Bradley's Nutation, 18Th-Century Analytic Argument, and the Contemporary Technical Communication Classroom
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Edmond Halley and His Recurring Comet
EDMOND HALLEY AND HIS RECURRING COMET “They [the astronomers of the flying island of Laputa] have observed ninety-three different comets and settled their periods with great exactness. If this be true (and they affirm it with great confidence), it is much to be wished that their observations were made public, whereby the theory of comets, which at present is very lame and defective, might be brought into perfection with other parts of astronomy.” — Jonathan Swift, GULLIVER’S TRAVELS, 1726 HDT WHAT? INDEX HALLEY’S COMET EDMOND HALLEY 1656 November 8, Saturday (Old Style): Edmond Halley was born. NEVER READ AHEAD! TO APPRECIATE NOVEMBER 8TH, 1656 AT ALL ONE MUST APPRECIATE IT AS A TODAY (THE FOLLOWING DAY, TOMORROW, IS BUT A PORTION OF THE UNREALIZED FUTURE AND IFFY AT BEST). Edmond Halley “Stack of the Artist of Kouroo” Project HDT WHAT? INDEX HALLEY’S COMET EDMOND HALLEY 1671 February 2, Friday (1671, Old Style): Harvard College was given a “3 foote and a halfe with a concave ey-glasse” reflecting telescope. This would be the instrument with which the Reverends Increase and Cotton Mather would observe a bright comet of the year 1682. ASTRONOMY HALLEY’S COMET HARVARD OBSERVATORY ESSENCE IS BLUR. SPECIFICITY, THE OPPOSITE OF ESSENCE, IS OF THE NATURE OF TRUTH. Edmond Halley “Stack of the Artist of Kouroo” Project HDT WHAT? INDEX HALLEY’S COMET EDMOND HALLEY 1676 Edmond Halley was for six weeks the guest of the British East India Company at their St. Helena colony in the South Atlantic for purposes of observation of the exceedingly rare transit of the planet Venus across the face of the sun. -
Dynamical Adjustments in IAU 2000A Nutation Series Arising from IAU 2006 Precession A
A&A 604, A92 (2017) Astronomy DOI: 10.1051/0004-6361/201730490 & c ESO 2017 Astrophysics Dynamical adjustments in IAU 2000A nutation series arising from IAU 2006 precession A. Escapa1; 2, J. Getino3, J. M. Ferrándiz2, and T. Baenas2 1 Dept. of Aerospace Engineering, University of León, 24071 León, Spain 2 Dept. of Applied Mathematics, University of Alicante, PO Box 99, 03080 Alicante, Spain e-mail: [email protected] 3 Dept. of Applied Mathematics, University of Valladolid, 47011 Valladolid, Spain Received 20 January 2017 / Accepted 23 May 2017 ABSTRACT The adoption of International Astronomical Union (IAU) 2006 precession model, IAU 2006 precession, requires IAU 2000A nutation to be adjusted to ensure compatibility between both theories. This consists of adding small terms to some nutation amplitudes relevant at the microarcsecond level. Those contributions were derived in previously published articles and are incorporated into current astronomical standards. They are due to the estimation process of nutation amplitudes by Very Long Baseline Interferometry (VLBI) and to the changes induced by the J2 rate present in the precession theory. We focus on the second kind of those adjustments, and develop a simple model of the Earth nutation capable of determining all the changes arising in the theoretical construction of the nutation series in a dynamical consistent way. This entails the consideration of three main classes of effects: the J2 rate, the orbital coefficients rate, and the variations induced by the update of some IAU 2006 precession quantities. With this aim, we construct a first order model for the nutations of the angular momentum axis of the non-rigid Earth. -
The Spin, the Nutation and the Precession of the Earth's Axis Revisited
