Editing Antikythera mechanism (section)

==Mechanics==
Information on the specific data obtained from the fragments is detailed in the supplement to the 2006 ''Nature'' article from Freeth et al.<ref name="freeth-06" />

===Operation===
On the front face of the mechanism, there is a fixed ring dial representing the [[ecliptic]], the twelve [[zodiac]]al signs marked off with equal 30-degree sectors. This matched with the Babylonian custom of assigning one twelfth of the ecliptic to each zodiac sign equally, even though the [[constellation]] boundaries were variable. Outside that dial is another ring which is rotatable, marked off with the months and days of the Sothic [[Egyptian calendar]], twelve months of 30 days plus five [[Intercalation (timekeeping)|intercalary days]]. The months are marked with the Egyptian names for the months transcribed into the [[Greek alphabet]]. The first task is to rotate the Egyptian calendar ring to match the current zodiac points. The Egyptian calendar ignored leap days, so it advanced through a full zodiac sign in about 120 years.<ref name=freeth-12/>

The mechanism was operated by turning a small hand crank (now lost) which was linked via a [[crown gear]] to the largest gear, the four-spoked gear visible on the front of fragment A, gear b1. This moved the date pointer on the front dial, which would be set to the correct Egyptian calendar day. The year is not selectable, so it is necessary to know the year currently set, or by looking up the cycles indicated by the various calendar cycle indicators on the back in the Babylonian [[ephemeris]] tables for the day of the year currently set, since most of the calendar cycles are not synchronous with the year. The crank moves the date pointer about 78 days per full rotation, so hitting a particular day on the dial would be easily possible if the mechanism were in good working condition. The action of turning the hand crank would also cause all interlocked gears within the mechanism to rotate, resulting in the simultaneous calculation of the position of the Sun and Moon, the [[Lunar phase|moon phase]], [[eclipse]], and calendar cycles, and perhaps the locations of [[List of gravitationally rounded objects of the Solar System#Planets|planets]].<ref name=freeth-09/>

The operator also had to be aware of the position of the spiral dial pointers on the two large dials on the back. The pointer had a "follower" that tracked the spiral incisions in the metal as the dials incorporated four and five full rotations of the pointers. When a pointer reached the terminal month location at either end of the spiral, the pointer's follower had to be manually moved to the other end of the spiral before proceeding further.<ref name=freeth-06 />{{rp|10}}

===Faces===
[[File:Computer graphic for front of Antikythera mechanism.jpg|thumb|right|Computer-generated front panel of the Freeth model]]

====Front face====
The front dial has two concentric circular scales. The inner scale marks the Greek signs of the zodiac, with division in degrees. The outer scale, which is a movable ring that sits flush with the surface and runs in a channel, is marked off with what appear to be days and has a series of corresponding holes beneath the ring in the channel.

Since the discovery of the mechanism more than a century ago, this outer ring has been presumed to represent a 365-day Egyptian solar calendar, but research (Budiselic, et al., 2020) challenged this presumption and provided direct statistical evidence there are 354 intervals, suggesting a lunar calendar.<ref name="budiselic"/> Since this initial discovery, two research teams, using different methods, independently calculated the interval count. Woan and Bayley calculate 354–355 intervals using two different methods, confirming with higher accuracy the Budiselic et al. findings and noting that "365 holes is not plausible".<ref name="Auto82-31"/> Malin and Dickens' best estimate is 352.3±1.5 and concluded that the number of holes (N) "has to be integral and the SE ([[standard error]]) of 1.5 indicates that there is less than a 5% probability that N is not one of the six values in the range 350 to 355. The chances of N being as high as 365 are less than 1 in 10,000. While other contenders cannot be ruled out, of the two values that have been proposed for N on astronomical grounds, that of Budiselic et al. (354) is by far the more likely."<ref name=budiselic /><ref name="Auto82-32"/><ref name="Auto82-33"/>

If one supports the 365&nbsp;day presumption, it is recognized the mechanism predates the [[Julian calendar]] reform, but the [[Sothic cycle|Sothic]] and [[Callippus|Callippic]] cycles had already pointed to a {{sfrac|365|1|4}}&nbsp;day solar year, as seen in [[Ptolemy III Euergetes|Ptolemy&nbsp;III]]'s attempted calendar reform of 238&nbsp;BC. The dials are not believed to reflect his proposed leap day ([[Epag.]]&nbsp;6), but the outer calendar dial may be moved against the inner dial to compensate for the effect of the extra quarter-day in the solar year by turning the scale backward one day every four years.

