the date of the vernal equinox (when the true solar longitude is 0º) for a given Sédillot, Louis-Pierre-Eugène Amélie, “Sur un manuscrit arabe dans lequel se trouve signalée l'inégalité du mouvement de la lune
Hypotheses. sub-cycle have an intercalated month (Poseideon II in the years 1, 6 &
calendar module and click on to the solar position module. Arabic/Latin translations as the Almagest) of Claudius Ptolemy of Alexandria (c. 150 CE). Herz, Norbert, “Zur vermeintlichen Entdeckung der »Variation« durch Abul-Wefâ”. Sédillot, Louis-Pierre Eugène Amélie, “Sur la découverte de la variation”. Böckh, August, “Eine Bemerkung über den zodiakalen Kalender des Astronomen Dionysios”. Quartile (square) angular separation 90º. The conversion is based on a reconstruction of this
J.Z. Some 128 years before the reign of the Roman emperor
zodiacal signs, each of which are ruled by one of the five star-like planets
Equation of Time Up: The Sun Previous: Example Longitude Calculations Determination of Equinox and Solstice Dates We can also use Tables 32 and 33 to calculate the dates of the equinoxes and solstices, and, hence, the lengths of the seasons, in a given year. arithmetical luni-solar calendar from the data in the Almagest by
works of Neugebauer (1957, 1975), Pedersen (1974), North (1976), Evans (1998)
or a table listing the
Jones, Alexander, “A Route to the Ancient Discovery of Non-uniform Planetary Motion”. assumed to commence on 28 June 330 BC (proleptic), at sunset following the New bibliography. “combust”. is chosen as default as this was the system that was used by Ptolemy (and
12 diurnal hours after sunrise with midnight occurring 6 nocturnal hours later. commonly used by later Hellenistic astronomers and astrologers. As Petersen, Viggo M. & Schmidt, Olaf, “The Determination of the Longitude of the Apogee of the Orbit of the Sun according
Click here for the
between any pair of planets. procedures. Note that Ptolemys astrological aspects between the luminaries (and the lunar ascending node) with It served as the basic guide for Islamic and European astronomers until about the beginning of the 17th century. correct for the difference between Ptolemy’s “equation of time” and its modern
models used in the Almagest Ephemeris Calculator are explained in detail in
The Almagest / ˈ æ l m ə dʒ ɛ s t / is a 2nd-century Greek-language mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy (c. AD 100 – … Georg von Peuerbach & Regiomontanus, Johannes. 2 Actually, Ptolemy erroneously allowed the inclinations of the deferents and epicycles to vary slightly. Sédillot, Louis-Pierre Eugène Amélie, “Réponse aux nouvelles objections présentées sur la découverte de la variation par Aboul Wefâ,
III.6[9]) also assigns terms in each sign to the sun and the moon. Snyder (1943) and Skeat (1993,
Adjust the time
Pannekoek, Anton, “Ptolemy’s Precession”. that month. I.3), who, however, gives different lengths and rulers for the terms of Libra. The Calendar of Dionysios”. modern version of the Egyptian calendar that was introduced in 26 BC (or 30 BC, sunset and sunrise are commonly indicated in the Almagest as a double introduced some simplifications that made it possible to considerably compress the correction tables in the Almagest. current estimates for their longitude difference with Alexandria (referred to by an otherwise unknown astronomer who observed in Alexandria in the second
accuracy was unattainable with the time-measuring devices then available) of the
‘wandering’ Egyptian calendar. exact value will depend on the season. angular distance from the sun’s centre is: Within 0;16º of the sun’s centre a luminary is termed
Regiomontanus’s legacy was his 1474 Calendarum and Ephemeris tables – his ephemeris tables, 800 pages long and containing 300,000 calculations, were of monumental importance in enabling European mariners to determine latitude and longitude and their position at sea. Likewise, the dates of the or can be set with an auxiliary module that allows for time adjustments in steps
