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Section of Astrophysics, Astronomy and Mechanics and Astronomy Astrophysics, of Section

nomical events. These events take place periodically a once periodically place events take year and These nomical events.

i, i, Greece , Department of Physics, Section of Astrophysics, Astronomy and Mechanics and Astronomy Astrophysics, of Section Physics, of , Department , ,

Anastasiou of Puget Sound Puget of , Thessaloniki, Greece , Thessaloniki, Speaker

[email protected] [email protected] [email protected] [email protected] [email protected]

H. Seiradakis H.

star and constellation risings and settings, known as a parapegma. The largest part of astrothis nine cites consecutive list their is sequence dependentsensitively on Inlatitude. geographic to order calculate the dates of these visible risings and settings, a software program has the of Sun the andstars coordinates for been package. The equatorial software using the Mathematica written, from first prin the equinoxes, of precession the account into taking calculated were They used. were 150 B.C. Among the surviving inscriptions of the Antikythera Mechanism, there is a portion of a list of 1 541 24, Thessalonik 24, 541 54124 541 24, Thessaloniki, Greece Thessaloniki, 24, 541 Greece Thessaloniki, 24, 541 15 June 2012 June 15 - - - - - mail: mail: mail: mail: mail: CopyrightCommonsunder owned by thethe terms author(s) theof Creative Attributio - - - - -

 f Lessons Array: Kilometre the Square to Antikythera From Kerastari, Greece 12 Aristotle University, Department of Mechanical Engineering Mechanical of Department University, Aristotle GR E Stella Drougou Stella Archaeology, and History of Department University, Aristotle GR E Efstathiou Kyriakos E James Evans University USA 98416 WA Tacoma, St., Warner 1500 North E GR E John Physics, of Department University, Aristotle GR Antikythera Mechanism Antikythera Magdalini University Aristotle Positional astronomy and the Parapegma of the of the Parapegma the and astronomy Positional

PoS(Antikythera & SKA)029

. 7 ]

ng, 3, 4 he a, cites - [2,

there are

. − 37.0°N and and thorough (a) [5] : a. Also the crucial - Magdalini Anastasiou Magdalini , sheds perhaps some pegma’, pegma’, a calendar of [1]

are are two pieces of flat plate

events thatevents refer to the signs of

− − 45°N. The sequence of the events events of C1 the signs of the zodiac

echanism , based on our joint M are are categorized as follows

a - research

astronomical 2

, thus forming a ‘para ]

he he 9 [2 cuse. Fig. Fig. 1 shows the Parapegma inscriptions from plates

b), Fragment 09, Fragment 20, Fragment 22 and - . ] on plate C1 on setting setting and (b) there are 2 , 8

7 [

e, e, the Antikythera Mechanism had two concentric annuli. The the the Greek letters is also found on some of the text fragments of

a and C1 used -

e e Parapegma of the Antikythera . ion were also taken into account. The dates of the occurrence of these b, w - of of th

its its front plat and their evening

direction ysis The The though inscriptions read on most of these fragments are quite incomplete.

. ]

6 [ b.

ring its apparent magnitude with the sky background brightness. Atmospheric extinction types types the of events mentioned

es of events of es mentioned in Parapegma the The

The The fragments of the Mechanism with Parapegma inscriptions In In the centre of One One of the main still questions not about answered the Antikythera is Mechanism where it towards this towards effects effects of proper motion. The visibility of a star at its position on the compa sky was determined by and atmospheric refract events were calculated for geographic latitudes between 25°N events and their position among the the signs of give zodiac a fit best 33.3°N between Syra marginally and Rhodes includes which the decrease of the theof decrease of obliquity the nutation aberration, and ecliptic, as well as, for the stars, t a and C1 aand - Introduction Typ