If one is in favour of the 354&nbsp;day evidence, the most likely interpretation is that the ring is a manifestation of a 354-day lunar calendar. Given the era of the mechanism's presumed construction and the presence of Egyptian month names, it is possibly the first example of the Egyptian civil-based [[lunar calendar]] proposed by [[Richard Anthony Parker]] in 1950.<ref name="Auto82-34"/> The lunar calendar's purpose was to serve as a day-to-day indicator of successive lunations, and would also have assisted with the interpretation of the lunar phase pointer, and the [[Metonic]] and [[Saros (astronomy)|Saros]] dials. Undiscovered gearing, synchronous with the rest of the Metonic gearing of the mechanism, is implied to drive a pointer around this scale. Movement and registration of the ring relative to the underlying holes served to facilitate both a 1-in-76-year [[Callippic cycle]] correction, as well as convenient lunisolar intercalation.

The dial also marks the position of the Sun on the ecliptic, corresponding to the current date in the year. The orbits of the Moon and the five planets known to the Greeks are close enough to the ecliptic to make it a convenient reference for defining their positions as well.

The following three [[Egyptian calendar#Months|Egyptian months]] are inscribed in [[History of the Greek alphabet|Greek letters]] on the surviving pieces of the outer ring:{{sfn|Jones|2017|page=97}}
* {{lang|grc-EG|ΠΑΧΩΝ}} ([[Pachon]])
* {{lang|grc-EG|ΠΑΥΝΙ}} ([[Payni]])
* {{lang|grc-EG|ΕΠΙΦΙ}} ([[Epiphi]])

The other months have been reconstructed; some reconstructions of the mechanism omit the five days of the Egyptian intercalary month. The Zodiac dial contains Greek inscriptions of the members of the zodiac, which is believed to be adapted to the [[tropical month]] version rather than the [[Sidereal month|sidereal]]:<ref name=freeth-06-1/>{{rp|8}}{{Failed verification|reason=This page mentions neither tropical nor sidereal|date=September 2016}}
[[Image:Antikythera model front panel Mogi Vicentini 2007.JPG|thumb|upright=1.3|Front panel of a 2007 re-creation]]
* {{lang|grc|ΚΡΙΟΣ}} ({{transliteration|grc|Krios}} [Ram], Aries)
* ΤΑΥΡΟΣ (Tauros [Bull], Taurus)
* ΔΙΔΥΜΟΙ (Didymoi [Twins], Gemini)
* ΚΑΡΚΙΝΟΣ (Karkinos [Crab], Cancer)
* ΛΕΩΝ (Leon [Lion], Leo)
* ΠΑΡΘΕΝΟΣ (Parthenos [Maiden], Virgo)
* ΧΗΛΑΙ (Chelai [Scorpio's Claw or Zygos], Libra)
* ΣΚΟΡΠΙΟΣ (Skorpios [Scorpion], Scorpio)
* ΤΟΞΟΤΗΣ (Toxotes [Archer], Sagittarius)
* ΑΙΓΟΚΕΡΩΣ (Aigokeros [Goat-horned], Capricorn)
* ΥΔΡΟΧΟΟΣ (Hydrokhoos [Water carrier], Aquarius)
* ΙΧΘΥΕΣ (Ichthyes [Fish], Pisces)

Also on the zodiac dial are single characters at specific points (see reconstruction at ref<ref name=isaw-1/>). They are keyed to a ''[[parapegma]]'', a precursor of the modern day [[almanac]] inscribed on the front face above and beneath the dials. They mark the locations of longitudes on the ecliptic for specific stars. The ''parapegma'' above the dials reads (square brackets indicate inferred text):