The spin, the nutation and the precession of the Earth’s axis revisited The spin, the nutation and the precession of the Earth’s axis revisited: A (numerical) mechanics perspective W. H. M¨uller [email protected] Abstract Mechanical models describing the motion of the Earth’s axis, i.e., its spin, nutation and its precession, have been presented for more than 400 years. Newton himself treated the problem of the precession of the Earth, a.k.a. the precession of the equinoxes, in Liber III, Propositio XXXIX of his Principia [1]. He decomposes the duration of the full precession into a part due to the Sun and another part due to the Moon, to predict a total duration of 26,918 years. This agrees fairly well with the experimentally observed value. However, Newton does not really provide a concise rational derivation of his result. This task was left to Chandrasekhar in Chapter 26 of his annotations to Newton’s book [2] starting from Euler’s equations for the gyroscope and calculating the torques due to the Sun and to the Moon on a tilted spheroidal Earth. These differential equations can be solved approximately in an analytic fashion, yielding Newton’s result. However, they can also be treated numerically by using a Runge-Kutta approach allowing for a study of their general non-linear behavior. This paper will show how and explore the intricacies of the numerical solution. When solving the Euler equations for the aforementioned case numerically it shows that besides the precessional movement of the Earth’s axis there is also a nu- tation present. -
212 Publications of the Some Pioneer
212 PUBLICATIONS OF THE SOME PIONEER OBSERVERS1 By Frank Schlesinger In choosing a subject upon which to speak to you this eve- ning, I have had to bear in mind that, although this is a meeting of the Astronomical Society of the Pacific, not many of my audience are astronomers, and I am therefore debarred from speaking on too technical a matter. Under these circumstances I have thought that a historical subject, and one that has been somewhat neglected by the, formal historians of our science, may be of interest. I propose to outline, very briefly of course, the history of the advances that have been made in the accuracy of astronomical measurements. To do this within an hour, I must confine myself to the measurement of the relative places of objects not very close together, neglecting not only measure- ments other than of angles, but also such as can be carried out, for example, by the filar micrometer and the interferometer; these form a somewhat distinct chapter and would be well worth your consideration in an evening by themselves. It is clear to you, I hope, in how restricted a sense I am using the word observer ; Galileo, Herschel, and Barnard were great observers in another sense and they were great pioneers. But of their kind of observing I am not to speak to you tonight. My pioneers are five in number ; they are Hipparchus in the second century b.c., Tycho in the sixteenth century, Bradley in the eighteenth, Bessel in the first half of the nineteenth century and Rüther fur d in the second half. -
Who Invented the Calculus? - and Other 17Th Century Topics Transcript
Who invented the calculus? - and other 17th century topics Transcript Date: Wednesday, 16 November 2005 - 12:00AM Location: Barnard's Inn Hall WHO INVENTED THE CALCULUS? Professor Robin Wilson Introduction We’ve now covered two-thirds of our journey ‘From Caliphs to Cambridge’, and in this lecture I want to try to survey the mathematical achievements of the seventeenth century – a monumental task. I’ve divided my talk into four parts – first, the movement towards the practical sciences, as exemplified by the founding of Gresham College and the Royal Society. Next, we’ll gravitate towards astronomy, from Copernicus to Newton. Thirdly, we visit France and the gradual movement from geometry to algebra (with a brief excursion into some new approaches to pi) – and finally, the development of the calculus. So first, let’s make an excursion to Gresham College. Practical science The Gresham professorships arose from the will of Sir Thomas Gresham, which provided for £50 per year for each of seven professors to read lectures in Divinity, Astronomy, Music, Geometry, Law, Physic and Rhetoric. As the Ballad of Gresham College later described it: If to be rich and to be learn’d Be every Nation’s cheifest glory, How much are English men concern’d, Gresham to celebrate thy story Who built th’Exchange t’enrich the Citty And a Colledge founded for the witty. From its beginning, Gresham College encouraged the practical sciences, rather than the Aristotelian studies still pursued at the ancient universities: Thy Colledg, Gresham, shall hereafter Be the whole world’s Universitie, Oxford and Cambridge are our laughter; Their learning is but Pedantry. -
