DOCSLIB.ORG

From Keplerian Orbits to Precise Planetary Predictions: the Transits of the 1630S

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
From Keplerian Orbits to Precise Planetary Predictions: the Transits of the 1630S MEETING VENUS C. Sterken, P. P. Aspaas (Eds.) The Journal of Astronomical Data 19, 1, 2013 From Keplerian Orbits to Precise Planetary Predictions: the Transits of the 1630s Steinar Thorvaldsen Department of Education, University of Tromsø, 9037 Tromsø, Norway Abstract. The first transits of Mercury and Venus ever observed were important for quite different reasons than were the transit of Venus observed in the eighteenth century. Good data of planetary orbits are necessary for the prediction of plane- tary transits. Under the assumption of the central position of the Sun, Johannes Kepler published the theory of elliptical orbital motion of the planets in 1609; this new astronomy made it possible to compute noticeably improved ephemerides for the planets. In 1627 Kepler published the Tabulae Rudolphinae, and thanks to these tables he was able to publish a pamphlet announcing the rare phenomenon of Mercury and Venus transiting the Sun. Although the 1631 transit of Mercury was only observed by three astronomers in France and in Switzerland, and the 1639 transit of Venus was only predicted and observed by two self-taught astronomers in the English countryside, their observation would hardly been possible without the revolutionary theories and calculations of Kepler. The Tabulae Rudolphinae count among Kepler’s outstanding astronomical works, and during the seventeenth cen- tury they gradually found entrance into the astronomical praxis of calculation among mathematical astronomers and calendar makers who rated them more and more as the most trustworthy astronomical foundation. 1. Introduction The worldwide fame of Johannes Kepler (1571–1630) is based above all on his con- tribution to celestial mechanics and astronomy. Aided by the accurate observations of Tycho Brahe, he published a mature system of the world based on elliptical astro- nomy, celestial physics and mathematical harmonies: Epitome astronomiae coper- nicanae (Kepler 1618–21/1995). His groundbreaking and innovative work reached beyond the three laws on which his fame mainly rests today. Kepler also practiced what he preached and made astronomical predictions by his laws. Starting in 1617, he published planetary ephemerides that showed a marked increase in accuracy as compared to other tables that were in use at the time. After Kepler had published the Tabulae Rudolphinae in 1627 (Kepler 1627/1969), more and more ephemerides were calculated on the basis of this work in the following decades. Because of the high reliability of Kepler’s tables, the Copernican doctrine gained more esteem (Gingerich 1968/1993). Although this was first restricted to the mathematical foundations of the system, as well as to Kepler’s laws, it was more and more accepted that the Copernican doctrine was not just a new and useful mathematical hypothesis, but a reflection of reality. Kepler, like many of the leading natural philosophers before him, had some explicit metaphysical guiding principles for his work. He firmly believed that God had created a harmonious well-ordered universe, and he saw his work as a God-given mission to understand its nature, principles and design (Kozhamthadam 1994; Methuen 1998; Martens 2000). The driving goal for Kepler was to carefully read the “book of Nature” and discover the orderly structure God had created in the universe. This 97 98 Thorvaldsen order of nature was supposed to be expressed in mathematical language and its quantitative calculations. Tycho Brahe had estimated the distance between the Sun and the Earth at 8 mil- lion kilometer. In Epitome Kepler estimated the solar distance to be 3469 Earth radii, actually the largest of his several estimates. This meant that the distance to the Sun was 24 million kilometers, and the solar parallax 1 arcminute. The solar parallax is the angle subtended by the equatorial radius of the Earth at its mean distance of the Sun. Kepler based his estimate on Tycho’s attempted measurements of the parallax of Mars and on his own calculations of eclipses, which had convinced him that a solar parallax of more than 10 gave unsatisfactory results (van Helden 1985, 1989). We know now that this solar distance was roughly seven times too small,1 and Kepler’s understanding of absolute distances within the solar system re- mained considerably faulty although he mainly worked with relative distances based on the Earth–Sun unit, the so called astronomical unit. On the basis of Tycho Brahe’s observations, Kepler early in his career had calcu- lated that Mercury would pass in front of the Sun at the end of May, 1607. He used a pinhole camera (camera obscura) to observe the event, and on May 28 a black spot was visible on the Sun’s image between clouds. He concluded that he had seen a transit of Mercury, and published his observation in the report Phaenomenon singulare seu Mercurius in Sole (Kepler 1609/1941). Later on, when the sunspots had been discovered by the newly invented telescope, he realized that he had seen a sunspot, and he admitted his error in print. 2. Mathematical solution Kepler was operating in a long-standing tradition of numerical calculation in astron- omy. His new planetary theory was much more complicated than anything that had been done before. In the earlier theories, the orbit of the Earth and the planets were represented by two large circles, the deferent and the epicycle. Kepler’s first law states that the planetary orbits are elliptical, and to compute areas inside the ellipse is not easy. For the astronomers time was represented by an angle, and in the Keplerian model there was no simple or exact way to find explicitly the position angle corresponding to a given time, and consequently there was no direct way to calculate the planetary position exactly from its date, as it had always been possible before Kepler. However, Kepler made his non-circular astronomy operational and computable by applying a set of innovative numerical methods (Thorvaldsen 2010). In fact it was the use of an auxiliary circle that aided Kepler at this point. One of the fundamental properties of the ellipse is the ratio-property, that for any Q and P on a line perpendicular to CD, see Fig. 1: QR/PR =constant (1) Kepler’s law states that time is proportional to the ellipse area ADP . This area is composed of the triangle ARP and the segment RDP . By Eq. 1 the triangle is proportional to the triangle ARQ and the segment is proportional to the segment RDQ. Consequently, time is proportional to the circle area ADQ which is β + e sin β (2) 1The currently accepted value of the solar parallax is 800. 794. The mathematical procedure behind computing the parallax based on transits of the Sun can be found in Teets (2003). From Keplerian Orbits to Precise Planetary Predictions 99 Figure 1. A is the position of the Sun and B is the center of the auxiliary circle. The planet is at P , and Q is its projection on the circle. Kepler’s problem is to determine the angle β (the eccentric anomaly). Here e is the constant AB and β the angle QBD called the eccentric anomaly. Analytically, Kepler expressed the problem by the equation M = β + e sin β where M is the quantity used to designate time (the Mean anomaly). Kepler measured M as a fraction of the area of the full circle, i.e. an area of 360◦ (216000, or 129600000). The Mean anomaly is proportional to the time elapsed, and itisasa function of time that we wish to find the position of the planet P . So the important problem is to find β when M and e are given. This transcendental equation is called Kepler’s equation and turned out to be a famous problem as it is fundamental in celestial dynamics (Colwell 1993). Kepler could only solve it by approximations (Swerdlow 2000; Thorvaldsen 2010). The problem was stated at the very end of Astronomia nova (Kepler 1609/1992, 600). In Epitome, book 5, part II, chapter 4 (Kepler 1618-21/1995, pp. 158–59) he gives a numerical example with three iterations as shown in Table 1. The eccentricity e is determined from the area of the triangle ABF , which he says he earlier had calculated to be 1191000. Table 1. Kepler’s numerical solution of his equation in Epitome, book 5, part II, chapter 4, compared to a simple computer iteration based on βn = M −e sin βn−1 in Microsoft Excel. Eccentricity e = 0.05774, and the Mean anomaly M = 50◦0901000 (= 0.87533 radians). The convergence is quite rapid in this case. Kepler in Epitome Calculated degrees radians radians iteration# 44◦ 250 0.77522 0.77522 β ◦ 0 46 44 0.81565 0.83492 β1 ◦ 0 00 47 44 6 0.83313 0.83253 β2 ◦ 0 00 47 42 17 0.83260 0.83262 β3 100 Thorvaldsen Kepler’s method can be described as a simple numerical “fixed point method”, that is, an iterative algorithm that generates a convergent sequence whose limit is the solution of the proposed problem: βn = M − e sin βn−1. He called his method to solve equations the regula positionum (rule of suppo- sition), probably an allusion to the classical method of regula falsi (rule of false position). But he made no closer examination of the speed of convergence or errors involved. Later, in his Tabulae Rudolphinae, Kepler solved the equation for a grid of uniformly spaced angles, that determined a set of non-uniformly spaced times. By an interpolation scheme the desired values of time could be determined, and hence the tedious iterations were avoided for the users of his tables. During the years 1614–1630 John Napier’s (1550–1617) discovery of logarithms rapidly spread within mathematics, and was exploited by Kepler to speed up the as- tronomical calculations and ease the pain of the process.
Load more