{| class="wikitable"
|-
| Α || {{lang|grc|ΑΙΓΟΚΕΡΩΣ ΑΡΧΕΤΑΙ<br />ΑΝΑΤΕΛΛΕΙΝ [...] Α}} || [[Capricorn (constellation)|Capricorn]] begins to rise
|rowspan="11" style="background:white;"| <!-- blank column to separate separate sides -->
| Ι || ΚΡΙΟΣ ΑΡΧΕΤΑΙ ΕΠΙΤΕΛΛΕΙΝ<br />[...] Α || [[Aries (constellation)|Aries]] begins to rise
|-
| || ΤΡΟΠΑΙ ΧΕΙΜΕΡΙΝΑΙ [...] Α || [[Winter solstice]]
| || ΙΣΗΜΕΡΙΑ ΕΑΡΙΝΗ [...] Α || [[March equinox|Vernal equinox]]
|-
| Β || [...] ΕΙ ΕΣΠΕΡΙ || ... evening
| Κ || [...] ΕΣΠΕΡΙΑ [...] ΙΑ || ... evening
|-
| Γ || [...] ΙΕΣΠΕΡΙ || ... evening
| Λ || ΥΑΔΕΣ ΔΥΝΟΥΣΙΝ<br />ΕΣΠΕΡΙΑΙ [...] ΚΑ || The [[Hyades (star cluster)|Hyades]] set in the evening
|-
| Δ || [...] ΥΔΡΟΧΟΟΣ ΑΡΧΕΤΑΙ<br />ΕΠΙΤΕΛΛΕΙΝΑ || [[Aquarius (constellation)|Aquarius]] begins to rise
| Μ || ΤΑΥΡΟΣ ΑΡΧΕΤΑΙ<br />Ε{Π}ΙΤΕΛΛΕΙΝΑ || [[Taurus (constellation)|Taurus]] begins to rise
|-
| Ε || [...] ΕΣΠΕΡΙΟΣ [...] Ι{Ο} || ... evening
| Ν || ΛΥΡΑ ΕΠΙΤΕΛΛΕΙ<br />ΕΣΠΕΡΙΛ [...] Δ || [[Lyra]] rises in the evening
|-
| Ζ || [...] ΡΙΑΙ [...] Κ || ... {evening}
| Ξ || ΠΛΕΙΑΣ ΕΠΙΤΕΛΛΕΙ<br />ΕΩΙΑ [...] Ι || The [[Pleiades]] rise in the morning
|-
| Η || ΙΧΘΥΕΣ ΑΡΧΟΝΤΑΙ<br />ΕΠΙΤΕΛΛΕΙΝ [...] Α || [[Pisces (constellation)|Pisces]] begins to rise
| Ο || ΥΑΣ ΕΠΙΤΕΛΛΕΙ ΕΩΙΑ [...] Δ || The [[Hyades (star cluster)|Hyades]] rise in the morning
|-
| Θ || [...] {Ι}Α ||
| Π || ΔΙΔΥΜΟΙ ΑΡΧΟΝΤΑ<br />ΕΠΙΤΕΛΛΕΙΝ [...] Α || [[Gemini (constellation)|Gemini]] begins to rise
|-
<!-- | || || -->
|rowspan="2;" colspan="3;" style="background:white;"| 
| Ρ || ΑΕΤΟΣ ΕΠΙΤΕΛΛΕΙ ΕΣΠΕΡΙΟΣ || [[Altair]] rises in the evening
|-
<!-- | || || -->
| Σ || ΑΡΚΤΟΥΡΟΣ ΔΥΝΕΙ Ε{Ω}{Ι}ΟΣ || [[Arcturus]] sets in the morning
|}

The ''parapegma'' beneath the dials reads:

{| class="wikitable"
|-
| Α || ΧΗΛΑΙ ΑΡΧΟΝΤΑ<br />ΕΠΙΤΕΛΛΕΙΝ [...] Α || [[Libra (constellation)|Libra]] begins to rise
|rowspan=12 style="background:white;"| <!-- blank column to separate separate sides -->
| Μ || ΚΑΡΚΙΝΟΣ ΑΡΧΕΤΑΙ<br />[...] Α || [[Cancer (constellation)|Cancer]] begins {to rise}
|-
| || {Ι}ΣΗΜΕΡΙΑ ΦΘΙΝΟΠΩΡΙΝΗ<br />[...] Α || [[September equinox|Autumnal equinox]]
| || ΤΡΟΠΑΙ ΘΕΡΙΝΑΙ [...] Α || [[Summer solstice]]
|-
| Β || [...] ΑΝΑΤΕΛΛΟΥΣΙΝ<br />ΕΣΠΕΡΙΟΙΙΑ || ... rise in the evening
| Ν || ΩΡΙΩΝ ΑΝΤΕΛΛΕΙ ΕΩΙΟΣ || [[Orion (constellation)|Orion]] precedes the morning
|-
| Γ || [...] ΑΝΑΤΕΛΛΕΙ ΕΣΠΕΡΙΑΙΔ || ... rise in the evening
| Ξ || {Κ}ΥΩΝ ΑΝΤΕΛΛΕΙ ΕΩΙΟΣ || [[Canis Major]] precedes the morning
|-
| Δ || [...] ΤΕΛΛΕΙΙ{Ο} || ... rise
| Ο || ΑΕΤΟΣ ΔΥΝΕΙ ΕΩΙΟΣ || [[Altair]] sets in the morning
|-
| Ε || ΣΚΟΡΠΙΟΣ ΑΡΧΕΤΑΙ<br />ΑΝΑΤΕΛΛΕΙΝΑ || [[Scorpio (constellation)|Scorpio]] begins to rise
| Π || ΛΕΩΝ ΑΡΧΕΤΑΙ<br />ΕΠΙΤΕΛΛΕΙΝ [...] Α || [[Leo (constellation)|Leo]] begins to rise
|-
| Ζ || [...] ||
| Ρ || [...] ||
|-
| Η || [...] ||
| Σ || [...] ||
|-
| Θ || [...] ||
| Τ || [...] ||
|-
| Ι || ΤΟΞΟΤΗΣ ΑΡΧΕΤΑΙ<br />ΕΠΙΤΕΛΛΕΙΝ [...] Α || [[Sagittarius (constellation)|Sagittarius]] begins to rise
| Υ || [...] ||
|-
| Κ || [...] ||
| Φ || [...] ||
|-
| Λ || [...] ||
| Χ || [...] ||
|}

At least two pointers indicated positions of bodies upon the ecliptic. A lunar pointer indicated the position of the Moon, and a mean Sun pointer was shown, perhaps doubling as the current date pointer. The Moon position was not a simple mean Moon indicator which would indicate movement uniformly around a circular orbit; rather, it approximated the acceleration and deceleration of the Moon's elliptical orbit, through the earliest extant use of [[epicyclic gearing]].

