The Curious Case of the Milankovitch Calendar
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Ast 443 / Phy 517
AST 443 / PHY 517 Astronomical Observing Techniques Prof. F.M. Walter I. The Basics The 3 basic measurements: • WHERE something is • WHEN something happened • HOW BRIGHT something is Since this is science, let’s be quantitative! Where • Positions: – 2-dimensional projections on celestial sphere (q,f) • q,f are angular measures: radians, or degrees, minutes, arcsec – 3-dimensional position in space (x,y,z) or (q, f, r). • (x,y,z) are linear positions within a right-handed rectilinear coordinate system. • R is a distance (spherical coordinates) • Galactic positions are sometimes presented in cylindrical coordinates, of galactocentric radius, height above the galactic plane, and azimuth. Angles There are • 360 degrees (o) in a circle • 60 minutes of arc (‘) in a degree (arcmin) • 60 seconds of arc (“) in an arcmin There are • 24 hours (h) along the equator • 60 minutes of time (m) per hour • 60 seconds of time (s) per minute • 1 second of time = 15”/cos(latitude) Coordinate Systems "What good are Mercator's North Poles and Equators Tropics, Zones, and Meridian Lines?" So the Bellman would cry, and the crew would reply "They are merely conventional signs" L. Carroll -- The Hunting of the Snark • Equatorial (celestial): based on terrestrial longitude & latitude • Ecliptic: based on the Earth’s orbit • Altitude-Azimuth (alt-az): local • Galactic: based on MilKy Way • Supergalactic: based on supergalactic plane Reference points Celestial coordinates (Right Ascension α, Declination δ) • δ = 0: projection oF terrestrial equator • (α, δ) = (0,0): -
Ephemeris Time, D. H. Sadler, Occasional
EPHEMERIS TIME D. H. Sadler 1. Introduction. – At the eighth General Assembly of the International Astronomical Union, held in Rome in 1952 September, the following resolution was adopted: “It is recommended that, in all cases where the mean solar second is unsatisfactory as a unit of time by reason of its variability, the unit adopted should be the sidereal year at 1900.0; that the time reckoned in these units be designated “Ephemeris Time”; that the change of mean solar time to ephemeris time be accomplished by the following correction: ΔT = +24°.349 + 72s.318T + 29s.950T2 +1.82144 · B where T is reckoned in Julian centuries from 1900 January 0 Greenwich Mean Noon and B has the meaning given by Spencer Jones in Monthly Notices R.A.S., Vol. 99, 541, 1939; and that the above formula define also the second. No change is contemplated or recommended in the measure of Universal Time, nor in its definition.” The ultimate purpose of this article is to explain, in simple terms, the effect that the adoption of this resolution will have on spherical and dynamical astronomy and, in particular, on the ephemerides in the Nautical Almanac. It should be noted that, in accordance with another I.A.U. resolution, Ephemeris Time (E.T.) will not be introduced into the national ephemerides until 1960. Universal Time (U.T.), previously termed Greenwich Mean Time (G.M.T.), depends both on the rotation of the Earth on its axis and on the revolution of the Earth in its orbit round the Sun. There is now no doubt as to the variability, both short-term and long-term, of the rate of rotation of the Earth; U.T. -
It Has Often Been Said That Studying the Depths of the Sea Is Like Hovering In
It has often been said that studying the depths of the sea is like hovering in a balloon high above an unknown land which is hidden by clouds, for it is a peculiarity of oceanic research that direct observations of the abyss are impracticable. Instead of the complete picture which vision gives, we have to rely upon a patiently put together mosaic representation of the discoveries made from time to time by sinking instruments and appliances into the deep. (Murray & Hjort, 1912: 22) Figure 1: Portrait of the H.M.S. Challenger. Prologue: Simple Beginnings In 1872, the H.M.S Challenger began its five- year journey that would stretch across every ocean on the planet but the Arctic. Challenger