This article describes and makes available computed data for the major synodic events for the inner (Mercury, Venus) and outer (Mars, Jupiter, Saturn) planets for the time period -800 to 1650.Fil: Carman, Christian Carlos. Universidad Nacional de Quilmes. Departamento de Ciencias Sociales. Instituto de Estudios Sociales de la Ciencia y la Tecnología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Duke, Dennis. University of Florida. Departament of Chemistry; Estados Unido

Carman, Christian Carlos

Duke, Dennis

English

CONICET Digital

2/5/2019 Tables of Synodic Events from -800 to 1650 Using Modern and Almagest Modelsdlib.nyu.edu/awdl/isaw/isaw-papers/15/ 1/3The original version of this work, which is the one that should be cited, can be found via<http://isaw.nyu.edu/publications/isaw-papers>.ISAW Papers 15 (2019)Tables of Synodic Events from -800 to 1650 Using Modern andAlmagest ModelsChristián C. Carman (Universidad Nacional de Quilmes, CONICET) and Dennis Duke (FloridaState University)Abstract: This article describes and makes available computed data for the major synodicevents for the inner (Mercury, Venus) and outer (Mars, Jupiter, Saturn) planets for the timeperiod -800 to 1650.Library of Congress Subject: Astronomy.We have computed the major synodic events for the inner (Mercury, Venus) and outer (Mars, Jupiter,Saturn) planets for the time period -800 to 1650. The events are computed using modern models(Bretagnon 1986) and the models from Ptolemy’s Almagest (Pedersen 2011). While ordinary ephemeridesgive planetary positions at a list of times, our tables give the times and positions of the planets for a list ofevents. Often in discussions of ancient astronomy it is helpful to be able to look up directly the time andpositions of such events for both modern models and the Almagest models.The events computed for the inner planets are: 1) superior conjunction of the true planet and the meanSun, 2) greatest elongation (east), 3) first station, 4) inferior conjunction of the true planet and the meanSun, 5) second station, and 6) greatest elongation (west).The events computed for the outer planets are: 1) conjunction of the true planet and the mean Sun, 2)first station, 3) opposition of the true planet and the mean Sun, and 4) second station.For each event we give the date/time and the corresponding true and mean longitudes of the planet andthe Sun. The accuracy of the computed times is about 1/28th of a second. This is accomplished in eachcase by an appropriate set of iterations and/or interpolations, and, no doubt needless to say, is far moreprecise that any possible observation timing by any ancient astronomer.We have also computed the date and time of first and last visibilities of the inner and outer planets atAlexandria (longitude 29;55 degrees east, latitude 31;13,12 degrees north) and Babylon (longitude 44;26degrees east, latitude 33;20 degrees north) for the same time period -800 to 1650 using the same modernand Almagest models.The events computed for the inner planets are: 1) first visibility of the planet in the west after sunset(EF), 2) last visibility of the planet in the west after sunset (EL), 3) first visibility of the planet in the eastbefore sunrise (MF), 4) and last visibility of the planet in the east before sunrise (ML).The events computed for the outer planets are: 1) first visibility of the planet in the east before sunrise(EF), 4) last visibility of the planet rising after sunset (AR), 3) first visibility of the planet setting beforesunrise (CS), and 4) last visibility of the planet in the west after sunset (EL). The AR and CS events arenot mentioned in ancient sources, but are included here for completeness.Computation of these visibility events requires a number of additional assumptions beyond thespecification