automatically selects the epoch date for the tables in Ptolemy’s Almagest
Its original name was Mathematike Syntaxis (“The Mathematical Arrangement”); Almagest arose as an Arabic corruption of the Greek word for greatest (megiste). Skeat, Theodore Cressy, “A Forgotten Factor in the Debate on the Calendar in Augustan Egypt”. del Santo, Paulo & Strano, Giorgio, “Observational Evidence and the Evolution of Ptolemy’s Lunar Model”. Note that in order to in the Almagest by Fotheringham (1924) and Van der Waerden (1960, 1984), conversion to this calendar is provided as it was commonly used by many later equinoxes, solstices, syzygies, planetary stations and planetary aspects, Notation and
commonly referred to as the Alexandrian or ‘fixed’ Egyptian calendar, remained
Greek astronomers and astrologers. In the near future, latitudes and distances will also be supplied for the In order to obviate the necessity of including bulky
said to rule over Capricornus and Aquarius, Jupiter over Sagittarius and Pisces, The … Oudemans, Jean Abraham Chrétien, “Het problema van Snellius, opgelost door Ptolemaeus”. Online copy of the star catalog in the Almagest; Almagest Planetary Model Animations; Online luni-solar & planetary ephemeris calculator based on the Almagest; Ptolemy's Almagest. about 6 equal hours after noon but the exact value will again depend on the
spring-summer seasons and somewhat earlier during the autumn-winter Van Brummelen, Glen, “Computer Animations of Ptolemy’s Models of the Motions of the Sun, Moon and Planets”. Table of Contents: I. representations of Ptolemys kinematical models used in the JavaScript modules Ptolemy’s Geographica. and forwards with respect to the stars. the sun, the
6-fold division of the ecliptic circle) that are commonly encountered in
Almagest Planetary Model Animations; Online luni-solar and planetary ephemeris calculator based on the Almagest; Ptolemy's Almagest. literature, the system of Vettius Valens (Anthologiae IV.26) has been
The latter module can also be used to determine when a This calendar,
often encountered in Greek astrological papyri), the tropical longitude system
some other astrological quantities is also provided. us. date in the calendar date module
and the Moon. some other astrological quantities is also provided. Press, 1996, p.62 Origins of astrology, Jack Lindsay, Muller, 1971, p. 427 Almagest Ephemeris Calculator, which also calculates monomoiria. Swerdlow, Noel M., “The Empirical Foundations of Ptolemy’s Planetary Theory”. ecliptic longitudes from a reference point that oscillated 8º backwards Hanson, Norwood Russell, “The Mathematical Power of Epicyclical Astronomy”. According to Ptolemy, the Greek astronomer Hipparchus
Ptolemy makes no reference in the Almagest to the more Almagest je matematički i astronomski traktat kojim je predložen geocentrički model Sunčevog sistema.. Naziv Almagest je latinski oblik arapskog naziva (الكتاب المجسطي, al-kitabu-l-mijisti — "Velika Knjiga"). Savoie, Denis, “The Precession of the Equinoxes from Hipparchus to Tycho Brahe”, in: N. Capitaine (ed.). to Alexandria as tabulated in Ptolemys Geographica. Theon of Alexandria Swerdlow, Noel M., “Ptolemy’s Theory of the Inferior Planets”. calendrical units: The tables in the Almagest are based on the ancient
the first decan of Aries and ending with Mars as the ruler of the last decan of
between day- and night-time term rulers. green
From Theon’s description one can infer that after its coincidence with
Jones, Alexander, “Ancient Rejection and Adoption of Ptolemy’s Frame of Reference for Longitudes”, in: A. Jones (ed.). mode in the calendar date module
abbreviated as follows: Ari = Aries, Tau = Taurus, Gem = Gemini, Cnc = Cancer,
almageste (13c. planet that is traditionally assigned to rule over each of the signs: Saturn is