was funded for a single reason; to examine the mysterious workings of the ocean below its surface, previously unexplored. Under steam power, it travelled over 100,000 km and compiled 50 volumes of data and observations on water depth, temperature and conditions, as well as collecting samples of the seafloor, water, and organisms. The devices used to collect this data, while primitive by today’s standards and somewhat imprecise, were effective at giving humanity its first in-depth look into the inner workings of the ocean. By lowering a measured rope attached to a 200 kg weight off the edge of the ship, scientists estimated the depth of the ocean. A single reading could take up to 80 minutes for the weight to reach bottom. Taking a depth measurement also necessitated that the Challenger stop moving, and accurate mapping required a precise knowledge of where the ship was in the world, using navigational tools such as sextants. -
The Mathematics of the Chinese, Indian, Islamic and Gregorian Calendars
Heavenly Mathematics: The Mathematics of the Chinese, Indian, Islamic and Gregorian Calendars Helmer Aslaksen Department of Mathematics National University of Singapore [email protected] www.math.nus.edu.sg/aslaksen/ www.chinesecalendar.net 1 Public Holidays There are 11 public holidays in Singapore. Three of them are secular. 1. New Year’s Day 2. Labour Day 3. National Day The remaining eight cultural, racial or reli- gious holidays consist of two Chinese, two Muslim, two Indian and two Christian. 2 Cultural, Racial or Religious Holidays 1. Chinese New Year and day after 2. Good Friday 3. Vesak Day 4. Deepavali 5. Christmas Day 6. Hari Raya Puasa 7. Hari Raya Haji Listed in order, except for the Muslim hol- idays, which can occur anytime during the year. Christmas Day falls on a fixed date, but all the others move. 3 A Quick Course in Astronomy The Earth revolves counterclockwise around the Sun in an elliptical orbit. The Earth ro- tates counterclockwise around an axis that is tilted 23.5 degrees. March equinox June December solstice solstice September equinox E E N S N S W W June equi Dec June equi Dec sol sol sol sol Beijing Singapore In the northern hemisphere, the day will be longest at the June solstice and shortest at the December solstice. At the two equinoxes day and night will be equally long. The equi- noxes and solstices are called the seasonal markers. 4 The Year The tropical year (or solar year) is the time from one March equinox to the next. The mean value is 365.2422 days. -
Islamic Calendar from Wikipedia, the Free Encyclopedia
Islamic calendar From Wikipedia, the free encyclopedia -at اﻟﺘﻘﻮﻳﻢ اﻟﻬﺠﺮي :The Islamic, Muslim, or Hijri calendar (Arabic taqwīm al-hijrī) is a lunar calendar consisting of 12 months in a year of 354 or 355 days. It is used (often alongside the Gregorian calendar) to date events in many Muslim countries. It is also used by Muslims to determine the proper days of Islamic holidays and rituals, such as the annual period of fasting and the proper time for the pilgrimage to Mecca. The Islamic calendar employs the Hijri era whose epoch was Islamic Calendar stamp issued at King retrospectively established as the Islamic New Year of AD 622. During Khaled airport (10 Rajab 1428 / 24 July that year, Muhammad and his followers migrated from Mecca to 2007) Yathrib (now Medina) and established the first Muslim community (ummah), an event commemorated as the Hijra. In the West, dates in this era are usually denoted AH (Latin: Anno Hegirae, "in the year of the Hijra") in parallel with the Christian (AD) and Jewish eras (AM). In Muslim countries, it is also sometimes denoted as H[1] from its Arabic form ( [In English, years prior to the Hijra are reckoned as BH ("Before the Hijra").[2 .(ﻫـ abbreviated , َﺳﻨﺔ ﻫِ ْﺠﺮﻳّﺔ The current Islamic year is 1438 AH. In the Gregorian calendar, 1438 AH runs from approximately 3 October 2016 to 21 September 2017.[3] Contents 1 Months 1.1 Length of months 2 Days of the week 3 History 3.1 Pre-Islamic calendar 3.2 Prohibiting Nasī’ 4 Year numbering 5 Astronomical considerations 6 Theological considerations 7 Astronomical -