Research on the Precession of the Equinoxes and on the Nutation of the Earth’S Axis∗
Research on the Precession of the Equinoxes and on the Nutation of the Earth’s Axis∗ Leonhard Euler† Lemma 1 1. Supposing the earth AEBF (fig. 1) to be spherical and composed of a homogenous substance, if the mass of the earth is denoted by M and its radius CA = CE = a, the moment of inertia of the earth about an arbitrary 2 axis, which passes through its center, will be = 5 Maa. ∗Leonhard Euler, Recherches sur la pr´ecession des equinoxes et sur la nutation de l’axe de la terr,inOpera Omnia, vol. II.30, p. 92-123, originally in M´emoires de l’acad´emie des sciences de Berlin 5 (1749), 1751, p. 289-325. This article is numbered E171 in Enestr¨om’s index of Euler’s work. †Translated by Steven Jones, edited by Robert E. Bradley c 2004 1 Corollary 2. Although the earth may not be spherical, since its figure differs from that of a sphere ever so slightly, we readily understand that its moment of inertia 2 can be nonetheless expressed as 5 Maa. For this expression will not change significantly, whether we let a be its semi-axis or the radius of its equator. Remark 3. Here we should recall that the moment of inertia of an arbitrary body with respect to a given axis about which it revolves is that which results from multiplying each particle of the body by the square of its distance to the axis, and summing all these elementary products. Consequently this sum will give that which we are calling the moment of inertia of the body around this axis. -
Positional Astronomy Coordinate Systems
Positional Astronomy Observational Astronomy 2019 Part 2 Prof. S.C. Trager Coordinate systems We need to know where the astronomical objects we want to study are located in order to study them! We need a system (well, many systems!) to describe the positions of astronomical objects. The Celestial Sphere First we need the concept of the celestial sphere. It would be nice if we knew the distance to every object we’re interested in — but we don’t. And it’s actually unnecessary in order to observe them! The Celestial Sphere Instead, we assume that all astronomical sources are infinitely far away and live on the surface of a sphere at infinite distance. This is the celestial sphere. If we define a coordinate system on this sphere, we know where to point! Furthermore, stars (and galaxies) move with respect to each other. The motion normal to the line of sight — i.e., on the celestial sphere — is called proper motion (which we’ll return to shortly) Astronomical coordinate systems A bit of terminology: great circle: a circle on the surface of a sphere intercepting a plane that intersects the origin of the sphere i.e., any circle on the surface of a sphere that divides that sphere into two equal hemispheres Horizon coordinates A natural coordinate system for an Earth- bound observer is the “horizon” or “Alt-Az” coordinate system The great circle of the horizon projected on the celestial sphere is the equator of this system. Horizon coordinates Altitude (or elevation) is the angle from the horizon up to our object — the zenith, the point directly above the observer, is at +90º Horizon coordinates We need another coordinate: define a great circle perpendicular to the equator (horizon) passing through the zenith and, for convenience, due north This line of constant longitude is called a meridian Horizon coordinates The azimuth is the angle measured along the horizon from north towards east to the great circle that intercepts our object (star) and the zenith. -
Section II: Summary of the Periodic Report on the State of Conservation, 2006