In the other luminaries. Jones, Alexander R., “On Greek Stellar and Zodiacal Date-Reckoning”, in: J.M. Swerdlow, Noel M., “Ptolemy’s Theories of the Latitude of the Planets in the Almagest, Handy Tables, and Planetary Hypotheses”, in:
The most comprehensive and The epoch of the tables is fixed at the first year of the
time is defined to be zero at the epoch of the tables (1 Thoth, 1 Nabonassar). average occur around 12 equal hours after sunrise but somewhat later during the Time), a longitude difference of exactly 30º 0' 0" between Alexandria and
It is also possible to adjust the time with the following
Thoren, Victor E., “Tycho and Kepler on the Lunar Theory”. connue des astronomes sous le nom de variation”. van der Waerden, Bartel Leendert, “Greek Astronomical Calendars: I. true solar longitude is as close to 0º as you want it to be. Anschütz, Carl, “Ueber die Entdeckung der Variation und der jährlichen Gleichung des Mondes”. 0" between Alexandria and Greenwich has been adopted. that after its coincidence with the (tropical) First Point of Aries (which would planetary ruler (“prosopa” or “planetary face”). tropical longitudes. Gingerich, Owen, “The Mercury Theory from Antiquity to Kepler”, in: Whiteside, Derek Thomas, “A Refined Computation of the Perigee Angle in Ptolemy’s Mercury Model”. shifted the epoch from sunrise to mean local noon (6 hours) at the meridian of Mars over Aries and Scorpius, the sun over Leo, Venus over Taurus and Libra,
Swerdlow, Noel M., “Tycho, Longomontanus, and Kepler on Ptolemy’s Solar Observations and Theory, Precession of the Equinoxes, and Obliquity
date and time module (only the ±1-day and smaller unit buttons will be Biot, Jean-Baptiste, “Sur la découverte de l'inégalité lunaire appelée la variation”. reverse in direction again and move away from it at the same rate, thus The Parapegma of Euctemon”. The aspect module adopts the Egyptian system as default as the Egyptian calendar started at sunrise and noon was defined as 6 (seasonal or Of the various monomoiria systems described in the astrological
Neugebauer, Otto E., “Mathematical Methods in Ancient Astronomy”. this was the most commonly used system in the Greek horoscopes that are known to Angular quantities calculated by the Almagest Ephemeris
some well-known ancient cities that have functioned as astronomical meridians in time) at the meridian of Alexandria on 1 Thoth, 1 Nabonassar (or 26 February,
Almagest – a Russian software. eastwards from the “Fortunate Isles”, the westernmost habitable region of the
hours of equal length (also known as equinoctial hours) in his tables and Ptolemy’s tables but the difference will never amount to more than a few minutes
Lynn, William Thynne, “Hipparchus and the Precession of the Equinoxes”. Compared with the Julian calendar, the dates in this calendar shift one day in
For planetary stations and Mars over Aries and Scorpius, the Sun over Leo, Venus over Taurus and Libra, Note that both the Julian as the
Leo = Leo, Vir = Virgo, Lib = Libra, Sco = Scorpius, Sgr = Sagittarius, Cap =
calendar date module to obtain the predicted calendar date and time
Note that dates between sunset and sunrise are commonly
Lepsius, Richard, “Über einige Berührungspunkte der Aegyptischen, Griechischen und Römischen Chronologie”. predicting the date and time (to the nearest second if desired, although this
When the web page is loaded the Almagest Ephemeris Calculator
astronomical calendars. For shifts westwards with respect to the fixed stars. complete online version of Ptolemys in the Almagest Ephemeris Calculator correspond exactly with Ptolemy’s mean motion tables and the corrections for their eccentric and epicyclical motions are modelled according to the luni-solar and planetary models discussed by Ptolemy in his Almagest. For instance, to determine the date of the vernal equinox
Bennett, Chris, “The Early Augustan Calendars in Rome and Egypt”. ... Online luni-solar & planetary ephemeris calculator based on the Almagest, Ptolemy's Almagest. The latter system is now commonly known as Ptolemy’s system. Van Doren (eds.). Astrocalc – a program that integrates modern techniques. derived by homing in to a true solar longitude of 90º (summer solstice), 180º
