Astronomical Calculations Research Articles

Atmospheric effects of the total solar eclipse of 4 December 2002 simulated with a high‐altitude global model

The atmosphere's response to the total solar eclipse of 4 December 2002 is studied using a prototype high‐altitude global numerical weather prediction model (NOGAPS‐ALPHA). Local reductions in solar ultraviolet (UV) radiation during the eclipse are estimated using astronomical calculations of umbral and penumbral surface trajectories and observed solar limb darkening at ∼200–300 nm. In NOGAPS‐ALPHA these UV eclipse shadows yield stratospheric radiative cooling rate footprints peaking near 27 K day−1, a value 2–3 times larger than assumed in previous modeling. Difference fields between NOGAPS‐ALPHA runs with and without this eclipse forcing reveal vertically deep middle atmospheric responses, with three‐dimensional horizontal structures very similar to the large‐scale “bow‐wave” response first proposed by Chimonas (1970). Such structure appears clearly only at later times when total eclipses have abated and gravity waves generated in the stratosphere have had time to propagate vertically. Bow‐wave amplitudes and direct thermal cooling responses are both small (≲1 K for temperature and ≲2–3 m s−1 for horizontal winds), contradicting some rocketsonde measurements that suggest much larger responses near 50–60 km altitude. We also find clear evidence of a bow‐wave‐like response in the model's surface pressure fields, with an amplitude ∼0.1–0.5 hPa, while surface air temperatures in NOGAPS‐ALPHA show ∼4 K cooling over Africa during the eclipse. Both findings are consistent with surface atmospheric data acquired during previous eclipse passages.

Laplace: the manHahnRoger, Pierre Simon Laplace, 1749–1827: A determined scientist. Harvard University Press, Cambridge, MA, 2005. pp. x+310, £21.95, €29.80, $35.00 (hardback).0-674-01892-3.

Roger Hahn, Pierre Simon Laplace, 1749–1827: A determined scientist. Harvard University Press, Cambridge, MA, 2005. pp. x+310, £21.95, €29.80, $35.00 (hardback). 0-674-01892-3. Although Laplace was, perhaps, the most important mathematical physicist between Newton and Maxwell and also a

남병철의 혼천의 연구 II 『의기집설』에 나오는 <혼천의용법>의 역해설

<TEX>$\ulcorner$</TEX>의기집설<TEX>$\lrcorner$</TEX>의 <혼천의설(渾天儀說)>, <혼천의제법(渾天儀製法)>에 이어서 이 논문에서는 <혼천의용법(渾天儀用法)>을 연구하였다. <혼천의용법(渾天儀用法)>의 원문을 해석하여 혼천의 의 설치, 관측 및 사용법, 천문이론과 계산방법 등을 15개 항목으로 정리하였다. 그리고 원문에서 제시하고 있는 그림을 이해하기 쉽도록 표현하였고 풀이과정을 상세히 기술하였다. 혼천의 사용법에서 소개하고 있는 천문학적 계산방법은 주로 구면 삼각법과 비례법을 이용하고 있으며, 천문학적 이론이나 계산과정을 체계적으로 자세히 다루고 있어 당시의 천문과학 수준을 알아 볼 수 있었다. This study is about <Honcheonui-yongbeop(Instructions for Use of an armillary sphere)>, which constitutes Honcheonui(an armillary sphere) put of <TEX>$\ulcorner$</TEX>Uigijipseol<TEX>$\lrcorner$</TEX> (Volume I) together with <Honcheonui-seol> and <Honchoenui-jebeop>-dealt with earlier than this subject. The study's construction on the text of <Honcheonui-yongbeop> is organized into 15 categories, including installation, observations, instructions for use, astronomical theories and formulas, etc. This study provides easy-to-understand illustrations of the figures shown in the original and contains detailed descriptions of the related calculation procedures. In the 'Instructions for Use of Honcheonui' discussed here, the readers are introduced to astronomical computation systems, mainly based on spherical trigonometry and proportional methods. The section also provides systematic and detailed reviews of astronomical theories and calculation procedures, allowing you to assess the level of astronomy knowledge at that time.