events that events to refer the rising and setting of stars, rising,their settii.e. their morning morning their risingevening zodiac. the mentioned mentioned on plate C1 C1 2. attached attached to Fragment C (C1 Fragment 28 The analysis that follows is thus based on t information of the autumn equinox taking place when the Sun enters the zodiac sign of Libra, is is written in a serarate line and at the beginning of Greek each line alphabet. there is These a ‘index separate letter letters’ of the in sequence capital almost certainly letters correspond found to the on small the astronomical events. Parapegmata zodiac were known to dial be widely used in ancient Greece and as ones well butof meteorological were also events astronomical calendars of only not Looking Looking carefully at the inner dial, small capital letters are observed above some of the divisions scale of each zodiac sign. These letters follow alphabet. the A similar sequence of sequence of the letters of the Greek the Mechanism describing astronomical phenomena. The largest of these fragments, C1 (for astronomical the type events section). the Each 9 following of consecutive event events, see was was built or where it was used. anal astronomical The following light outer one displayed the Egyptian calendar and the inner one 1. Positional astronomy and the Parapegma of the Antikythera Mechanism the Antikythera of the Parapegma and astronomy Positional PoS(Antikythera & SKA)029

a and its -

are are dubious ) ) and visible ones a star cluster or a a star cluster or a ng ng basic spherical

Magdalini Anastasiou Magdalini arge arge errors both in the in in the east or the west ληθινοί

ἀ : ] 9

star [ b. The red letters

- reek reek text from plate C1 show show quite l

b and its translation in English. in translation its b and a - - The The computation of these events is

a and C1 defined as defined - : : The G

t. he he year that a star (or a star cluster or a

3 Upper

day day of the year that a star (or

plates plates C1 Sun Sun in conjunction (morning rising and evening

of of the plate C1 the the last day of the year that a star (or

the the first events events morning setting and evening rising and evening setting morning this this is for the : The Greek text from plate C1 from text Greek The :

): ):

in in the east or the west respectively). Therefore, we can have four ): ): this is the first day of t

): ): this is the ms ( mr er

( (

Sun

Lower . can can not be read nowadays.

More precisely, these visible events are events visible these precisely, More ΤΕΛΛΕΙ” ΤΕΛΛΕΙ” (rises) or “ΔΥΝΕΙ” (sets) (placing the ) is seen setting. ) seen is rising. ) seen is Parapegma Parapegma inscriptions from ). The true ones occur when the Sun and the star are on the horizon and so they are ΕΠΙ i.e i.e they are the events of practical interes “ star events star this this type subject athe always The of is events, star, verbor astar a cluster constellation. morning morning setting evening rising morning morning rising

The The ) and two in opposition ( in ) and two opposition

• • • The The visible events are observable and events these are the ones that used were by farmers, In In antiquity, the star events were differentiated into true ones ( In The The ινόμενοι

φα constellation constellation known a priori. a known priori. constellation) becomes visible above the eastern horizon in the morning twilight (after a period when it was hidden below the horizon or when it was just above the horizon but hidden by the Sun) the of brightness unobservable. unobservable. The calculation of the trigonometry, yet the results dates of these events occur. to are reported they in which signs zodiac as the is as of the events well sequence easy usi sailors, complicated as the depression of the Sun below the horizon and the altitude of the star are not evening) evening) (placing the types of events: two with the star and setting the ( 2.1 used is respectively), followed by the adjective “ΕΩΙΟΣ” (in the morning) or “ΕΣΠΕΡΙΟΣ” (in the Fig. Fig. 1: letters or letters that English. in translation Positional astronomy and the Parapegma of the Antikythera Mechanism the Antikythera of the Parapegma and astronomy Positional PoS(Antikythera & SKA)029

n α H he (1) (3) (2) of of 365

horizon horizon that the

in in steps of , ° star’s

1 titude - al ’s ’s position were followed followed by t ble ble a star cluster or a in in

and and the inner the dial inner of the

ition ition of the star and Magdalini Anastasiou Magdalini ° ts /sign, /sign, the sidereal time the and 15 certa -

the the geographic latitude, all all possi

ST φ , the ) odiac on odiac , were: e, for two of course cases, at

rial coordinates the starrial coordinates of and

star even star

), i.e. .