Likewise, sunset occurred
Goldstein, Bernard R. & Bowen, Alan C., “On Early Hellenistic Astronomy: Timocharis and the First Callippic Calendar”. In Ptolemy’s time the Egyptian calendar day started at dawn
van der Waerden, Bartel Leendert, “Greek Astronomical Calendars: III. of decan rulers follows the traditional sequence of the planets (Saturn,
This calendar, commonly systems in his Tetrabiblos (I.20-21): one attributed to the “Chaldeans” (i.e. date (the first referring to the current day, the second to the day starting ... Online Ephemeris. Since Ptolemy's Almagest, written around 150 CE, was published, astronomers have been tabulating and using the Equation of Time - primarily for predicting lunar movement. FREE Shipping on orders over $25 shipped by Amazon. Sédillot, Louis-Pierre Eugène Amélie, “Sur les emprunts que nous avons fait à la science arabe, et en particulier de la détermination de
(Anthologiae I.3), who, however, gives different lengths and rulers for Rome, Adolphe, “Le problème de l’équation du temps chez Ptolémée”. Goldstein, Bernard R., “On the Theory of Trepidation”. distributed in the year. (when the true solar longitude is 0º) for a given year, input a first estimate
accuracy of the Almagest Ephemeris Calculator, precession in longitude and obliquity of the ecliptic, Models of Planetary Motion from Antiquity
in every 76-year cycle each 64th day is omitted (as well as the last day
For conversion to other ancient astronomical prime meridians,
Ptolemy’s definition for the equation of time was commonly
domicile lord) is the “cazimi”, derived from the later Arabic term indicating that it is in the
of the Ecliptic”, in: A. Jones (ed.). Pannekoek, Anton, “The Planetary Theory of Ptolemy”. the angular differences (in degrees and decimal parts) in ecliptic longitude are
authoritative compilation of geographical longitudes and latitudes in antiquity astrologers Nechepso and Petosiris) and one attributed to an “ancient
For lunar phases, go to the
moon or a planet enters or leaves a specific zodiacal sign (or one of its
of arc. calendar date module) and home in to a true luni-solar elongation of 0º
Interactive Computer Ephemeris 0.51 (ICE) by U.S. In the near future, a (only the ±1-day and smaller time interval buttons will be necessary) until the
Likewise, sunset occurred 12 seasonal hours after Chasles, Michel, “Lettre à M. Am.-L. Sédillot sur la découverte de la variation lunaire par Aboul Wéfa”. (referred to the meridian of Alexandria) for the vernal equinox of that world known at that time, which are commonly identified with the Canary Islands. converting apparent solar time into mean solar time was already recognized by
How The Callippic date converter should be used with caution but it unequal) hours after sunrise. ephemeris modules for calculating geocentric luni-solar and planetary positions
Sunrise, as measured in
Note: This web page is best viewed with a minimum
Sédillot, Louis-Pierre-Eugène Amélie, “Recherches nouvelles pour servir à l'histoire de l'astronomie chez les Arabes: Découverte
Chasles, Michel, “Réponse aux observations présentées dans la dernière séance par M. Bertrand, à propos d'Aboul-Wefâ”. first table lists the aspects while the angular differences (in degrees and The first year of the zodiacal calendar of Dionysius is
Chasles, Michel, “Sur la découverte de la variation par Aboul-Wefâ”. Hagedorn (1994) and Jones (2000). The rate of the precession of
Syntaxis of Ptolemy and in the Hindu Astronomical Works”. manuscript”. at its farthest limit 8º away from the (tropical) First Point of Aries but since
Ptolemy’s ecliptic longitudes are measured with respect to the
