Hipparchus applied Apollonius's epicycle/eccenter construction to the motion of the Sun and the Moon, but not to the planets. There are speculations about epicyclic gears for planets in the Antikythera mechanism, but apparently they did not survive. On the other hand, a few centuries later Ptolemy had well advanced models for all the planets, and even introduced equant to make them more accurate. What happened in between? Who first applied epicycles to planetary motions?

Lucio Russo even speculated about dynamical ideas from this time period concerning celestial motions based on some passages from Plutarch and Strabo. What is the consensus on that?


3 Answers 3


Actually, I've found some sources that suggest that Apollonius applied epicycles to planetary motion:

From here:

Apollonius also was an important person in founding Greek mathematical astronomy. He used geometrical models to explain planetary theory. He introduced systems of eccentric and epicyclic motion to explain the motion of the planets.

From here:

Apollonius was also an important founder of Greek mathematical astronomy, which used geometrical models to explain planetary theory. Ptolemy in his book Syntaxis says Apollonius introduced systems of eccentric and epicyclic motion to explain the apparent motion of the planets across the sky. This is not strictly true since the theory of epicycles certainly predates Apollonius. Nevertheless, Apollonius did make substantial contributions particularly using his great geometric skills. In particular, he made a study of the points where a planet appears stationary, namely the points where the forward motion changes to a retrograde motion or the converse.

From here:

Lastly, from references in Ptolemy’s Almagest, it is known that Apollonius introduced the systems of eccentric and epicyclic motion to explain planetary motion. Of particular interest was his determination of the points where a planet appears stationary.

And Wikipedia, by the way, uses the slightly dubious phrasing:

The hypothesis of eccentric orbits, or equivalently, deferent and epicycles, to explain the apparent motion of the planets and the varying speed of the Moon, is also attributed to him.

This last passage, of course, does not state outright that he applied the theory to planetary orbits.

  • 1
    $\begingroup$ Sorry, what I meant by "applied" is used it to fit actual observations. Apollonius did some theoretical analysis of the epicycle construction, but Wikipedia says "all this was theory and had not been put to practice" before Hipparchus.en.wikipedia.org/wiki/Hipparchus#Orbit_of_the_Moon $\endgroup$
    – Conifold
    Oct 30, 2014 at 23:58
  • $\begingroup$ Ahh, that makes a bit of a difference. Thanks. $\endgroup$
    – HDE 226868
    Oct 31, 2014 at 0:04
  • $\begingroup$ Apollonius (of Perga) was a contemporary of Hypparchus. $\endgroup$ Nov 3, 2014 at 20:46
  • 1
    $\begingroup$ It looks as though these "sources" are all copied from one another. $\endgroup$
    – fdb
    Jan 5, 2015 at 15:53
  • $\begingroup$ And all of them are based on Ptolemy. $\endgroup$ Mar 7, 2015 at 13:55

You can look in Wikipedia for the list of astronomers between Hipparchus and Ptolemy, or for more detail consult Neugebauer. (Or Ptolemy himself:-)

The problem is that 90% of our knowledge about astronomy before Ptolemy (except Babylonian for which we have an independent source) is based on Ptolemy books, and this is not an exaggeration. An evidence of this is Neugebauer's History of Ancient Mathematical astronomy. The first volume is an analysis of Ptolemy, the second of EVERYTHING else (Including Hipparchus, Babylonians, Egyptians, and everything in between), and the 3-d volume is Appendixes, tables plates etc.

EDIT. Wikipedia lists the following astronomers in the period between Hipparchus and Ptolemy: Aglaonice, Agrippa, Andronicus of Cyrrhus, Hypcicles, Geminus, Menelaus and Theon of Smyrna (these two are contemporaries of Ptolemy), Posidonius, Seleucus of Seleucia, Theodosius of Bythinia.

Of these, Ptolemy mentions: Agrippa, Theon of Smyrna and Menelaus. One book of Geminus still exists. All others are just mentioned somewhere in other sources.

EDIT 2. There is no consensus about Russo's speculations. The fact is that most of the Greek pre-Ptolemy astronomy is lost. (Including almost everything that Hipparchus wrote. Only one minor work of Hipparchus survives.) I am inclined to think that Russo is right in his general conclusions.

  • $\begingroup$ Is it known what those astronomers did? I remember from reading Ptolemy's passages that he only compares himself to Hipparchus and nobody else, maybe to make his own work look more substantial. $\endgroup$
    – Conifold
    Nov 3, 2014 at 23:39
  • $\begingroup$ Ptolemy credits those he cites with some observations. (Menelaus with a theorem). As I said, the problem is that Ptolemy is the only important source that survived. Even what Hypparchus did we mainly know from Ptolemy. $\endgroup$ Nov 4, 2014 at 0:17

(Source: Pierre Duhem, 1908, To Save The Phenomena)

According to Duhem, Ptolemy’s model was the first to fit observation - i.e., to “save the phenomena” of planetary motion. What Ptolemy did that previous philosophers had failed to do was to combine epicycles and eccentrics - each planet being borne of an epicycle whose centre described a circle eccentric to the world.

The reason that Ptolemy was the first to combine the two appears to be that Hipparchus proved that his model could be formulated using either epicycles or eccentrics.

What Hipparchus proved was that the course of the sun can be represented either by supposing that this star describes a circle eccentric to the world, or by letting it be carried by an epicycle, provided the revolution of this epicycle is achieved in exactly the same time in which its centre has completed a circle concentric with the world.

Having demonstrated the equivalence of the eccentric and epicyclic hypotheses, subsequent philosophers used either one or the other, but not both, thus failing to save the phenomena. Only Ptolemy combined the two to save the phenomena.

Although Hipparchus did not extend his model to include the planets, Theon of Smyrna, in his Astronomia, wrote that Adrastus of Aphrodisias said Hipparchus held that his method could be applied to each planet.

So who tried using epicycles between Hipparchus and Ptolemy?

By the time of Hipparchus astronomy had come to be dominated by the peripatetics - i.e., the followers of Aristotle’s physics - and they weren’t having any of this epicycle nonsense. For the Peripatetics, epicycles/eccentrics were contrary to natural principles.

Prior to Aristotle, Plato had declared astronomy to be the domain of the mathematician and had appealed to mathematicians to formulate a purely mathematical astronomy which “saved the phenomena” of planetary motion. Plato’s attitude was that the human mind was too feeble to comprehend the true nature of the superlunary spheres and therefore we must be content to have a mathematical theory which at least allowed us to make predictions that fit observation regardless of “truth”.

According to Duhem, almost all of what we know of the period between Hipparchus and Ptolemy consists of the peripatetic criticisms of epicycles/eccentrics. However, Duhem does cite the example of Adrastus of Aphrodisias who lived shortly before Ptolemy and proposed a model using epicycles.

According to the testimony of Theon of Smyrna, Adrastus of Aphrodisias ascribed to each planet an orbital shell contained by two spherical surfaces concentric with the universe. Within the shell is a full sphere occupying its entire thickness. The planet is then set into this full sphere. The orbital shell carries the full sphere in its revolution around the centre of the world while the full sphere turns on its axis. By means of this mechanism the planet describes an epicycle whose centre traverses a circle concentric with the world.

Theon is said to have constructed an orrery based on the model of Adrastus.

Duhem cites no other example of a philosopher using epicycles between Hipparchus and Ptolemy. Curiously, both Adrastus and Theon were peripatetics who justified the use of epicycles by arguing that they were the “accidental” consequence of the combination of the revolutionary and rotational movements of the planetary spheres.


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