Commission 31: Time

The most intensely discussed and controversial issue in time keeping has been the proposal before the International Telecommunications Union (ITU) to redefine Coordinated Universal Time (UTC) so as to replace leap seconds by leap hours. Should this proposal be adopted, the practice of inserting leap seconds would cease after a specific date. Should the Earth's rotation continue to de-accelerate at its historical rate, the next discontinuity in UTC would be an hour inserted several centuries from now. Advocates of this proposal cite the need to synchronize satellite and other systems, such as GPS, Galileo, and GLONASS, which did not exist and were not envisioned when the current system was adopted. They note that leap second insertions can be and have been incorrectly implemented or accounted for. Such errors have to date had localized impact, but they could cause serious mishaps involving loss of life. For example, some GPS receivers have been known to fail simply because there was no leap second after a long enough interval, other GPS receivers failed because the leap second information was broadcast more than three months in advance, and some commercial software used for internet time-transfer Network Time Protocol (NTP) could either discard all data received after a leap second or interpret it as a frequency change. The ambiguity associated with the extra second could also disrupt financial accounting and certain forms of encryption. Those opposed to the proposal question the need for a change, and also point out the costs of adjusting to the proposed change and its inconvenience to amateur astronomers and others who rely upon astronomical calculations published in advance. Reports have been circulated that the cost of checking and correcting software to accommodate the new definition of UTC would be many millions of dollars for some systems. In October 2005 American Astronomical Society asked the ITU for a year's time to study the issue. This commission has supported the efforts of the IAU's Committee on the Leap Second to make an informed recommendation, and anticipates considerable discussion at the IAU's 26th General Assembly in 2006.

Oligocene climate dynamics

A planktonic and benthic foraminiferal stable isotope stratigraphy of the Oligocene equatorial Pacific (Ocean Drilling Program, Site 1218) was generated at 6 kyr resolution between magnetochrons C9n and C11n.2n (∼26.4–30 Ma on a newly developed astronomically calibrated timescale). Our data allow a detailed examination of Oligocene paleoceanography, the evolution of the early cryosphere, and the influence of orbital forcing on glacioeustatic sea level variations. Spectral analysis reveals power and coherency for obliquity (40 kyr period) and eccentricity (∼110, 405 kyr) orbital bands, with an additional strong imprint of the eccentricity and 1.2 Myr obliquity amplitude cycle, driving ice sheet oscillations in the Southern Hemisphere. Planktonic and benthic foraminifera δ18O are used to constrain the magnitude and timing of major fluctuations in ice volume and global sea level change. Glacial episodes, related to obliquity and eccentricity variations, occurred at 29.16, 27.91, and 26.76 Ma, corresponding to glacioeustatic sea level fluctuations of 50–65 m. Alteration of high‐latitude temperatures and Antarctic ice volume had a significant impact on the global carbon burial and equatorial productivity, as cyclic variations are also recorded in the carbon isotope signal of planktonic and benthic foraminifera, the water column carbon isotope gradient, and estimated percent carbonate of bulk sediment. We also investigate the implications of a close correspondence between oxygen and carbon isotope events and long‐term amplitude envelope extrema in astronomical calculations during the Oligocene, and develop a new naming scheme for stable isotope events, on the basis of the 405 kyr eccentricity cycle count.

천문 계산용 고성능 클러스터 구축

A high performance computing cluster for astronomical computations has been built at Korea Astronomy Observatory. The 64 node cluster interconnected with Gigabit Ethernet is composed of 128 Intel Xeon processors, 160 GB memory, 6 TB global storage space, and an LTO (Linear Tape-Open) tape library. The cluster was installed and has been managed with the Open Source Cluster Application Resource (OSCAR) framework. Its performance for parallel computations was measured with a three-dimensional hydrodynamic code and showed quite a good scalability as the number of computational cells increases. The cluster has already been utilized for several computational research projects, some of which resulted in a few publications, even though its full operation time is less than one year. As a major resource of the testbed, the cluster has been used for Grid computations, too.

