Historical Values of the Earth's Clock Error Δ and the Calculation of Eclipses:
01 Aug 2004-Journal for the History of Astronomy (Science History Publications)-Vol. 35, Iss: 120, pp 327-336
TL;DR: In this article, the effect of variations in the Earth's rate of rotation (LOD) or, equivalently, the length of the day (LOD), on the position of the Moon and Sun in the historical past is discussed.
Abstract: Numerous observations of the Moon, Sun and planets are recorded in ancient and medieval history. These observations which include many eclipses and lunar and planetary conjunctions frequently attract the interest of historians of astronomy. If the positions of the Moon and Sun (and to a lesser extent the planets) in the historical past are to be computed with high precision, it is usually necessary to make satisfactory allowance for the effect of variations in the Earth's rate of rotation, or, equivalently, the length of the day (LOD). Long-term variations in the LOD are mainly produced by lunar and solar tides, but other causes such as the continuing rise of land that was glaciated during the last ice-age are also significant. Although actual changes in the LOD amount to only a few hundredths of a second over several thousand years, the cumulative effect (known as ~T) of these minute changes can be very large. For instance, the estimated value of ~T at the epoch 1000 B.C. is as much as 7 hours. During this interval, the Moon can change position by nearly 4°. It is therefore a matter of concern that at present there appears to be a degree of confusion and misapprehension among historians of astronomy over the choice of values of ~T that should be used in making retrospective computations of lunar and solar positions. Accurate knowledge of the value of ~T is often crucial in assessing the local circumstances of solar eclipses. Neglect of variations in the Earth's spin rate would materially affect the calculated positions of where these phenomena could be seen on the Earth's surface. In this paper we shall try to elucidate the necessary procedures and in particular draw attention to several important points regarding ~T in the calculation of solar eclipses. We shall place special emphasis on three specific issues: the adopted time-scale, the importance of tidal friction in the ephemeris of the Moon, and the enumeration of ~T at various epochs in the past.
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TL;DR: A new algorithm SG2 is proposed that is faster than the three others and offers the same level of accuracy than the most accurate, i.e., maximum error in solar vector for a multi-decadal time period, with an example of a 50-year period: 1980–2030.
107 citations
Cites background from "Historical Values of the Earth's Cl..."
...Morrison and Stephenson (2004) proposed polynomial approximations for three different periods: 1961-1986, 1986-2005, 2005-2050....
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01 Jan 2009
TL;DR: A supplement to the "Five Millennium Canon of Solar Eclipses" as mentioned in this paper includes additional information for each eclipse that could not be included in the original 648-page publication because of size limits.
Abstract: This catalog is a supplement to the "Five Millennium Canon of Solar Eclipses." It includes additional information for each eclipse that could not be included in the original 648-page publication because of size limits. The data tabulated for each eclipse include the catalog number, canon plate number, calendar date, Terrestrial Dynamical Time of greatest eclipse, (Delta)T, lunation number, Saros number, eclipse type, Quincena Lunar Eclipse parameter, gamma, eclipse magnitude, geographic coordinates of greatest eclipse (latitude and longitude), and the circumstances at greatest eclipse (i.e., Sun altitude and azimuth, path width, and central line duration). The Canon and the Catalog both use the same solar and lunar ephemerides as well as the same values of (Delta)T. This 1-to-1 correspondence between them will enhance the value of each. The researcher may now search, evaluate, and compare eclipses graphically (Canon) or textually (Catalog).
34 citations
Cites background from "Historical Values of the Earth's Cl..."
...All values of ∆T, based on Morrison and Stephenson (2004), assume a value for the Moon’s secular acceleration of –26 arcsec/cy(2)....
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...All values of ∆T, based on Morrison and Stephenson (2004), assume a value for the Moon’s secular acceleration of –26 arcsec/cy2....
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...Published determinations of ∆T from historical eclipse records have assumed a secular acceleration of –26 arcsec/cy(2) (Morrison and Stephenson, 2004)....
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...A detailed analysis of these measurements fitted with cubic splines for ∆T from –500 to +1950 is presented in Table 2-1 and includes the standard error for each value (Morrison and Stephenson, 2004). a. World time zones are actually based on UTC....
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...Morrison and Stephenson (2004) propose a simple parabolic relation to estimate the standard error (σ), which is valid over the period 1000 BCE to 1200 CE:...
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TL;DR: Other astronomical references in the Epic are analyzed, without assuming the existence of an eclipse, and it is speculated that these references, plus the disputed eclipse reference, may refer to that specific eclipse.