It also tracked the precession of the Moon's elliptical orbit around the ecliptic in an 8.88&nbsp;year cycle. The mean Sun position is, by definition, the current date. It is speculated that since significant effort was taken to ensure the position of the Moon was correct,<ref name=freeth-06-1/>{{rp|20, 24}} there was likely to have also been a "true sun" pointer in addition to the mean Sun pointer, to track the elliptical anomaly of the Sun (the orbit of Earth around the Sun), but there is no evidence of it among the fragments found.<ref name=freeth-12/> Similarly, neither is there the evidence of planetary orbit pointers for the five planets known to the Greeks among the fragments. But see [[#Proposed gear schemes|Proposed gear schemes]] below.

Mechanical engineer Michael Wright demonstrated there was a mechanism to supply the lunar phase in addition to the position.<ref name=wright-05/> The indicator was a small ball embedded in the lunar pointer, half-white and half-black, which rotated to show the phase (new, first quarter, half, third quarter, full, and back). The data to support this function is available given the Sun and Moon positions as angular rotations; essentially, it is the angle between the two, translated into the rotation of the ball. It requires a [[differential (mechanical device)|differential gear]], a gearing arrangement that sums or differences two angular inputs.

====Rear face====
[[File:Computer graphic for back of Antikythera mechanism.jpg|thumb|right|Computer-generated back panel]]
In 2008, scientists reported new findings in ''[[Nature (journal)|Nature]]'' showing the mechanism not only tracked the [[Metonic calendar]] and predicted [[solar eclipses]], but also calculated the timing of panhellenic athletic games, such as the [[ancient Olympic Games]].<ref name=freeth-08/> Inscriptions on the instrument closely match the names of the months that are used on calendars from [[Epirus]] in northwestern Greece and with the island of [[Corfu]], which in antiquity was known as Corcyra.<ref name=wilford-08/><ref name=connor-08/><ref name="Auto82-35"/>

On the back of the mechanism, there are five dials: the two large displays, the Metonic and the [[Saros (astronomy)|Saros]], and three smaller indicators, the so-called Olympiad Dial,<ref name=freeth-08/> which has been renamed the Games dial as it did not track Olympiad years (the four-year cycle it tracks most closely is the Halieiad),<ref name="Auto82-36"/> the [[Callippic cycle|Callippic]], and the [[exeligmos]].<ref name=freeth-06 />{{rp|11}}

The Metonic dial is the main upper dial on the rear of the mechanism. The Metonic cycle, defined in several physical units, is 235 [[Lunar month#Synodic month|synodic months]], which is very close (to within less than 13 one-millionths) to 19 tropical years. It is therefore a convenient interval over which to convert between lunar and solar calendars. The Metonic dial covers 235 months in five rotations of the dial, following a spiral track with a follower on the pointer that keeps track of the layer of the spiral. The pointer points to the synodic month, counted from new moon to new moon, and the cell contains the [[Hellenic calendars#Corinthian|Corinthian month names]].<ref name=freeth-08 /><ref name="Auto82-37"/><ref name="auto1"/>

# {{lang|grc-x-doric|ΦΟΙΝΙΚΑΙΟΣ}} ({{transliteration|grc|Phoinikaios}})
# ΚΡΑΝΕΙΟΣ (Kraneios)
# ΛΑΝΟΤΡΟΠΙΟΣ (Lanotropios)
# ΜΑΧΑΝΕΥΣ (Machaneus, ''"mechanic"'', referring to [[Zeus]] the inventor)
# ΔΩΔΕΚΑΤΕΥΣ (Dodekateus)
# ΕΥΚΛΕΙΟΣ (Eukleios)
# ΑΡΤΕΜΙΣΙΟΣ (Artemisios)
# ΨΥΔΡΕΥΣ (Psydreus)
# ΓΑΜΕΙΛΙΟΣ (Gameilios)
# ΑΓΡΙΑΝΙΟΣ (Agrianios)
# ΠΑΝΑΜΟΣ (Panamos)
# ΑΠΕΛΛΑΙΟΣ (Apellaios)

Thus, setting the correct solar time (in days) on the front panel indicates the current lunar month on the back panel, with resolution to within a week or so.