A long-term numerical solution for the insolation quantities of the Earth

We present here a new solution for the astronomical computation of the insolation quantities on Earth spanning from −250 Myr to 250 Myr. This solution has been improved with respect to La93 (Laskar et al. 1993) by using a direct integration of the gravitational equations for the orbital motion, and by improving the dissipative contributions, in particular in the evolution of the Earth-Moon System. The orbital solution has been used for the calibration of the Neogene period (Lourens et al. 2004), and is expected to be used for age calibrations of paleoclimatic data over 40 to 50 Myr, eventually over the full Palaeogene period (65 Myr) with caution. Beyond this time span, the chaotic evolution of the orbits prevents a precise determination of the Earth's motion. However, the most regular components of the orbital solution could still be used over a much longer time span, which is why we provide here the solution over 250 Myr. Over this time interval, the most striking feature of the obliquity solution, apart from a secular global increase due to tidal dissipation, is a strong decrease of about 0.38 degree in the next few millions of years, due to the crossing of the s6 + g5 − g6 resonance (Laskar et al. 1993). For the calibration of the Mesozoic time scale (about 65 to 250 Myr), we propose to use the term of largest amplitude in the eccentricity, related to g2 − g5, with a fixed frequency of 3.200 �� /yr, corresponding to a period of 405 000 yr. The uncertainty of this time scale over 100 Myr should be about 0.1%, and 0.2% over the full Mesozoic era.

Astronomic calibration of the late Oligocene through early Miocene geomagnetic polarity time scale

At Ocean Drilling Program (ODP) Site 1090 (subantarctic South Atlantic), benthic foraminiferal stable isotope data (from Cibicidoides and Oridorsalis) span the late Oligocene through early Miocene (∼24–16 Ma) at a temporal resolution of ∼5 ky. Over the same interval, a magnetic polarity stratigraphy can be unequivocally correlated to the geomagnetic polarity time scale (GPTS), thereby providing direct correlation of the isotope record to the GPTS. In an initial age model, we use the newly derived age of the Oligocene/Miocene (O/M) boundary of 23.0 Ma of Shackleton et al. [Geology 28 (2000) 447], revised to the new astronomical calculation (La2003) of Laskar et al. [Icarus (in press)] to recalculate the spline ages of Cande and Kent [J. Geophys. Res. 100 (1995) 6093]. We then tune the Site 1090 δ18O record to obliquity using La2003. In this manner, we are able to refine the ages of polarity chrons C7n through C5Cn.1n. The new age model is consistent, within one obliquity cycle, with previously tuned ages for polarity chrons C7n through C6Bn from Shackleton et al. [Geology 28 447–450 (2000)] when rescaled to La2003. The results from Site 1090 provide independent evidence for the revised age of the Oligocene/Miocene boundary of 23.0 Ma. For early Miocene polarity chrons C6AAr through C5Cn, our obliquity-scale age model is the first to allow a direct calibration to the GPTS. The new ages are generally within one obliquity cycle of those obtained by rescaling the Cande and Kent [J. Geophys. Res. 100 (1995) 6093] interpolation using the new age of the O/M boundary (23.0 Ma) and the same middle Miocene control point (14.8 Ma) used by Cande and Kent [J. Geophys. Res. 100 (1995) 6093].

Variable Star Network: World Center for Transient Object Astronomy and Variable Stars

Abstract Variable Star Network (VSNET) is a global professional-amateur network of researchers in variable stars and related objects, particularly in transient objects, such as cataclysmic variables, black-hole binaries, supernovae, and gamma-ray bursts. The VSNET has been playing a pioneering role in establishing the field of transient object astronomy, by effectively incorporating modern advances in observational astronomy and global electronic networks, as well as collaborative progress in theoretical astronomy and astronomical computing. The VSNET is now one of the best-featured global networks in this field of astronomy. We review the historical progress, design concept, associated technology, and a wealth of scientific achievements powered by VSNET.

Examination of early Chinese records of solar eclipses

The earliest Chinese historical text that contains systematic records of solar eclipses is the <italic>Spring and Autumn Annals.</italic> In historical periods before the Spring and Autumn period (i.e. the Xia, Shang and Western Zhou Dynasties), solar eclipse records are vague and sporadic. Although numerous scholars have investigated these records in the past two thousand years, it has been rather difficult for them to reach final conclusions. With recent advancements both in astronomical computation and in historic chronology, there has been significant progress in the study of the alleged early Chinese records of solar eclipses. These records include the reference to the solar eclipse of the Three Miao and of Zhongkang in the legends of the Xia dynasty, the expressions such as "three flames ate the Sun", "the Sun and the Moon were eclipsed" and "the Sun was zhi" in the oracle-bone inscriptions of the Shang Dynasty, and the passages of "the sky became extremely dark", "the day dawned twice" and "the Sun was eclipsed" in the literature of the Zhou Dynasty.