Abstract: Plutarch and Heraclitus believed a certain passage in the 20th book of the Odyssey (“Theoclymenus's prophecy”) to be a poetic description of a total solar eclipse. In the late 1920s, Schoch and Neugebauer computed that the solar eclipse of 16 April 1178 B.C.E. was total over the Ionian Islands and was the only suitable eclipse in more than a century to agree with classical estimates of the decade-earlier sack of Troy around 1192–1184 B.C.E. However, much skepticism remains about whether the verses refer to this, or any, eclipse. To contribute to the issue independently of the disputed eclipse reference, we analyze other astronomical references in the Epic, without assuming the existence of an eclipse, and search for dates matching the astronomical phenomena we believe they describe. We use three overt astronomical references in the epic: to Bootes and the Pleiades, Venus, and the New Moon; we supplement them with a conjectural identification of Hermes's trip to Ogygia as relating to the motion of planet Mercury. Performing an exhaustive search of all possible dates in the span 1250–1115 B.C., we looked to match these phenomena in the order and manner that the text describes. In that period, a single date closely matches our references: 16 April 1178 B.C.E. We speculate that these references, plus the disputed eclipse reference, may refer to that specific eclipse.
26 citations
TL;DR: In this paper, the authors provide geoscientists with the most accurate set of the Earth's astro-climatic parameters and daily insolation quantities, able to describe the Short-Term Orbital Forcing (STOF) as represented by the everchanging incoming solar radiation.
24 citations
Cites methods from "Historical Values of the Earth's Cl..."
...UT is studied and adjusted using ancient astronomical observations and following Morrison and Stephenson (2004) for the interval 9999 BC700 BC, the difference TT−UT (which, for our purposes we can assume as TDB−UT) follows a parabolic relationship such that for BC10000 = 1/1/- 9999 = JD−1931076.0…...
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...UT is studied and adjusted using ancient astronomical observations and following Morrison and Stephenson (2004) for the interval 9999 BC700 BC, the difference TT−UT (which, for our purposes we can assume as TDB−UT) follows a parabolic relationship such that for BC10000 = 1/1/9999 = JD−1931076....
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01 Jan 2014
TL;DR: In this paper, the authors examine the relation of astronomy to mechanics in the ancient Greek world, and argue that we should imagine astronomy and mechanics in conversation with one another, rather than in a simple, one-way transmission of influence.
Abstract: The ancient Greek art of spbairopoiia was devoted to the building of models of the universe such as celestial globes and annillary spheres. But it also included the construction of geared mechanisms that replicated the motions of the Sun, Moon, and planets, such as the famous orrery that Cicero attributed to Archimedes or the spectacular Antikythera mechanism, found in an ancient shipwreck of about 60 BC. Was sphairopoiia merely an imitative art, in which the modelers followed the precepts of the theoretical astronomers? Or could theoretical astronomy also learn something from the art of mechanics? In this paper, we examine the relation of astronomy to mechanics in the ancient Greek world, and argue that we should imagine astronomy and mechanics in conversation with one another, rather than in a simple, one-way transmission of influence.
16 citations
References
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15 Apr 1995-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences
TL;DR: In this paper, results from previous analyses of lunar occupations in the period AD 1600-1955.5, and from high-precision data in AD 1955.5-1990, are included in the dataset considered in this paper.
Abstract: Records of solar and lunar eclipses in the period 700 BC to AD 1600, originating from the ancient and medieval civilizations of Babylon, China, Europe and the Arab world, are amassed and critically appraised for their usefulness in answering questions about the long-term variability of the Earth’s rate of rotation. Results from previous analyses of lunar occupations in the period AD 1600-1955.5, and from high-precision data in AD 1955.5-1990, are included in the dataset considered in this paper.
199 citations
27 Nov 1984-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences
TL;DR: In this paper, the magnitudinal and temporal behaviour of non-tidal variations of the Earth's rotation over the past 2700 years was evaluated. But, as would be expected if tidal friction were the only mechanism affecting the Earth’s rotation, there are also non-fractional changes present that vary on timescales ranging from decades to millennia.
Abstract: Occultations of stars by the Moon, and solar and lunar eclipses are analysed for variations in the Earth’s rotation over the past 2700 years. Although tidal braking provides the dominant, long-term torque, it is found that the rate of rotation does not decrease uniformly as would be expected if tidal friction were the only mechanism affecting the Earth’s rotation. There are also non-tidal changes present that vary on timescales ranging from decades to millennia. The magnitudinal and temporal behaviour of these non-tidal variations are evaluated in this paper.
144 citations
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TL;DR: In this article, it was shown that the average measured increase in the length of the day is 1.8 ms per century, from which it was concluded that besides the tidal contribution there is another long-term component acting to decrease the Earth's rate of spin, which is consistent with recent measurements made by artificial satellites.
32 citations