Based on the fact that the calendar month names are consistent with all the evidence of the Epirote calendar and that the Games dial mentions the very minor Naa games of Dodona (in Epirus), it has been argued that the calendar on the mechanism is likely to be the Epirote calendar, and that this calendar was probably adopted from a Corinthian colony in Epirus, possibly Ambracia.<ref name="auto1"/> It has been argued that the first month of the calendar, Phoinikaios, was ideally the month in which the autumn equinox fell, and that the start-up date of the calendar began shortly after the astronomical new moon of 23 August 205 BC.<ref name="Auto82-38"/>

The Games dial is the right secondary upper dial; it is the only pointer on the instrument that travels in an anticlockwise direction as time advances. The dial is divided into four sectors, each of which is inscribed with a year indicator and the name of two [[Panhellenic Games]]: the "crown" games of [[Isthmian Games|Isthmia]], [[Ancient Olympic Games|Olympia]], [[Nemean Games|Nemea]], and [[Pythian Games|Pythia]]; and two lesser games: Naa (held at [[Dodona]])<ref name=bbc-08/> and the [[Halieia]] of Rhodes.<ref name="Auto82-39"/> The inscriptions on each one of the four divisions are:<ref name=freeth-06 /><ref name=freeth-08/>

{| class="wikitable"
 |+ Olympic dial
 |-
 ! Year of the cycle
 ! Inside the dial inscription
 ! Outside the dial inscription
 |-
 ! 1
 | LΑ
 | ΙΣΘΜΙΑ (Isthmia)<br />ΟΛΥΜΠΙΑ (Olympia)
 |-
 ! 2
 | LΒ
 | ΝΕΜΕΑ (Nemea)<br />NAA (Naa)
 |-
 ! 3
 | LΓ
 | ΙΣΘΜΙΑ (Isthmia) <br />ΠΥΘΙΑ (Pythia)
 |-
 ! 4
 | LΔ
 | ΝΕΜΕΑ (Nemea)<br />ΑΛΙΕΙΑ (Halieia)
 |}

The Saros dial is the main lower spiral dial on the rear of the mechanism.<ref name=freeth-06 />{{rp|4–5, 10}} The Saros cycle is 18 years and {{frac|11|1|3}} days long (6585.333... days), which is very close to 223 synodic months (6585.3211 days). It is defined as the cycle of repetition of the positions required to cause solar and lunar eclipses, and therefore, it could be used to predict them—not only the month, but the day and time of day. The cycle is approximately 8 hours longer than an integer number of days. Translated into global spin, that means an eclipse occurs not only eight hours later, but one-third of a rotation farther to the west. Glyphs in 51 of the 223 synodic month cells of the dial specify the occurrence of 38 lunar and 27 solar eclipses. Some of the abbreviations in the glyphs read:{{citation needed|date=October 2019}}
* Σ = ΣΕΛΗΝΗ ("Selene", Moon)
* Η = ΗΛΙΟΣ ("Helios", Sun)
* H\M = ΗΜΕΡΑΣ ("Hemeras", of the day)
* ω\ρ = ωρα ("hora", hour)
* N\Y = ΝΥΚΤΟΣ ("Nuktos", of the night)

The glyphs show whether the designated eclipse is solar or lunar, and give the day of the month and hour. Solar eclipses may not be visible at any given point, and lunar eclipses are visible only if the Moon is above the horizon at the appointed hour.<ref name=freeth-06-1 />{{rp|6}} In addition, the inner lines at the cardinal points of the Saros dial indicate the start of a new [[full moon cycle]]. Based on the distribution of the times of the eclipses, it has been argued the start-up date of the Saros dial was shortly after the astronomical new moon of 28 April 205 BC.<ref name="Carman Evans" />

The Exeligmos dial is the secondary lower dial on the rear of the mechanism. The exeligmos cycle is a 54-year triple Saros cycle that is 19,756 days long. Since the length of the Saros cycle is to a third of a day (namely, 6,585 days plus 8 hours), a full exeligmos cycle returns the counting to an integral number of days, as reflected in the inscriptions. The labels on its three divisions are:<ref name=freeth-06 />{{rp|10}}
* Blank or o ? (representing the number zero, assumed, not yet observed)
* H (number 8) means add 8 hours to the time mentioned in the display
* Iϛ (number 16) means add 16 hours to the time mentioned in the display

Thus the dial pointer indicates how many hours must be added to the glyph times of the Saros dial in order to calculate the exact eclipse times.{{citation needed|date=October 2019}}

===Doors===
[[File:Manual2021-X MOUSSAS SAROS.jpg|thumb|ΣΚΓ, indicating the [[Saros cycle]] of 223 months]]
The mechanism has a wooden casing with a front and a back door, both containing inscriptions.<ref name=freeth-08/><ref name=freeth-06-1/> The back door appears to be the 'instruction manual'. On one of its fragments is written "76 years, 19 years" representing the [[Callippic cycle|Callippic]] and [[Metonic cycle|Metonic]] cycles. Also written is "223" for the [[Saros cycle]]. On another one of its fragments, it is written "on the spiral subdivisions 235" referring to the Metonic dial.