Exact solutions for the spatial de Vaucouleurs and Sérsic laws and related quantities

Using the Mathematica package, we find exact analytical expressions for the so-called de-projected De Vaucouleurs and Sersic laws as well as for related spatial (3D) quantities, such the mass, gravitational potential, the total energy and the central velocity dispersion, generally involved in astronomical calculations expressed in terms of the Meijer G functions.

Astronomical forcing in Late Eocene marine sediments

We use an X-ray fluorescence (XRF) Core Scanner to obtain records of elemental concentrations in sediment cores from Ocean Drilling Program (ODP) Leg 171B, Site 1052 (Blake Nose, Atlantic margin of northern Florida).This record spans the Middle to Late Eocene, as indicated by bio- and magnetostratigraphy, and displays cyclicity that can be attributed to the orbital forcing of a combination of climate, ocean circulation, or productivity. We use the XRF counts of iron and calcium as a proxy of the relative contribution from calcium carbonate and terrestrial material to construct a new composite depth record. This new composite depth record provides the basis to extend the astronomically calibrated geological time scale into the Middle Eocene and results in revised estimates for the age and duration of magnetochrons C16 through C18. In addition, we find an apparent change in the dominance of orbitally driven changes in obliquity and climatic precession at around 36.7 Ma on our new time scale. Long term amplitude modulation patterns of eccentricity and obliquity in the data do not seem to match the current astronomical model any more, suggesting the possibility of new constraints on astronomical calculations.

Reversible adaptive regularization: perturbed Kepler motion and classical atomic trajectories

Reversible and adaptive integration methods based on Kustaanheimo–Stiefel regularization and modified Sundman transformations are applied to simulate general perturbed Kepler motion and to compute classical trajectories of atomic systems (e.g. Rydberg atoms). The new family of reversible adaptive regularization methods also conserve angular momentum and exhibit superior energy conservation and numerical stability in long–time integrations. The schemes are appropriate for scattering, for astronomical calculations of escape time and long–term stability, and for classical and semiclassical studies of atomic dynamics. The components of an algorithm for trajectory calculations are described. Numerical experiments illustrate the effectiveness of the reversible approach.

Shaykh Aḥmad Shākir and the Adoption of a Scientifically-Based Lunar Calendar

AbstractThe computation of the Muslim lunar calendar has been a subject of controversy for centuries. In the twentieth century, the debate surfaced again in different parts of the Muslim world. In Egypt, the distinguished jurist Aḥmad Shākir added his voice to the debate by writing a short treatise or risāla in which he argued that a calendar based on crescent sighting should be abandoned in favour of one based on scientific and astronomical computation. After providing some background information on Shākir and the lunar debate in Egypt and elsewhere in the Muslim world, I present an annotated translation of Shākir's treatise.

La ville des géographes français de l'époque moderne, XVIIe-XVIIIe siècles

French Geographers' View of the City in the Modern Period, 17th - 18th Century This article attempts to reconstruct the sources of the way geographers used to talk about cities. The importance of Antiquity, of Ptolomaic science and the : major preoccupation with the exact : location of places using astronomical calculations led to a parallel view of stellar and urban systems, and gave rise . to a flattering discourse reproduced in : comparisons borrowed from society. The cities, listed and observed one after another by the same scholars, were poor candidates for such systématisation, hence the early crisis of definitions that was accelerated during the revolutionary period. The number of human beings - a criterion of replacement - also covered other hidden meanings. It did. however, enable a profound change in the elements entering into the definition, which shifted from the very concrete (buildings, dwellings, intra-muros areas) to the immaterial (functions, patterns, environments).