H with with no free parameters, a new

constellation of of the star, foragain two cases, with ly ly 2 tables with star

SunEast - e

d visible visible Star u - t i i,j t zodiac zodiac l t on a daily basis, we have 2 tables ” (begins to rise) (placing the constellatio a , υ in in the range between

4 j

  SunEast 

- to be se    cos cos ΛΛΕΙΝ 

and the Star -   the the coordinates equatorial i,j sin sin sin TE  ST H A the the last day of the year that a star (or ΕΠΙ e e division of each sign the of z   / zimuth zimuth

a is is      odiac constellation to the next to the constellation odiac

cos sin sin sin cos cos cos the the altitude (the horizon coordinates) odiac odiac constellations together with the fact that there is always an

in the evening twilight. the evening in of of Sun’s depression υ

): ): this

= 1 to 365) need e e first scal

the declination the ( declination ΤΕΛΛΕΙΝ i es

( and and , δ

. sidereal found, times the the equato Using calculate the calculate Sun - i ΑΝΑ s, for a certain depression of the Sun, to calculate the pos , δ unset, unset, as all 4 events have to be investigated. And as the Sun’s equatorial setting seen setting seen Sun wa

- i and and a certain latitude, we calculate the sidereal tim ) ) is indicate indicate that these statements are used to mark the position of the Sun, when it

ning ning the the azimuth able able of 141×365 values of (A is is sm zodiac statements zodiac

eve

: : a t of sidereal time sidereal of he basic equations of spherical trigonometry that were used trigonometry of spherical basic equations he A

thus thus for 141 values of Sun’s depression. Consequent So So for a and latitude acertain certain depression of the Sun, found have we the position of More More precisely, using the equatorial coordinates of the Sun, T In order to find a way to calculate the visible events In this type of events, the subject is always a • The calculation of the position of a star for a certain depression of the Sun depression certain a star of a for position of the calculation The The Sun in the east and in the the west. in the and east in Sun

Positional Astronomy for the calculation thefor of Astronomy Positional rosses the boundaries from z from one boundaries rosses the the the star. In order for the depression of the Sun to no longer be a free parameter, all calculations were repeated for all values 0.1°, formed sunrise sunrise and at s coordinates (α values same the we latitude, the where where right andascension the hour angle. the Sun was set The The main idea at position. its star visible the is to whether determine a find to criterion 3.1 3. software program was written from first principles, using the Mathematica software package. phrase phrase “ΑΡΧΕΤΑΙ in the east). The use of the z atindex inscribed letter th Mechani c constellation 2.2 Positional astronomy and the Parapegma of the Antikythera Mechanism the Antikythera of the Parapegma and astronomy Positional PoS(Antikythera & SKA)029

- Is in

Star

- (the

i,j of of the

read read

, υ in in these

° 2 tables of function function that h h . Using these SunWest -

B and and one

Star -

i,j mr

) ) to be determined.

Magdalini Anastasiou Magdalini up wit similarly located. similarly

in in the eastern sky, we ] ] published numerical

ing 10 SunWest - place place in the sky above the

end Star was visible was or visible not at each of e year that starthe is visible -

values easily located. The the located. The day of easily i,j

1.0° (in steps of 0.1°). So we

m – , υ Nawar [ iven iven sky brightness question question left to be answered was:

SunWest - , one of the visible ] ] who published values of the maximum Star star when an starare place takes event when - 15.0° and

i,j – 12 ] ] also published independent measurements e e used: (a)

5 [

. the eastern and the western sky. the western and eastern the able able of 141×365 values of (A will will be visible on the given sky brightness. This

. The Sun’s depression changes per 1 ) ) or (A

a t m for (the last day it is seen rising) are rising) seen is it (the last day et et al

are located by examining these recordings at valuesrecordings these by all are located examining

SunEast altitude thealtitude of - er such such recordings

of of Vega (11/11), the first day of the year that Vega is and and es

Star are not, therefore, free parameters. The dates of the the of dates The parameters. are not, free therefore, - , again i,j mr and and

, υ ar’s period of visibility (the star rises and sets in the evening). they they

, in 150 B.C f f the Sun and the star, the er

, ,

Tousey Tousey and Koomen [

values

’ ms SunEast and -

, nd nd (b) Koomen stern stern sky, we record again for each depression of the Sun the first and Star - mr Olympia of of a star in order to be visible at a g i,j

/1) is the last day the of year that is Vega and visible againis at minimum we m in in

in in the through through the 141×365 values of ‘visible/not visible’ shows shows two examples of Vega

with with the Sun in the east 1 owing owing the position o of of visible/not visible visible/not of of (21 Vega etermination of the visibility of a star a of of the visibility etermination