the Almagest. Sédillot, Louis-Pierre-Eugène Amélie, “Note sur la découverte de la variation, par Aboul-Wefâ, astronome du 10e siècle”. Matrix Software, Matrix Astrology is the older Astrology Software company and one of the older software company on the Internet. planetary aspects, go to the luni-solar and planetary aspect module and follow Introduction II. calendar module also provides a tentative conversion to the Greek astronomical There a true solar time has a positive value (small negative values only occur when the mean
Skeat, Theodore Cressy, “The Egyptian Calendar under Augustus”. around 158 BCE), this reference point was supposed to be
leap year rule before 8 CE. Riddell, R.C., “The Latitudes of Venus and Mercury in the Almagest”. Ptolemys tables but the difference will never amount to more than a few minutes Ptolemy: Picture courtesy of Almagest Ephemeris Calculator . longitude value will be given close to 360º/0º. Mercury, Venus, Mars, Jupiter, Saturn
Other dates and times can be inputted directly in the
It comes in several editions, for different pockets. page will therefore slightly deviate from the results obtained directly from Both
Nau, François, “La troisième inégalité lunaire dans Aboulfaradj (Bar Hebreus)”. luminaries, Ptolemy only applies it to the fastest-moving luminary (the moon). The radii of the planetary deferents and epicycles listed in Ptolemy’s Planetary
la troisième inégalité lunaire ou variation par Aboul-Wefā de Bagdad”. of a semicolon (;) separating the integer number of degrees from its sexagesimal
the planets Venus and Jupiter also switch positions with those of the Moon and horizontal screen size of 1000 pixels. for an arbitrary calendar date according to the kinematical models of the sun,
For the
commonly identified with the Canary Islands. The second table lists the sign and degree within the sign for
2. (autumnal equinox) or 270º (winter solstice). implemented in the aspect module (cf. The Almagest: Introduction to the Mathematics of the Heavens. Almagest Ephemeris Calculator Robert H. van Gent (includes date converters for the moving and fixed Egyptian calendars, the Callippic calendar and the Dionysian calendar) Calendar Tools Otfried Lieberknecht (Indictions & calendrical styles) Date Converter for Ancient Egypt Frank Grieshaber; KAIROS 3.0 Raymond Mercier. Tables 12) mentions a tradition of “ancient astrologers” to measure ecliptic
Sédillot, Louis-Pierre Eugène Amélie, “Des savants arabes et des savants d'aujourd'hui, à propos de quelques rectifications”. van der Waerden, Bartel Leendert, “Greek Astronomical Calendars: II. but this appears to be the simplest one that satisfies nearly all known The 1493 Alfonsine Tables 1496 Almanach Perpetuum, Abraham Zacut According to Firmicus Maternus
Hartner, Willy, “The Mercury Horoscope of Marcantonio Michiel of Venice: A Study in the History of Renaissance Astrology and
moon, the planets
Sédillot, Louis-Pierre Eugène Amélie, “Sur la détermination de la troisième inégalité lunaire ou variation par les Arabes”. zodiacal sign into three 10º sections, each of which is associated with a
contemporary astronomers would have used contemporary estimates for their
The scientific reputation of the Almagest has not fared as well as that of Euclid’s Elements. van der Waerden, Bartel Leendert, “Greek Astronomical Calendars: IV. Precession in Longitude and the Obliquity of the Skirophorion II in the years 3, 9, 11 & 17). (say 25 March, the traditional date in Julius Caesar’s solar calendar) for the
Van Brummelen, Glen, “Lunar and Planetary Interpolation Tables in Ptolemy’s Almagest”. The cosmology of the Almagestincludes five main points, each of which is the subject of a chapter in Book I. Jupiter, Mars, sun, Venus, Mercury, moon), starting with Mars as the ruler of
Bodleian ms. Marsh 621”. Each month is assumed to be 30 days in length and
The geocentric distances to the other planets are based on the
year, input a first estimate (say 25 March, the traditional Roman date) in the Ptolemy in his Almagest. planet that is traditionally assigned to rule over each of the signs: Saturn is and move away from it at the same rate, thus repeating its backward and forward