Sensitivity of paleoclimate simulation results to season definitions

According to the Milankovitch theory, slow variations of the Earth's orbital parameters change the amplitude of the seasonal cycle of insolation and are considered to be the main forcing mechanism of glacial‐interglacial cycles. Because of the precession and changes in eccentricity the length of seasons also varies. No absolute phasing is then possible between the insolation curves of two different periods. Various solutions to compare different periods have been given either for astronomical computations [e.g., Berger and Loutre, 1991; Laskar et al., 1993] or for model simulations [e.g., Kutzbach and Otto‐Bliesner, 1982; Mitchell et al., 1988], but the sensitivity of model results to the different possible solutions has never been quantified. Our results, based on simulations of the last interglacial climate, 126 kyr B.P., where changes in the length of the seasons are large, clearly show that phase leads or lags between the various solutions used introduce biases in the analysis of insolation and climate change of the same order of magnitude as the Milankovitch forcing. Our main conclusions are that (1) when comparing various model simulations, the date of the vernal equinox (i.e., the phasing of the seasonal cycle of insolation) as well as the definition of seasons must be the same for all models in order to avoid artificial differences; (2) seasons based on astronomical positions are preferred to seasons defined with the same lengths as today, since they better account for the phasing of insolation curves. However, insolation is not the only forcing in most atmospheric general circulation model simulations. We also discuss the impact of the calendar hidden behind the definition of the seasonal cycle of the other boundary conditions, such as sea ice or sea surface temperatures.

Phase calibration of VHF spatial interferometry radars using stellar sources

This work describes a method for phase calibration of spatial interferometry (SI) systems, which have recently seen increasing use in the wind profiling community. The various available techniques are inherently dependent on any phase imbalance in the system. The imbalance is caused by a path length difference between the multiple receivers, which is typically corrected at the time of construction. Aging of the system and other environmental changes can cause a modification in the path lengths, however. An obvious method for calibrating an SI system involves examining the phase differences between the receivers for a signal produced by a source with known location. For physically small systems, this can be accomplished by pointing the antenna beam toward a man‐made source, such as a simple transmitter with the same center frequency as the radar. For large MST (mesosphere/stratosphere/troposphere) radar systems, such as the Middle and Upper (MU) Atmosphere radar, this method is impractical. The present work describes the calibration of the MU radar using the radio star Cygnus A as a source of known location. As the radio star traverses the beam, the MU radar passively tracks it by measuring the phase differences of the cosmic noise signal received on spatially separated receivers. Since the location of Cygnus A is known from astronomical calculations, any phase imbalance can be compensated. Data from May 1992 show the usefulness of the method.

The Ptolemy Inequality and Minkowskian Geometry

lABI * ICDI + IBCI * IDAI = IACI IBDI, (1.1) where IABI denotes Euclidean length. 'Ptolemy's theorem' (we do not know whether he actually discovered it) proves to be so useful because it is equivalent to the trigonometric addition formulae. If BD is a diameter of length 2 R and angle ADB = e, angle BDC = 7q then sin e cos -q + cos ( sin -q = sin(e + 7q) follows easily. Ptolemy's methods are described in [1] and [3]; his tables were used in astronomical calculations for a thousand years. We call a quadrilateral 'cyclic' if its vertices lie in the given order on a circle. When the quadrilateral ABCD is not cyclic the sides and diagonals satisfy a strict inequality

A reappraisal of the geomagnetic polarity time scale to 4 MA using data from the Turkana Basin, East Africa

Recalibration of the Pliocene and early Pleistocene geomagnetic time scale using the K‐Ar dated fluvial sequence of the Turkana Basin in East Africa agrees with calibrations based on astronomical calculations. Ages estimated here are: Olduvai Subchron, 1.78–1.96 Ma; Réunion Subchrons, 2.11–2.15 Ma and 2.19–2.27 Ma; Matuyama‐Gauss boundary, 2.60 Ma; Kaena Subchron 3.02–3.09 Ma; Mammoth Subchron, 3.21–3.29 Ma; Gauss‐Gilbert boundary, 3.57 Ma.

The Jewish Calendar, A Lunar Eclipse and the Date of Christ’s Crucifixion

Astronomical calculations have been used to reconstruct the Jewish calendar in the first century AD and to date a lunar eclipse that biblical and other references suggest followed the Crucifixion. The evidence points to Friday 3 April AD 33 as the date of the Crucifixion. This was Nisan 14 in the official Jewish calendar, thus Christ died at precisely the time when the Passover lambs were slain. The date 3 April AD 33 is consistent with the evidence for the start of Jesus’ ministry, with the gospel reference to 46 years to build the temple and with the symbolism of Christ as our Passover lamb. The mention of a solar eclipse at the Crucifixion in some texts of Luke is discussed and explained. A new chronology of the life of Christ is suggested.