===Gearing===
The mechanism is remarkable for the level of miniaturisation and the complexity of its parts, which is comparable to that of 14th-century [[astronomical clock]]s. It has at least 30 gears, although mechanism expert Michael Wright has suggested the Greeks of this period were capable of implementing a system with many more gears.<ref name=freeth-09/>

There is debate as to whether the mechanism had indicators for all five of the planets known to the ancient Greeks. No gearing for such a planetary display survives and all gears are accounted for—with the exception of one 63-toothed gear (r1) otherwise unaccounted for in fragment D.<ref name=freeth-12/>

Fragment D is a small quasi-circular constriction that, according to Xenophon Moussas, has a gear inside a somewhat larger hollow gear. The inner gear moves inside the outer gear reproducing an epicyclical motion that, with a pointer, gives the position of planet Jupiter.<ref name="auto"/> The inner gear is numbered 45, "ME" in Greek, and the same number is written on two surfaces of this small cylindrical box.

The purpose of the front face was to position astronomical bodies with respect to the [[celestial sphere]] along the ecliptic, in reference to the observer's position on the Earth. That is irrelevant to the question of whether that position was computed using a heliocentric or geocentric view of the [[Solar System]]; either computational method should, and does, result in the same position (ignoring ellipticity), within the error factors of the mechanism. The epicyclic Solar System of [[Ptolemy]] ({{circa|100 AD}}–{{circa|170 AD}})—hundreds of years after the apparent construction date of the mechanism—carried forward with more epicycles, and was more accurate predicting the positions of planets than the view of [[Nicolaus Copernicus|Copernicus]] (1473–1543), until [[Johannes Kepler|Kepler]] (1571–1630) introduced the possibility that orbits are ellipses.<ref name=amrp-07-2/>

Evans et al. suggest that to display the mean positions of the five [[classical planets]] would require only 17 further gears that could be positioned in front of the large driving gear and indicated using individual circular dials on the face.<ref name=cte-10/>

Freeth and Jones modelled and published details of a version using gear trains mechanically similar to the lunar anomaly system, allowing for indication of the positions of the planets, as well as synthesis of the Sun anomaly. Their system, they claim, is more authentic than Wright's model, as it uses the known skills of the Greeks and does not add excessive complexity or internal stresses to the machine.<ref name=freeth-12/>

The gear teeth were in the form of [[equilateral triangle]]s with an average circular pitch of 1.6&nbsp;mm, an average wheel thickness of 1.4&nbsp;mm and an average air gap between gears of 1.2&nbsp;mm. The teeth were probably created from a blank bronze round using hand tools; this is evident because not all of them are even.<ref name="freeth-12"/> Due to advances in imaging and [[X-ray computed tomography|X-ray]] technology, it is now possible to know the precise number of teeth and size of the gears within the located fragments. Thus the basic operation of the device is no longer a mystery and has been replicated accurately. The major unknown remains the question of the presence and nature of any planet indicators.<ref name=freeth-06-1 />{{rp|8}}

A table of the gears, their teeth, and the expected and computed rotations of important gears follows. The gear functions come from Freeth et al. (2008)<ref name=freeth-08/> and for the lower half of the table from Freeth et al. (2012).<ref name=freeth-12/> The computed values start with 1 year per revolution for the b1 gear, and the remainder are computed directly from gear teeth ratios. The gears marked with an asterisk (*) are missing, or have predecessors missing, from the known mechanism; these gears have been calculated with reasonable gear teeth counts.<ref name=freeth-08/><ref name=freeth-06-1/> (Lengths in days are calculated assuming the year to be 365.2425 days.)