Downloading the Application Form at the Following Address
Hanno Collaborato A queSto NumeRo: IL NUOVO SAGGIATORE f. K. A. Allotey, L. Belloni, BOLLETTINO DELLA SOCIETÀ ITALIANA DI FISICA G. Benedek, A. Bettini, t. m. Brown, Nuova Serie Anno 26 • N. 5 settembre-ottobre 2010 • N. 6 novembre-dicembre 2010 f. Brunetti, G. Caglioti, R. Camuffo, A. Cammelli, e. Chiavassa, DIRETTORE RESPONSABILE ViCeDiRettoRi ComitAto scieNtifiCo L. Cifarelli, e. De Sanctis, A. Di Carlo, Luisa Cifarelli Sergio focardi G. Benedek, A. Bettini, i. Di Giovanni, R. fazio, f. ferrari, Giuseppe Grosso S. Centro, e. De Sanctis, S. focardi, R. Gatto, A. Gemma, e. iarocci, i. ortalli, L. Grodzins, G. Grosso, f. Guerra, f. Palmonari, R. Petronzio, f. iachello, W. Kininmonth, e. Longo, P. Picchi, B. Preziosi S. mancini, P. mazzoldi, A. oleandri, G. onida, V. Paticchio, f. Pedrielli, A. Reale, G. C. Righini, N. Robotti, W. Shea, i. talmi, A. tomadin, m. Zannoni, A. Zichichi Sommario 3 EDITORIALE / EDITORIAL 84 50 anni di laser. Tavola rotonda al XCVI Congresso Nazionale della SIF SCieNZA iN PRimO PIANO G. C. Righini 5 Quantum simulators and 86 Assemblea di ratifica delle elezioni quantum design delle cariche sociali della SIF per il R. fazio, A. tomadin triennio 2011-2013 10 La rivoluzione della plastica nel 87 African Physical Society settore fotovoltaico f. K. A. Allotey A. Di Carlo, A. Reale, t. m. Brown, 90 Nicola Cabibbo and his role in f. Brunetti elementary-particle theory Percorsi R. Gatto 23 The tabletop measurement of the News helicity of the neutrino 92 The Italian graduate profile survey L. Grodzins A. Cammelli 30 Giulio Racah (1909-1965): 96 Premio Fermi 2010 modern spectroscopy A. -
Calculation of Moon Phases and 24 Solar Terms
Calculation of Moon Phases and 24 Solar Terms Yuk Tung Liu (廖²棟) First draft: 2018-10-24, Last major revision: 2021-06-12 Chinese Versions: ³³³qqq---文文文 简简简SSS---文文文 This document explains the method used to compute the times of the moon phases and 24 solar terms. These times are important in the calculation of the Chinese calendar. See this page for an introduction to the 24 solar terms, and this page for an introduction to the Chinese calendar calculation. Computation of accurate times of moon phases and 24 solar terms is complicated, but today all the necessary resources are freely available. Anyone familiar with numerical computation and computer programming can follow the procedure outlined in this document to do the computation. Before stating the procedure, it is useful to have a basic understanding of the basic concepts behind the computation. I assume that readers are already familiar with the important astronomy concepts mentioned on this page. In Section 1, I briefly introduce the barycentric dynamical time (TDB) used in modern ephemerides, and its connection to terrestrial time (TT) and international atomic time (TAI). Readers who are not familiar with general relativity do not have to pay much attention to the formulas there. Section 2 introduces the various coordinate systems used in modern astronomy. Section 3 lists the formulas for computing the IAU 2006/2000A precession and nutation matrices. One important component in the computation of accurate times of moon phases and 24 solar terms is an accurate ephemeris of the Sun and Moon. I use the ephemerides developed by the Jet Propulsion Laboratory (JPL) for the computation. -
Lessons from Reading Clavius