‘

d values values es es sing the Mathematica software package, we these interpolated values, to any position on he depression the Sun of depression and the he able able ), ), i.e. all possible star’s horizon coordinates with the Sun in the the west. in Sun the with coordinates star’s possible horizon all ), ), i.e. T T Looking U Whether Whether a star is visible at its position depends on the sky background brightness. Two So So kn The The

the corresponding columns corresponding the and the setting) star the seen is first day visible visible examples. The day of the visible Sun, is from the and altitude atdifference thus is visible minimum visible Sun. from the difference altitude visible’ visible’ the last day of the year of the st the visible of The dates depression. Sun’s of these these 141 x 365 positions in the eastern and in 141×365 the western sky, record for each depression of the Sun the first and the last day of th (the star rises and sets in the morning). Looking through the 141×365 values of ‘visible/not determines determines whether the star of magnitude function was investigated by apparent magnitude values, another interpolating function was formed in order position on the for sky (A the visibility of a star at this Using function, we calculated whether the star magnitude its of of of sky brightness B, in the form of tables at several altitudes of the Sun. the of depressions the Sun, several for from distances azimuthal and several horizon the sky, again, for any altitude of the Sun between now know, for each position of the star, the sky brightness and we need a sources sources of measured values of sky brightness wer tables of the sky twilight brightness B as a function horizon, of the azimuthal thedistance of the sky depression patch away of from the the Sun and the Sun altitude of below the sky the patch above the horizon a SunWest 3.2 at position? starits the visible Positional astronomy and the Parapegma of the Antikythera Mechanism the Antikythera of the Parapegma and astronomy Positional coordinates PoS(Antikythera & SKA)029

the

The

9.95 9.62 star’s 13.09 20.23 42.04 72.16 16.35 15.95 15.01 14.07 13.12 12.18 11.24 10.88 10.61 and the the and altitude between between aberration, the Sun’s Sun’s the of of Vega in Difference Difference

procedures procedures were

and and Magdalini Anastasiou Magdalini

(°) 9.09 1.35 1.95 2.01 2.07 2.12 2.18 2.24 2.88 2.95 3.62 5.61 17.23 40.04 71.16 Star’s Star’s altitude mr of Vega apparent

described described

arapegma arapegma of the Antikythera

45°N (in steps of 0.5°).

5/1 – 15/1 7/12 15/1 15/1 16/1 17/1 18/1 19/1 20/1 20/1 21/1 21/1 19/1 Date Date Visible Visible in the the in 17/10 Julian Julian calendar he he above ng ng into account changes due to on on the p

a, one refers to a star (Arcturus), two , t

4 3 2 1 9 8 7 6 5 15 14 13 12 11 10 ------

itude (°) ------], taki alues for the visible Sun’s

3 range range 25°N alt 6 1

the the Hyades were identified with Aldebaran while

identify identify Lyra with the star Vega and Aquila with the

and and three refer to two open star clusters (Pleiades and Smith [

- we

star’s 11.86 11.48 10.50 10.14 10.45 10.81 14.10 21.67 40.74 70.31 16.74 15.77 14.79 13.82 12.84 , clusters and the the and altitude between between the Sun’s Sun’s the Difference Difference

Duffett

.45 (°) 1.86 2.48 2.50 3.14 4 5.81 1.74 1.77 1.79 1.82 1.84 10.10 18.67 38.74 69.31 Star’s Star’s of of Vega = 0.23). = altitude

apparent

k (Lyra and Aquila)

ed ed by Peter

used 30/1 Date Date in the the in 12/11 12/11 11/11 11/11 12/11 13/11 18/11 28/11 21/12 17/11 16/11 15/11 14/11 13/11 Visible Visible Julian Julian for all geographic latitudes in the calendar 100 B.C. quatorial quatorial coordinates of both the Sun and the stars were calculated using the

- and constellations and he he basic spherical trigonometric equations for the computation of risings and settings , in 150 ,B.C. ( in

. Results using Nawar’s sky brightness v

From From the star events mentioned on Fragment C1 The The e As As t

1 7 6 5 4 3 2 9 8 des). des). From the two constellations 13 12 11 10 15 14 Stars Stars ------(°)