{| class="wikitable"
|+ The Antikythera Mechanism: known and proposed gears and accuracy of computation
|-
! Gear name<ref group=table>Change from traditional naming: X is the main year axis, turns once per year with gear B1. The B axis is the axis with gears B3 and B6, while the E axis is the axis with gears E3 and E4. Other axes on E (E1/E6 and E2/E5) are irrelevant to this table.</ref>
! Function of the gear/pointer
! Length of time for a full circular revolution
! Mechanism formula<ref group=table>"Time" is the interval represented by one complete revolution of the gear.</ref>
! Computed interval
! Gear direction<ref group=table>As viewed from the front of the Mechanism.  The "natural" view is viewing the side of the Mechanism the dial/pointer in question is actually displayed on.</ref>
|-
! x
| Year gear
| 1 tropical year
| 1 (by definition)
| 1 year (presumed)
| clockwise<ref group=table>The Greeks, being in the northern hemisphere, assumed proper daily motion of the stars was from east to west, anticlockwise when the ecliptic and zodiac is viewed to the south. As viewed on the front of the Mechanism.</ref>
|-
! b
| The Moon's orbit
| 1 sidereal month (27.321661 days)
| Time(b) = Time(x) * (c1/b2) * (d1/c2) * (e2/d2) * (k1/e5) * (e6/k2) * (b3/e1)
| 27.321 days<ref group=table name=epicycle>On average, due to epicyclic gearing causing accelerations and decelerations.</ref>
| clockwise
|-
! r
| Lunar phase display
| 1 synodic month (29.530589 days)
| Time(r) = 1 / (1 / Time(b2: ''mean sun'' or sun3: ''true sun'')) – (1 / Time(b)))
| 29.530 days<ref group=table name=epicycle/>
|
|-
! n*
| Metonic pointer
| Metonic cycle / 5 turns = 1387.94 days
| Time(n) = Time(x) * (l1/b2) * (m1/l2) * (n1/m2)
| 1387.9 days
| anticlockwise<ref group=table name=boxside>Being on the reverse side of the box, the "natural" rotation is the opposite</ref>
|-
! o*
| Games dial pointer
| 4 years (5551.8 days)
| Time(o) = Time(n) * (o1/n2)
| 4.00 years
| clockwise<ref group=table name=boxside/><ref group=table>This was the only visual pointer naturally travelling in the anticlockwise direction.</ref>
|-
! q*
| Callippic pointer
| 27758.8 days
| Time(q) = Time(n) * (p1/n3) * (q1/p2)
| 27758 days
| anticlockwise<ref group=table name=boxside/>
|-
! e*
| Lunar orbit precession
| 8.88 years (3244.37 days)
| Time(e) = Time(x) * (l1/b2) * (m1/l2) * (e3/m3)
| 8.8826 years
| anticlockwise<ref group=table>Internal and not visible.</ref>
|-
! g*
| Saros cycle
| Saros time / 4 turns = 1646.33 days
| Time(g) = Time(e) * (f1/e4) * (g1/f2)
| 1646.3 days
| anticlockwise<ref group=table name=boxside/>
|-
! i*
| Exeligmos pointer
| 19755.8 days
| Time(i) = Time(g) * (h1/g2) * (i1/h2)
| 19756 days
| anticlockwise<ref group=table name=boxside/>
|-
! colspan="6" style="text-align: center;" |The following are proposed gearing from the 2012 Freeth and Jones reconstruction:
|-
! sun3*
| True sun pointer
| 1 mean year
| Time(sun3) = Time(x) * (sun3/sun1) * (sun2/sun3)
| 1 mean year<ref group=table name=epicycle/>
| clockwise<ref group=table name=retro>Prograde motion; retrograde is obviously the opposite direction.</ref>
|-
! mer2*
| Mercury pointer
| 115.88 days (synodic period)
| Time(mer2) = Time(x) * (mer2/mer1)
| 115.89 days<ref group=table name=epicycle/>
| clockwise<ref group=table name=retro/>
|-
! ven2*
| Venus pointer
| 583.93 days (synodic period)
| Time(ven) = Time(x) * (ven1/sun1)
| 584.39 days<ref group=table name=epicycle/>
| clockwise<ref group=table name=retro/>
|-
! mars4*
| Mars pointer
| 779.96 days (synodic period)
| Time(mars) = Time(x) * (mars2/mars1) * (mars4/mars3)
| 779.84 days<ref group=table name=epicycle/>
| clockwise<ref group=table name=retro/>
|-
! jup4*
| Jupiter pointer
| 398.88 days (synodic period)
| Time(jup) = Time(x) * (jup2/jup1) * (jup4/jup3)
| 398.88 days<ref group=table name=epicycle/>
| clockwise<ref group=table name=retro/>
|-
! sat4*
| Saturn pointer
| 378.09 days (synodic period)
| Time(sat) = Time(x) * (sat2/sat1) * (sat4/sat3)
| 378.06 days<ref group=table name=epicycle/>
| clockwise<ref group=table name=retro/>
|}
 
''Table notes:''
{{reflist|group=table|30em}}

There are several gear ratios for each planet that result in close matches to the correct values for synodic periods of the planets and the Sun. Those chosen above seem accurate, with reasonable tooth counts, but the specific gears actually used are unknown.<ref name=freeth-12/>

==== Known gear scheme ====
[[file:AntikytheraMechanismSchematic-Freeth12.png|thumb|upright=1.4|A hypothetical schematic representation of the gearing of the Antikythera Mechanism, including the 2012 published interpretation of existing gearing, gearing added to complete known functions, and proposed gearing to accomplish additional functions, namely true sun pointer and pointers for the five then-known planets, as proposed by Freeth and Jones, 2012.<ref name=freeth-12/> Based also upon similar drawing in the Freeth 2006 Supplement<ref name=freeth-06-1/> and Wright 2005, Epicycles Part 2.<ref name="wright-05-1"/> Proposed (as opposed to known from the arte<!-- 'e' - this article uses British spelling -->fact) gearing crosshatched.]]

It is very probable there were planetary dials, as the complicated motions and periodicities of all planets are mentioned in the manual of the mechanism. The exact position and mechanisms for the gears of the planets is unknown. There is no coaxial system except for the Moon. Fragment D that is an epicycloidal system, is considered as a planetary gear for Jupiter (Moussas, 2011, 2012, 2014) or a gear for the motion of the Sun (University of Thessaloniki group).