Christopher Clavius, S.J. Calendar Reform Lessons from Clavius Conclusion Lessons from reading Clavius Anders O. F. Hendrickson Concordia College Moorhead, MN MathFest, Pittsburgh August 5, 2010 Christopher Clavius, S.J. Calendar Reform Lessons from Clavius Conclusion Outline 1 Christopher Clavius, S.J. 2 Calendar Reform 3 Lessons from Clavius 4 Conclusion Christopher Clavius, S.J. Calendar Reform Lessons from Clavius Conclusion Christopher Clavius, S.J. (1538–1612) Christopher Clavius, S.J. Calendar Reform Lessons from Clavius Conclusion Clavius’s life Born in Bamberg c. 1538 1555 received into the Society of Jesus by St. Ignatius Loyola 1556–1560 studied philosophy at Coimbra 1561–1566 studied theology at the Collegio Romano 1567–1612 professor of mathematics at Collegio Romano 1570 published Commentary on the Sphere of Sacrobosco 1574 published edition of Euclid’s Elements c. 1572–1582 on papal calendar commission c. 1595 retired from teaching, focused on research 1612 died in Rome Christopher Clavius, S.J. Calendar Reform Lessons from Clavius Conclusion Clavius as teacher As a teacher, Clavius Taught elementary (required) courses in astronomy Led a seminar for advanced students Fought for status of mathematics in the curriculum Christopher Clavius, S.J. Calendar Reform Lessons from Clavius Conclusion Calendar Reform: Solar How to keep the calendar in synch with solar year (365.24237 days, equinox to equinox): Julian calendar: 365.25 days Gregorian calendar: omit 3 leap days every 400 years; hence 365.2425 days Christopher Clavius, S.J. Calendar Reform Lessons from Clavius Conclusion Calendar Reform: Lunar Easter is the first Sunday after the first full moon on or after the vernal equinox. -
Gangale 2000 the MARTIAN TIME POLL: ONE MARTIAN YEAR OF
Gangale_2000 THE MARTIAN TIME POLL: ONE MARTIAN YEAR OF DATA Thomas Gangale* And Marilyn Dudley-Rowley** ABSTRACT The design of a Martian timekeeping system must be as much a social construct as an astronomical one if it is to gain wide acceptance within the Martian community. Not only must such a system accurately mark the passage of the Martian diurnal and annual cycles; it must also incorporate features that satisfy human social needs. What kind of a clock and calendar do Martians want? The Martian Time Web Site began conducting an online poll in September 1998. The Martian Time Poll consists of 25 questions on the basic elements of Martian timekeeping. The results of the first Martian year of data are reported and discussed. KEYWORDS: timekeeping, Mars calendars, Mars clocks, measurement as social construct. 1. INTRODUCTION As we humans establish ourselves as a multiplanetary species, spreading throughout the Solar System during this new century, we will leave behind the 24-hour day and the 365-day year. These are cycles that are peculiar to Earth, and as a product of billions of years of evolution on this planet, we are designed to operate by them. Humans will have no use for diurnal periods that are hundreds of hours long. Similarly, years of 12 or 29 times the duration of the terrestrial year (the orbital periods of Jupiter and Saturn, respectively) will be of no practical use in human affairs. We define a standard unit, the second, in as abstract a way as possible for the physical sciences, but time is a social measurement, first and foremost. -
Goals: 1) Solve a Different Cultures Astronomy Problem. 2) Look at the Interaction Between Science, Religion and Culture
Science of Easer Problem Set – Due 18 April 2013 Goals: 1) Solve a different cultures astronomy problem. 2) Look at the interaction between science, religion and culture. 3) Practice making scientific models based upon observations. 1) (25 points) A major problem in Medieval European astronomy was to predict when Easter would occur. This involved finding when the lunar calendar (cycle) would sync up with the solar calendar (cycle). This problem was not unique to Medieval Europe. Often a culture’s oldest calendar is a lunar calendar. Then most cultures adopt a solar calendar. The culture will want to celebrate the old holidays (tied to the phase of the moon) at the same time of year (spring, summer, etc.) Medieval European astronomers were asked to predict when the first full moon will be after the first day of spring (vernal equinox). During this time Europe used the Julian year. The Julian calendar reform established a cycle of 3 years of 365 days followed by a leap year of 366 days so that the average year in a four year period would be 365.25 days long, i.e. the time from one vernal equinox to the next is 365.25 days. We will use the same solar calendar. For the time from one full moon to the next we will use a more exact number, 29.53059 days. The main question is, do these two calendars sync up with each other? Namely are there two integers, M and N, such that M years and N months have the same number of days? If so then after M years Easter will once again occur on the same day. -