------Parameters Parameters Sun’s altitude star Altair. the Concerning two open precession of the equinoxes, the decrease in the obliquity of the ecliptic, nutation and and nutation the of the ecliptic, obliquity decrease in the the equinoxes, of precession proper of motion. effects stars, the as, the asfor well refer to constellations Hya around 150 around 4.1 procedures describ are are functions of the geographic latitude of the observer repeated for the location of the dates of all star events Mechanism calculations were done for 150 B.C. as the construction of the Mechanism has been placed 4. Table Table 1 Olympia Positional astronomy and the Parapegma of the Antikythera Mechanism the Antikythera of the Parapegma and astronomy Positional PoS(Antikythera & SKA)029

(4) (5) were were

by the -

: ] 5 ites while in thewhile s , 1

4 (Fig. (Fig. 2). 1

[

] 1  4 Magdalini Anastasiou Magdalini [1 Z

inates inates were calculated 11 cos   varies varies with location, three s plate it was read that the

k formula was calculated was

ccording ccording to the zodiac sign to

) s ) ) the apparent zenith of distance the ° (

following following Z cos 0.025    two events in the parapegma are listed in 5.11

b was used. This inscription determines the  -  10.3

h s compared to the calculated sequence 7 i

wo wo types of analysis were done: (a) an analysis  1.02 t when a h

- : :     covering covering reasonable values for ancient

- tan phenomena anphenomena error 0of days assigned, is

the the air mass and

 X As As the extinction coefficient R ), the total sequence error sequence (e total ), the  φ re re determined causes astronomical objects to appear higher in the theyskyin appear objects than to astronomical higher causes

m m m k X k Z e R we

         error error equals the number of days that the first event lies back of the

of a star was calculated using the the using of calculated a star was = 0.17, 0.23, 0.30

are reported to to occur. are reported

k m

For each latitude ( latitude For each

he true altitude. true he events

More accurate formulas for the extinction were also tested, with insignificantly equence equence of the events of plate C1

) is t ) is star lity. Near the horizon, the altitude of a star increases significantly (by up to about ‘Sequence ‘Sequence errors’ ° ( is is the extinction coefficient, . ter calculating the dates of the events,

k h For the zodiac analysis, the inscription of C1 The The s Af Atmospheric Atmospheric extinction reduces the brightness of a star as seen from Earth. The corrected Atmospheric refraction Atmospheric Zodiac analysis Zodiac Sequence analysis Sequence Atmospheric extinction Atmospheric Atmospheric refraction Atmospheric

Results or or the Pleiades, a total apparent magnitude and mean equatorial coord autumn autumn equinox takes place when the Sun enters the sign of Libra. Using the duration of the following event. following 5.2 relation of the days of the year to the signs of the zodiac as on thi 5.1 program time the thatorder agrees the actualwith opposite case the assigned according according to the sequence of the star events and (b) an analysis a the which different different cases with examined. results. different 5. where where star, due to atmospheric refraction. where where 4.3 apparent magnitude are are in rea following equation empirical the using account, into taken was effect This 0.5°). from from the ten brightest stars of the cluster magnitude). (results hardly differ if one uses the total cluster 4.2 Positional astronomy and the Parapegma of the Antikythera Mechanism the Antikythera of the Parapegma and astronomy Positional f PoS(Antikythera & SKA)029

or or

of of the

dashed and and the e mized mized in ) ) us red

top

month month names ( , the calendrical ] ithin ithin this zone 6 deviates from the

1 w Magdalini Anastasiou Magdalini [ whose whose

(Fig. (Fig. 2).

, lie lie errors get errors get mini

, the Geminos

using using the Nawar ones ones found for the true events,

a ‘Zodiac ‘Zodiac errors’ for each of the six -

. was calculated was

as places of origin and/or 0 ) z that that the Parapegma of the Antikythera

defined. defined.

