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Look up at the night sky and the stars seem fixed. To notice that they are not, you need a careful record of where they were, made long ago, and a second record to compare it with. Hipparchus made such a record more than 2,100 years ago, and used older observations to find one of the slowest motions in astronomy. This post covers his catalogue, his discovery, his trigonometry, and a 2022 find that changed what we know about him.
Who was Hipparchus?
According to the MacTutor biography of Hipparchus from the University of St Andrews, he was born about 190 BC in Nicaea, now İznik in Turkey, and died about 120 BC, probably on the island of Rhodes. His observations place him in Alexandria in 146 BC and on Rhodes in 127 and 126 BC.
Almost everything he wrote is lost. Only one work survives, a Commentary on Aratus and Eudoxus, and MacTutor calls it "certainly not one of his major works". Most of what we know comes from Ptolemy's Almagest, written about three centuries later, which used his results without always explaining them.
What was in his star catalogue?
MacTutor says the catalogue is believed to have held about 850 stars and was probably completed around 129 BC. For centuries historians argued about how it recorded positions and whether Ptolemy simply copied it.
New evidence arrived in 2022. Gysembergh, Williams and Zingg (2022), in the Journal for the History of Astronomy, used multispectral imaging on a palimpsest, a manuscript whose original text had been scraped off and written over. They recovered part of Hipparchus' catalogue. Their abstract reports three findings:
The catalogue was written in equatorial coordinates, the system astronomers still use.
Ptolemy's later catalogue "was not based solely on data from Hipparchus' Catalogue".
The numbers are consistent with an accuracy within 1° of the true positions, which would make it "significantly more accurate" than Ptolemy's.
What is precession, and how did he find it?
The Earth's axis slowly wobbles like a spinning top, so the points where the Sun crosses the celestial equator, the equinoxes, creep westward against the stars. MacTutor explains that Hipparchus came to this while trying to pin down the length of the year. There are two kinds: the time for the Sun to return to the same place among the stars (the sidereal year) and the time for the seasons to repeat (the tropical year). If they differ, the equinoxes must be drifting.
MacTutor describes how, probably starting from Babylonian data and checking against older Greek observations, he found the tropical year 1/300 of a day shorter than 365¼ days, and the sidereal year 1/144 of a day longer. MacTutor says these values give a precession rate of 1° per century.
Worked example: how long is one full cycle?
1° per century is 3,600″ every 100 years, or 36″ per year.
A full circle is 360° = 1,296,000″. At 36″ per year, one cycle takes 1,296,000 ÷ 36 = 36,000 years.
MacTutor gives the modern rate as 50.26″ per year. Then 1,296,000 ÷ 50.26 ≈ 25,790 years.
So his rate was too slow, but he had found a motion that takes tens of thousands of years from records spanning only a few centuries.
How far away did he think the Moon was?
MacTutor reports that Hipparchus put the Moon's distance between 59 and 67 Earth radii, using an eclipse and a range for the Sun's distance.
Check it with modern data. The NASA Moon fact sheet gives the Moon's mean distance as 384,400 km, and the NASA Earth fact sheet gives the Earth's mean radius as 6,371 km. 384,400 ÷ 6,371 ≈ 60.3 Earth radii, inside his range.
Did Hipparchus invent trigonometry?
MacTutor quotes the historian Toomer: it "seems highly probable that Hipparchus was the first to construct a table of chords". A chord is the straight line joining two points on a circle. If the angle at the centre is 2a and the radius is R, the chord is 2R sin a. A table of chords lets you solve triangles without starting from scratch each time. Not everyone gives him priority: Mansfield and Wildberger (2017) argue that the Babylonian tablet Plimpton 322 is a ratio-based trigonometric table more than a millennium older.
MacTutor describes the historian Toomer's reconstruction. Hipparchus divided the circle into 360° of 60′ each, and chose the radius so that it is measured in the same arcminutes as the circumference.
Worked example: where does 3438 come from?
The circumference is 360 × 60 = 21,600 arcminutes.
Radius = circumference ÷ 2π = 21,600 ÷ 6.2832 ≈ 3,437.7, rounded to 3,438.
So half the chord of 2a is 3,438 sin a. For a = 30°, the chord of 60° is 2 × 3,438 × 0.5 = 3,438, equal to the radius, as it should be for a regular hexagon.
MacTutor adds that the only surviving trace of his tables is in Indian tables thought to be based on them. Our post on Aryabhata's astronomy covers the Indian sine tradition.
Common mistakes: confusing chord with sine (a chord is twice the sine of half the angle, scaled by the radius), and thinking precession means the stars move. The stars barely move; our reference points on the sky do.
What can a student take from Hipparchus?
Write things down carefully. His catalogue was useful for centuries because it was precise. Your own error log works the same way.
Compare records to find slow changes. Precession only shows up when you compare old data with new.
Give a range, not just a number. His 59 to 67 Earth radii was honest about uncertainty and contained the truth.
Practise by computing the chord of 90° in Hipparchus' units, then checking it against 2R sin 45°. If the link between chords and sines is shaky, the Fermi Concept Library covers every concept in physics, chemistry, biology, mathematics and computing, one idea at a time. For the next chapter of the story, read our post on Ptolemy and the Almagest.
Tonight, note where Orion or the Plough sits at 9 pm, and check again at 9 pm a month later: the pattern will have shifted west by about 30°. That is the Earth's orbit, not precession, which is far too slow to see in a lifetime.
