Brahe’s description of the instruments he designed to push naked eye accuracy to its physical limit.
What Survives of Him
Hipparchus is a strange figure to write about, because the evidence for his greatness is almost entirely secondhand. We have one commentary on a poem about constellations, and everything else comes through authors who read him.
What can be said with confidence is that the magnitude scale in every modern star chart is his, that trigonometry as a practical technique begins with his table of chords, that the precession of the equinoxes was his discovery, and that the first measured distance to another world was his calculation. For an astronomer whose books are gone, that is an unusually durable set of survivals.
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