Rhodes Rhodes and Syracuse Dodona Dodona and Bouthrotos 8

curves) curves) and the total zodiac error (e were

ºN. ºN. 0 . = 0.17, 0.23, 0.3 0.23, = 0.17, solid solid

37 k odiac odiac

Corcyra, expected, expected, i.e. –

black

s ), the total zodiac zodiac total error (e ), the rather rather the sequence the and thesequence zodiac analysis φ he he cities of have have been reported in the past

) ) zodiac sign, we assign an error of 0 days while in the opposite case y . T a e - th between between 33.3ºN anism ) sky brightness values. brightness ) sky or each latitude ( latitude or each F ed ed error is set equal to the number of days by which the event bottom ( The The total sequence error (e aking into account both aking into

. T The The errors in both analyses are much smaller than the 2 y y close to it and Results and geographic latitude geographic and Results

Mechanism was made of visible risings and settings. and settings. risings visible of was made Mechanism the geographic zone reall Antikythera Mech Fig. Fig. curves) vs. geographic latitude for the events on Koomen plate C1 confirming thus what it was 5.3 boundaries boundaries of each of the signs of the z star events were estimated: when the event takes place within the boundaries of the correct (as mentioned on plate C1 the assign sign. correct Positional astronomy and the Parapegma of the Antikythera Mechanism the Antikythera of the Parapegma and astronomy Positional Sun’s passage through each one of the zodiac signs, by described PoS(Antikythera & SKA)029

s the and

of of 14 In In the N

(a) that that our 37.0°N;

–

. . clima , we do not really nism nism to be made.

of of 14 hours. . for the Magdalini Anastasiou Magdalini

quite quite large sequence zodiac zodiac statements, is

most most probably

clima . udoxus of of 14 hours with lower Egypt Furthermore

lima latitude latitude where the longest day wa c , lie between latitudes of 39º ended ended up with ] is is a very good confirmation

7 the the 1 [ e based on the calendrical data the calendrical based on e

This

And And the actual latitude of Alexandria, where

. 9

of of Euctemon 31.5°N.

the the latitude of best fit obtained Mechanism – 30°33´

, Ptolemy , Ptolemy identifies the spherical spherical trigonometry, tements tements reveals that the parapegma works best for geographic 37.0°N. The method was also applied to other parapegmata and ythera parapegma ythera parapegma was composed. of of the parapegma are too small in number to decisively establish Ptolemy Ptolemy reported a very detailed parapegma, for five different

– ], is is found to be 9 ethod to detect a problematical parapegma to adetect problematical ethod Almagest Geminos’ parapegmata of Euctemon and E Euctemon parapegmata of Geminos’ less favored. less

, 1 8 day day [1 solar calendar of the

- °22´. °22´. Using for for Eudoxus’ parapegma, false citations were detected. These two analyses

part of the parapegma, with seven star events and two e e method described above

while while Phaseis or or even from rules of thumb or schematic patterns or questionable mathematical

n n Ptolemy’s seem thus to be to thus seem i . It should be pointed out, however, that (a) the limited number of preserved events andpreserved events of number that limited (a) be pointed the out, however, . It should

the ability our the of ability m Using Using th and and A A small The analysis for Geminos’ parapegma Three Three other parapegmata were examined in order to check our method of calculation: In the Yet, Yet, the preserved events match match the luni

N N ll Conclusions Other parapegmata Other

(b) (b) the historical uncertainties of the way the parapegma was actually formed do strong not statement allow about a the geographic association of the Antikythera Mecha Rather, the star phases can be taken as suggesting a likely band of latitudes 33.3°N and they do make it appear unlikely acceptabl been have Epirus that that cities might of northern the parapegma could have been designed for the preserved preserved on Fragment C of the analysis of Antikythera these events Mechanism. and sta A new method of latitudes in the range 33.3°N astronomical in the case of Ptolemy, the results corroborate very well the describes geographic region that Ptolemy marked marked 7. hours hours was found to be in the range 27.8° results. sensible analysis yields of method error values geographic geographic latitudes. We investigated the star events referring to the tables of ascensions in the and a latitude of 30 14 hours 31°13´. is and worked, lived Ptolemy 6. and parapegma Ptolemy’s some some kind) calculations. However, the fact that the Antikythera Mechanism data fit reasonably well with our numerical solutions of real the observations. from originated likely dataits (b) very and accurate was parapegma real events strongly supports that 40º the latitude for which the Antik know whether the parapegma was created from direct observations or under the influence of an already existing ‘body of knowledge’ (which must ultimately have rested on observations of Positional astronomy and the Parapegma of the Antikythera Mechanism the Antikythera of the Parapegma and astronomy Positional we PoS(Antikythera & SKA)029

/1 , , 32

361. - Journal for Journal

. , (2012).