of the models. We use the arcus visionis (AV) model of the Almagest, which depends upon2/5/2019 Tables of Synodic Events from -800 to 1650 Using Modern and Almagest Modelsdlib.nyu.edu/awdl/isaw/isaw-papers/15/ 2/3the specification of an AV distance of the Sun below the horizon at the moment the planet is on thehorizon. For both the modern and Almagest models we give results for two sets of parameters. The first setuses the default convention of the program PLSV (Swerdlow 2004) that the apparent planet, i.e. correctedfor refraction (Meeus 1998, 101), is on the horizon and the Sun is depressed below the horizon at a set ofAV values specific to each planet and event type that generally follow Schoch (Schoch 1924). The secondset assumes the true planet is on the horizon and uses the values from the Almagest XIII 7 (Toomer 1984)except that for the AR and CS events we use half the AV value since the Sun is on the opposite horizon asthe planet.In all cases the date given for the visibility events cannot be considered as more than indicative, sincesuch events are in reality sensitive not only to the AV values but also to local weather, obscurations of thehorizon, azimuth differences of the planet and the Sun, etc. It is the case, however, that our results for themodern model do match fairly closely with the results from PLSV.There are ten files for each planet. Here is the key to the otherwise cryptic file names:1. planet1650 (where ‘planet’ is one of planet names): YMDH calendar dates for Alexandria, then thecorresponding JD’s for Greenwich, then for the outer planets the mean and true longitudes of theplanet and the Sun for the synodic events conjunction, first station, opposition, second station. Forthe inner planets, as above but the events are superior conjunction, greatest elongation (east), firststation, inferior conjunction, second station, greatest elongation (west).2. planet1650pt, as above but using the Almagest models for the longitudes. The YMDH calendardates and the corresponding JD’s are both for Alexandria.3. planet1650v: modern models, YMDH and JD’s for Alexandria, then for the outer planets thelongitude and latitude, the longitude of the Sun, the azimuth and altitude of the planet, and thealtitude and azimuth of the Sun. The altitude of the planet is always -0.5667 degrees, whichcorresponds approximately to an apparent, i.e. refraction corrected, altitude of 0 degrees. Theobserver is assumed to be in Alexandria. For the outer planets the event sequence isMF,AR,CS,EL. For the inner planets the sequence is EF,EL,ML,MF.4. planet1650v1: the same as planet1650v except that the true altitude of the planet is 0 degrees,which is the convention used in the Almagest.5. planet1650vb: the same as planet1650v except the observer is assumed to be in Babylon.6. planet1650v1b: the same as planet1650v1 except the observer is assumed to be in Babylon.7. planet1650ptv: the same as planet1650v except the Almagest models are used.8. planet1650ptv1: the same as planet1650v1 except the Almagest models are used.9. planet1650ptvb: the same as planet1650vb except the Almagest models are used.10. planet1650ptv1b: the same as planet1650v1b except the Almagest models are used.ReferencesPierre Bretagnon and Jean-Louis Simon 1986, Planetary Programs and Tables from –4000 to +2800,Willmann-Bell, Richmond.Jean Meeus 1998, Astronomical Algorithms, 2nd edition, Willmann-Bell, Richmond.Noel Swerdlow 2004, Planetary, Stellar, and Lunar Visibility, v 3.1, http://www.alcyone.de, by RainerLange and Noel Swerdlow.Olaf Pedersen 2011, A Survey of the Almagest, with Annotation and New Commentary by Alexander Jones,Sources and Studies in the History of Mathematics and Physical Sciences. Springer, New York.Carl Schoch 1924, The “Arcus Visionis” of the Planets in the