The Sun gear is operated from the hand-operated crank (connected to gear a1, driving the large four-spoked mean Sun gear, b1) and in turn drives the rest of the gear sets. The Sun gear is b1/b2 and b2 has 64 teeth. It directly drives the date/mean sun pointer (there may have been a second, "true sun" pointer that displayed the Sun's elliptical anomaly; it is discussed below in the Freeth reconstruction). In this discussion, reference is to modelled rotational period of various pointers and indicators; they all assume the input rotation of the b1 gear of 360 degrees, corresponding with one tropical year, and are computed solely on the basis of the gear ratios of the gears named.<ref name=freeth-06/><ref name=freeth-08/><ref name=ieeecomp1/>

The Moon train starts with gear b1 and proceeds through c1, c2, d1, d2, e2, e5, k1, k2, e6, e1, and b3 to the Moon pointer on the front face. The gears k1 and k2 form an [[epicyclic gearing|epicyclic gear system]]; they are an identical pair of gears that do not mesh, but rather, they operate face-to-face, with a short pin on k1 inserted into a slot in k2. The two gears have different centres of rotation, so the pin must move back and forth in the slot. That increases and decreases the radius at which k2 is driven, also necessarily varying its angular velocity (presuming the velocity of k1 is even) faster in some parts of the rotation than others. Over an entire revolution the average velocities are the same, but the fast-slow variation models the effects of the elliptical orbit of the Moon, in consequence of [[Kepler's laws of planetary motion#Position as a function of time|Kepler's second and third laws]]. The modelled rotational period of the Moon pointer (averaged over a year) is 27.321 days, compared to the modern length of a lunar sidereal month of 27.321661 days. The pin/slot driving of the k1/k2 gears varies the displacement over a year's time, and the mounting of those two gears on the e3 gear supplies a precessional advancement to the ellipticity modelling with a period of 8.8826 years, compared with the current value of precession period of the moon of 8.85 years.<ref name=freeth-06/><ref name=freeth-08/><ref name=ieeecomp1/>

The system also models the [[lunar phase|phases of the Moon]]. The Moon pointer holds a shaft along its length, on which is mounted a small gear named r, which meshes to the Sun pointer at B0 (the connection between B0 and the rest of B is not visible in the original mechanism, so whether b0 is the current date/mean Sun pointer or a hypothetical true Sun pointer is unknown). The gear rides around the dial with the Moon, but is also geared to the Sun—the effect is to perform a [[differential gear]] operation, so the gear turns at the synodic month period, measuring in effect, the angle of the difference between the Sun and Moon pointers. The gear drives a small ball that appears through an opening in the Moon pointer's face, painted longitudinally half white and half black, displaying the phases pictorially. It turns with a modelled rotational period of 29.53 days; the modern value for the synodic month is 29.530589 days.<ref name=freeth-06/><ref name=freeth-08/><ref name=ieeecomp1/>

The Metonic train is driven by the drive train b1, b2, l1, l2, m1, m2, and n1, which is connected to the pointer. The modelled rotational period of the pointer is the length of the 6939.5 days (over the whole five-rotation spiral), while the modern value for the [[Metonic cycle]] is 6939.69 days.<ref name=freeth-06/><ref name=freeth-08/><ref name=ieeecomp1/>

The [[Olympiad]] train is driven by b1, b2, l1, l2, m1, m2, n1, n2, and o1, which mounts the pointer. It has a computed modelled rotational period of exactly four years, as expected. It is the only pointer on the mechanism that rotates anticlockwise; all of the others rotate clockwise.<ref name=freeth-06/><ref name=freeth-08/><ref name=ieeecomp1/>

The Callippic train is driven by b1, b2, l1, l2, m1, m2, n1, n3, p1, p2, and q1, which mounts the pointer. It has a computed modelled rotational period of 27758 days, while the modern value is 27758.8 days.<ref name=freeth-06/><ref name=freeth-08/><ref name=ieeecomp1/>

The Saros train is driven by b1, b2, l1, l2, m1, m3, e3, e4, f1, f2, and g1, which mounts the pointer. The modelled rotational period of the Saros pointer is 1646.3 days (in four rotations along the spiral pointer track); the modern value is 1646.33 days.<ref name=freeth-06/><ref name=freeth-08/><ref name=ieeecomp1/>

The Exeligmos train is driven by b1, b2, l1, l2, m1, m3, e3, e4, f1, f2, g1, g2, h1, h2, and i1, which mounts the pointer. The modelled rotational period of the exeligmos pointer is 19,756 days; the modern value is 19755.96 days.<ref name=freeth-06/><ref name=freeth-08/><ref name=ieeecomp1/>

It appears gears m3, n1-3, p1-2, and q1 did not survive in the wreckage. The functions of the pointers were deduced from the remains of the dials on the back face, and reasonable, appropriate gearage to fulfill the functions was proposed and is generally accepted.<ref name=freeth-06/><ref name=freeth-08/><ref name=ieeecomp1/>