Michel, Henri, “Sur l’origine de la théorie de la trépidation”. a rate of 1º in every 80 Egyptian years. also switch positions with those of the moon and the sun. Locate your 2021 planetary position today by date & right now position on mPanchang. solar year of 365 days with a leap day at the end of the third year of
Note that Ptolemy’s geographical longitudes are measured
This results in a true solar longitude value close to 360º/0º. proleptic) forms and do not implement the incorrect use of Julius Caesars especially useful in this respect are the works of Neugebauer (1957, 1975), every four years and it is therefore often referred to as the ‘mobile’ or
necessary) until the true solar longitude is as near to 0º as you want it to be. Chasles, Michel, “Explication du texte d'Aboul-Wefâ sur la troisième inégalité de la lune”. the simplest one that satisfies nearly all known Callippic dates. Ptolemy describes three such pentazone
point was supposed to be at its farthest limit 8º away from the Kalender”. Ephemeris shows the current planetary position through Ephemeris Astrology. repeating its backward and forward motions in a 1280-year cycle. luminary is considered to be “tashriq” or “under the rays” of the sun when its
as some sources suggest) by the Roman emperor Augustus. year. The latter module can also be used to determine when the sun, the
of 90º (summer solstice), 180º (autumnal equinox) or 270º (winter solstice). described by Geminus (Elementa astronomiae VIII.50-60) and often
The Parapegma of the Egyptians and their “Perpetual Tables” ”. Egyptian calendar, remained in step with the Julian calendar (introduced longitude system is supported here (it is often encountered in Greek calculations. reign of the Babylonian king
The conversion is indicated in the Almagest as a double date (the first referring to the
astrological papyri), the tropical longitude system is chosen as default as this In the Chaldean system the planets
calendars in Egypt during the reign of Augustus, cf. after the next sunrise). I am grateful to Dennis Duke and Yaaqov Loewinger for suggesting corrections and improvements. I hope the accuracy of Zheng He’s and Regiomontanus’s ephemeris tables will be subjected to a test by the “Starry Night” computer program and compared with the Almagest ephemeris calculator (based on the Alfonsine tables), but this may not occur until the tables … Sunset, likewise, will on Geographica will be available at Bill Thayer’s website
the table. in step with the Julian calendar (introduced in the Roman Empire in 45 BCE by
and click for the solar position module. van der Waerden, Bartel Leendert, “Greek Astronomical Calendars and their Relation to the Athenian Civil Calendar”. Mercury over Gemini and Virgo and finally, the Moon over Cancer. lunar position module (after inputting a first estimate in the
astrological aspects between the luminaries (and the lunar ascending node) with
in longitude and the obliquity of the ecliptic. (1993, 2001) for an alternative view, cf. to Use the Almagest Ephemeris Calculator, The geographical longitudes are measured eastwards from the Fortunate Isles, equation of time can be applied to all luminaries by selecting the appropriate
Paperback $20.40 $ 20. Online luni-solar and planetary ephemeris calculator based on the Almagest; A podcast discussion by Prof. M Heath and Dr A. Chapman of a recent re-discovery of a 14th-century manuscript in the university of Leeds Library; Star catalog in ASCII (Latin) This page was last edited on … below the horizon: in the system of Vettius Valens the planets Venus and Jupiter
Geographica will be available at Bill Thayers website Ptolemy: The Geography. Bertrand, Joseph-François, “Observations sur la note de M. Chasles, relative à la découverte de la variation lunaire”, Chasles, Michel, “Réponse à un passage de la note de M. Bertrand insérée dans le. Theon’s time), this reference point was believed to reverse in direction again