State of Conservation of World Heritage Properties in Europe SECTION II workmanship, and setting is well documented. UNITED KINGDOM There are firm legislative and policy controls in place to ensure that its fabric and character and Maritime Greenwich setting will be preserved in the future. b) The Queen’s House by Inigo Jones and plans for Brief description the Royal Naval College and key buildings by Sir Christopher Wren as masterpieces of creative The ensemble of buildings at Greenwich, an genius (Criterion i) outlying district of London, and the park in which they are set, symbolize English artistic and Inigo Jones and Sir Christopher Wren are scientific endeavour in the 17th and 18th centuries. acknowledged to be among the greatest The Queen's House (by Inigo Jones) was the first architectural talents of the Renaissance and Palladian building in England, while the complex Baroque periods in Europe. Their buildings at that was until recently the Royal Naval College was Greenwich represent high points in their individual designed by Christopher Wren. The park, laid out architectural oeuvres and, taken as an ensemble, on the basis of an original design by André Le the Queen’s House and Royal Naval College Nôtre, contains the Old Royal Observatory, the complex is widely recognised as Britain’s work of Wren and the scientist Robert Hooke. outstanding Baroque set piece. Inigo Jones was one of the first and the most skilled 1. Introduction proponents of the new classical architectural style in England. On his return to England after having Year(s) of Inscription 1997 travelled extensively in Italy in 1613-14 he was appointed by Anne, consort of James I, to provide a Agency responsible for site management new building at Greenwich. -
On the IAU 2000 Nutation Consistency with IAU 2006 Precession Draft Note
On the IAU 2000 nutation consistency with IAU 2006 precession Draft note∗ Alberto Escapay and Nicole Capitainez Abstract The Earth precession-nutation model of the International Astronomical Union (IAU) is composed of the IAU 2006 precession and IAU 2000 nu- tation. The IAU 2006 precession, which is consistent with both dynamical theory and the IAU 2000 nutation, was adopted to replace the precession part of the IAU 2000 precession-nutation. In that process, it was noticed that very slight adjustments were required to the IAU 2000 nutation ampli- tudes in order to ensure consistency at the micro arcsecond level with the IAU 2006 precession. The formulae for these adjustments provided by Cap- itaine et al. (2005) were implanted in part of the standards and software for computing nutation (e.g., SOFA and IERS Conventions 2010). However, IAU has not adopted any resolution on that direction, so formally such an inconsistency remains. Moreover, it has been shown recently (Escapa et al. 2017) that a few additional terms should be added to the 2005 expressions. We examine the drawbacks that have arisen as a consequence of the lack of such a resolution and propose different options to address them within the framework of IAU 2006 precession and IAU 2000 nutation. They run from just supplementing current IAU resolutions to clarify the content and termi- nology of the IAU precession-nutation model, to adopting a potential new resolution that would also ensure dynamical consistency between precession and nutation. ∗This draft will be submitted to publication yDepartment of Aerospace Engineering, University of Leon,´ E-24071 Leon,´ Spain; [email protected] zSYRTE, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universites,´ F-75014 Paris, France; [email protected] 1 1 Introduction Nowadays, the International Astronomical Union (IAU) precession-nutation model is based on IAU 2000A nutation (Mathews et al. -
The Information Order of Isaac Newton's Principia Mathematica
SIMON SCHAFFER The Information Order of Isaac Newton’s Principia Mathematica THE HANS RAUSING LECTURE 2008 UPPSALA UNIVERSITY SALVIA SMÅSKRIFTER 1 2 THE HANS RAUSING LECTURE 2008 The Information Order of Isaac Newton’s Principia Mathematica SIMON SCHAFFER Professor of History of Science, University of Cambridge UPPSALA UNIVERSITY 3 SALVIA SMÅSKRIFTER, NO. 11 © Författaren Tryck Wikströms, Uppsala 2008 ISBN 978-91-506-2040-5 4 Contents The Information Order of Isaac Newton’s Principia Mathematica 7 What I may seem to the World 7 Information Orders and Credit Economies 12 Tides and Currents: A Tonkin Resolution 23 Comets and Pendulums: Information Obscured by Clouds 36 In Heaven as it is on Earth 49 Author’s biographical sketch 59 5 6 The Information Order of Isaac Newton’s Principia Mathematica Simon Schaffer What I may seem to the world “I know not what I may seem to the world, but as to myself, I seem to have been only like a boy playing on the sea-shore and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.” 1 It is one of the most celebrated of Isaac Newton’s obiter dicta. Like many such, its provenance is a bit hazy. The literary reference is surely to a passage from John Milton’s great redemptive poem Paradise Regained (1671) where, in dialogue with Satan, Christ praises divine illumination above pagan learning.2 But the statement’s immediate relation with Newton is more ambiguous. The earliest version is to be found in an Oxford conversation of April 1730, three years after Newton’s death, between the gossipy man of letters Joseph Spence and the Jacobite, freemason and court tutor Andrew Ramsay. -