Babylonian Observations, Monthly Noticesof the Royal Astronomical Society, Volume 84, Issue 9, 14 July, 731-734.Gerald J. Toomer 1984, Ptolemy’s Almagest, translated and Annotated, Duckworth, London.Appendix 1: Links to data as Microsoft Excel SpreadsheetsMercury Venus Mars Jupiter Saturn2/5/2019 Tables of Synodic Events from -800 to 1650 Using Modern and Almagest Modelsdlib.nyu.edu/awdl/isaw/isaw-papers/15/ 3/3mercury1650.xlsx venus1650.xlsx mars1650.xlsx jupiter1650.xlsx saturn1650.xlsxmercury1650pt.xlsx venus1650pt.xlsx mars1650pt.xlsx jupiter1650pt.xlsx saturn1650pt.xlsxmercury1650v.xlsx venus1650v.xlsx mars1650v.xlsx jupiter1650v.xlsx saturn1650v.xlsxmercury1650v1.xlsx venus1650v1.xlsx mars1650v1.xlsx jupiter1650v1.xlsx saturn1650v1.xlsxmercury1650vb.xlsx venus1650vb.xlsx mars1650vb.xlsx jupiter1650vb.xlsx saturn1650vb.xlsxmercury1650v1b.xlsx venus1650v1b.xlsx mars1650v1b.xlsx jupiter1650v1b.xlsx saturn1650v1b.xlsxmercury1650ptv.xlsx venus1650ptv.xlsx mars1650ptv.xlsx jupiter1650ptv.xlsx saturn1650ptv.xlsxmercury1650ptv1.xlsx venus1650ptv1.xlsx mars1650ptv1.xlsx jupiter1650ptv1.xlsx saturn1650ptv1.xlsxmercury1650ptvb.xlsx venus1650ptvb.xlsx mars1650ptvb.xlsx jupiter1650ptvb.xlsx saturn1650ptvb.xlsxmercury1650ptv1b.xlsx venus1650ptv1b.xlsx mars1650ptv1b.xlsx jupiter1650ptv1b.xlsx saturn1650ptv1b.xlsxAppendix 2: Links to Data as CSV FilesMercury Venus Mars Jupiter Saturnmercury1650.csv venus1650.csv mars1650.csv jupiter1650.csv saturn1650.csvmercury1650pt.csv venus1650pt.csv mars1650pt.csv jupiter1650pt.csv saturn1650pt.csvmercury1650v.csv venus1650v.csv mars1650v.csv jupiter1650v.csv saturn1650v.csvmercury1650v1.csv venus1650v1.csv mars1650v1.csv jupiter1650v1.csv saturn1650v1.csvmercury1650vb.csv venus1650vb.csv mars1650vb.csv jupiter1650vb.csv saturn1650vb.csvmercury1650v1b.csv venus1650v1b.csv mars1650v1b.csv jupiter1650v1b.csv saturn1650v1b.csvmercury1650ptv.csv venus1650ptv.csv mars1650ptv.csv jupiter1650ptv.csv saturn1650ptv.csvmercury1650ptv1.csv venus1650ptv1.csv mars1650ptv1.csv jupiter1650ptv1.csv saturn1650ptv1.csvmercury1650ptvb.csv venus1650ptvb.csv mars1650ptvb.csv jupiter1650ptvb.csv saturn1650ptvb.csvmercury1650ptv1b.csv venus1650ptv1b.csv mars1650ptv1b.csv jupiter1650ptv1b.csv saturn1650ptv1b.csvAppendix 3: Links to Data as HTML Tablesmercury1650.html venus1650.html mars1650.html jupiter1650.html saturn1650.htmlmercury1650pt.html venus1650pt.html mars1650pt.html jupiter1650pt.html saturn1650pt.htmlmercury1650v.html venus1650v.html mars1650v.html jupiter1650v.html saturn1650v.htmlmercury1650v1.html venus1650v1.html mars1650v1.html jupiter1650v1.html saturn1650v1.htmlmercury1650vb.html venus1650vb.html mars1650vb.html jupiter1650vb.html saturn1650vb.htmlmercury1650v1b.html venus1650v1b.html mars1650v1b.html jupiter1650v1b.html saturn1650v1b.htmlmercury1650ptv.html venus1650ptv.html mars1650ptv.html jupiter1650ptv.html saturn1650ptv.htmlmercury1650ptv1.html venus1650ptv1.html mars1650ptv1.html jupiter1650ptv1.html saturn1650ptv1.htmlmercury1650ptvb.html venus1650ptvb.html mars1650ptvb.html jupiter1650ptvb.html saturn1650ptvb.htmlmercury1650ptv1b.html venus1650ptv1b.html mars1650ptv1b.html jupiter1650ptv1b.html saturn1650ptv1b.htmlISAW Papers (ISSN 2164-1471) is a publication of the Institute for the Study of the Ancient World, NewYork University. This article was suggeasted for publication by Alexander Jones as a member of the ISAWfaculty.©2019 Christián C. Carman and Dennis Duke. Distributed under the terms of the Creative CommonsAttribution 4.0 International license.

Tables of Synodic Events from -800 to 1650 Using Modern and Almagest Models

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Tables of Synodic Events from -800 to 1650 Using Modern and Almagest Models

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