Alfred Wegener's Hypothesis on Continental Drift and Its Discussion in Petermanns Geographische Mitteilungen
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Electronic Publication Information Center Polarforschung 75 (1), 29 – 35, 2005 (erschienen 2006) Alfred Wegener’s Hypothesis on Continental Drift and Its Discussion in Petermanns Geographische Mitteilungen (1912 – 1942) by Imre Josef Demhardt1 Abstract: Certainly not the first to notice the obvious key-and-lock shape of crossed when the famous first publication of Wegener’s hypo- Brazil and Africa, in 1911 the meteorologist Alfred Wegener was nevertheless thesis on continental drift appeared in the April and May among the first scientists to link hitherto isolated scientific arguments to these empirical observation and develop a hypothesis conclusively explaining the issues of PGM 1912. Given this double anniversary, it might architecture of the Earth’s surface which over the years evolved into an intense be timely to recall some of the circumstances, which led to this debate with his adversaries. Although cautioned by his colleague and father- publication and to shed some light on probably little known in-law Wladimir Köppen not to interfere with the discussion of geological matters as a meteorologist – and therefore as an outsider – he presented his aspects of the debate it triggered in the columns of this leading thoughts to the “Geologische Vereinigung” in Frankfurt am Main on 6 January geographical journal in the three decades thereafter. 1912 and first published them in ‘Petermanns Geographische Mitteilungen’, one of the leading geographical monthlies of international reputation, in April 1912 in a paper entitled “Die Entstehung der Kontinente” (The Origin of the Alfred Wegener (1880-1930, Fig. -
Sothic Cycle - Wikipedia
12/2/2018 Sothic cycle - Wikipedia Sothic cycle The Sothic cycle or Canicular period is a period of 1,461 Egyptian civil years of 365 days each or 1,460 Julian years averaging 365¼ days each. During a Sothic cycle, the 365-day year loses enough time that the start of its year once again coincides with the heliacal rising of the star Sirius (Ancient Egyptian: Spdt or Sopdet, "Triangle"; Greek: Σῶθις, Sō̂this) on 19 July in the Julian calendar.[1][a] It is an important aspect of Egyptology, particularly with regard to reconstructions of the Egyptian calendar and its history. Astronomical records of this displacement may have been responsible for the later establishment of the more accurate Julian and Alexandrian calendars. Sirius (bottom) and Orion (right). The Winter Triangle is formed Contents from the three brightest stars in the northern winter sky: Sirius, Mechanics Betelgeuse (top right), and Discovery Procyon (top left). Chronological interpretation Observational mechanics and precession Problems and criticisms Notes References External links Mechanics The ancient Egyptian civil year, its holidays, and religious records reflect its apparent establishment at a point when the return of the bright star Sirius to the night sky was considered to herald the annual flooding of the Nile.[2] However, because the civil calendar was exactly 365 days long and did not incorporate leap years until 22 BC, its months "wandered" backwards through the solar year at the rate of about one day in every four years. This almost exactly corresponded to its displacement against the Sothic year as well. (The Sothic year is about a minute longer than a solar year.)[2] The sidereal year of 365.25636 days is only valid for stars on the ecliptic (the apparent path of the Sun across the sky), whereas Sirius's displacement ~40˚ below the ecliptic, its proper motion, and the wobbling of the celestial equator cause the period between its heliacal risings to be almost exactly 365.25 days long instead.