James Short and John Harrison: Personal Genius and Public Knowledge
Science Museum Group Journal James Short and John Harrison: personal genius and public knowledge Journal ISSN number: 2054-5770 This article was written by Jim Bennett 10-09-2014 Cite as 10.15180; 140209 Research James Short and John Harrison: personal genius and public knowledge Published in Autumn 2014, Issue 02 Article DOI: http://dx.doi.org/10.15180/140209 Abstract The instrument maker James Short, whose output was exclusively reflecting telescopes, was a sustained and consistent supporter of the clock and watch maker John Harrison. Short’s specialism placed his work in a tradition that derived from Newton’s Opticks, where the natural philosopher or mathematician might engage in the mechanical process of making mirrors, and a number of prominent astronomers followed this example in the eighteenth century. However, it proved difficult, if not impossible, to capture and communicate in words the manual skills they had acquired. Harrison’s biography has similarities with Short’s but, although he was well received and encouraged in London, unlike Short his mechanical practice did not place him at the centre of the astronomers’ agenda. Harrison became a small part of the growing public interest in experimental demonstration and display, and his timekeepers became objects of exhibition and resort. Lacking formal training, he himself came to be seen as a naive or intuitive mechanic, possessed of an individual and natural ‘genius’ for his work – an idea likely to be favoured by Short and his circle, and appropriate to Short’s intellectual roots in Edinburgh. The problem of capturing and communicating Harrison’s skill became acute once he was a serious candidate for a longitude award and was the burden of the specially appointed ‘Commissioners for the Discovery of Mr Harrison’s Watch’, whose members included Short. -
Back Matter (PDF)
[ 395 ] INDEX TO THE PHILOSOPHICAL TRANSACTIONS, S e r ie s A, V o l . 193. A. Abney (W. de W.). The Colour Sensations in Terms of Luminosity, 259. Atmospheric electricity—experiments in connection with precipitation (Wilson), 289. Bakebian Lectube. See Ewing and Kosenhain. C. Colour-blind, neutral points in spectra found by (Abney), 259. Colour sensations in terms of luminosity (Abney), 259. Condensation nuclei, positively and negatively charged ions as (W ilson), 289. Crystalline aggregates, plasticity in (Ewing and Rosenhain), 353. D. Dawson (H. M.). See Smithells, Dawson, and Wilson VOL. CXCIII.— Ao : S F 396 INDEX. Electric spark, constitution of (Schuster and Hemsalech), 189; potential—variation with pressure (Strutt), 377. Electrical conductivity of flames containing vaporised salts (Smithells, Dawson, and Wilson), 89. Electrocapillary phenomena, relation to potential differences between‘solutions (Smith), 47. Electrometer, capillary, theory of (Smith), 47. Ewing (J. A.) and Rosenhain (W.). The Crystalline Structure of Metals.—Bakerian Lecture, 353. F. Filon (L. N. G ). On the Resistance to Torsion of certain Forms of Shafting, with special Reference to the Effect of Keyways, 309. Flames, electrical conductivity of, and luminosity of salt vapours in (Smithells, Dawson, and Wilson), 89. G. Gravity balance, quartz thread (Threlfall and Pollock), 215. H. Hemsalech (Gustav). See Schuster and Hemsalech. Hertzian oscillator, vibrations in field of (Pearson and Lee), 159. Hysteresis in the relation of extension to stress exhibited by overstrained iron (Muir), 1. I. Ions, diffusion into gases, determination of coefficient (Townsend), 129. Ions positively and negatively charged, as condensation nuclei (Wilson), 289. Iron, recovery of, from overstrain (Muir), 1.