Journal of the of Journal , ,

Magdalini Anastasiou Magdalini /7 (1974) /7

. Journal of the Optical Optical the of Journal A calendar computer computer calendar A Princeton, 2006. Princeton,

The Moon and the and Moon The , , 36 (1993), 311 (1993), 36

– , ,

ISAW Papers ISAW , , , n.s., 64 ,

ntikythera Mechanism ntikythera

. oral presentation in the XXIII ICHST ICHST the XXIII in presentation oral , New York, 1990. York, , New Interdisciplinary Science Reviews Science Interdisciplinary , , New York, 1998 New

, ,

, ogy) Ideas and Instruments in Social Social in Instruments and Ideas ogy)

Vistas in Astronomy in Vistas hera Mechanism hera ,

. roduction to the Phenomena the to roduction New York, 2007 York, New

, 183 -

Richmond, 1998. Richmond,

39. . , - 44 (2013) (accepted). (2013) 44 17. 91.

– – 356 - The visibility of stars and planets during twilight during planets and stars of visibility The ements of the brightness of the twilight sky the twilight of the brightness of ements Geminos’s Int Geminos’s g the ancient Greek astronomical calculator known as the Antikythera as the Antikythera known calculator astronomical Greek the ancient g 43 (1953), 177 (1953), 43

The Cosmos in the Antikyt the in Cosmos The

41 (2010), 1 (2010), 41

Measur (2008), 614 (2008), (2006), 587 (2006), The astronomical events of the Parapegma of the Antikythera Mechanism Antikythera the of Parapegma the of events astronomical The

., (1952), 353 (1952), 105. .,

- Gears from the Greeks: The Antikythera Mechanism Mechanism Antikythera The the Greeks: from Gears Astronomy with your personal computer personal your with Astronomy 454 444

42 Calendars with Olympiad display and eclipse prediction on the Antikythera Antikythera the on prediction eclipse and display Olympiad with Calendars Decodin

Astronomy and the limits of vision of limits the and Astronomy

2 August 2009, Budapest, Hungary. The presentation was reflecting work by A. by work reflecting was The presentation Hungary. Budapest, 2009, 2 August Solar anomaly and planetary displays in the A the in displays planetary and anomaly Solar et et al et et al

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Smith, Sky twilight brightness and colour during high solar activity solar high during colour and brightness twilight Sky . The Parapegma of the Antikythera Mechanism Antikythera the of Parapegma The Astronomical Algorithms Astronomical - al et et al et The history and practice of ancient astronomy ancient of practice and history The Nature Nature , et et al. , , (1983), 99 (1983), 43 ar, ar, - w

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ournal for the History of Astronomy of History the for ournal The The authors acknowledge the critical role of the National Archaeological Museum in Mechanism Optical Society of America of Society Optical Planets America Society of (International Congress of History of Science Technol and Science of History of Congress (International July 28 Context, preparation. in is currently which work Bitsakis, Y. and T. Jones, Freeth texts in classical and Near Eastern societies Eastern Near and classical in texts Mechanism from 27 (2007), Astronomy of the History J [15] [16] [17] [12] [13] [14] [10] [11] [8] [9] [5] [6] [7] [3] [4] [1] [2] eferences R Athens Athens and its staff in obtaining the original data. M. A. acknowledges a Ph. D. grant from the University Aristotle Positional astronomy and the Parapegma of the Antikythera Mechanism the Antikythera of the Parapegma and astronomy Positional Acknowledgements PoS(Antikythera & SKA)029

stronomica stronomica Magdalini Anastasiou Magdalini Opera a Opera , vol. II, II, , vol.

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. . Claudii Ptolemaei Opera quae exstant omnia exstant quae Opera Ptolemaei Claudii Provisional translation of Ptolemy's Phaseis Ptolemy's of translation Provisional Leipzig, 1907 Leipzig, , , A. Jones, A. Jones, J. L. Heiberg, ed., ed., J.Heiberg, L.

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