Recommended publications
  • The 1761 Transit of Venus and Hell's Transition to Fame
    Chapter 3 A New Node of Science in Action: The 1761 Transit of Venus and Hell’s Transition to Fame I reckon there is no one interested in astronomy who does not wait impa- tiently to learn what was observed during the recent meeting of Venus with the Sun, especially since there is no other encounter between celes- tial bodies from which we are able to ascertain with a greater degree of exactness the still unknown, or not yet sufficiently well defined, paral- laxes of the Sun and Venus. Eustachio Zanotti 17611 1 A Golden Opportunity The above assessment of Hell’s Bolognese colleague Eustachio Zanotti could hardly have been more to the point. The passage (or transit) of Venus in front of the Sun as seen from the Earth is a rare astronomical phenomenon: it comes in pairs separated by eight years, after which it does not take place for more than a whole century. The first transit of Venus observed by means of astro- nomical equipment was in 1639. Since then, transits of Venus have occurred in the years 1761 and 1769, 1874 and 1882, and 2004 and 2012—but they will not happen again until 2117 and 2125. The 1639 transit of Venus made no immediate impact and (as far is known) was only observed by two amateur astronomers in the English countryside.2 By contrast, the pre-calculated transits of 1761 and 1 Eustachio Zanotti, De Veneris ac Solis Congressu Observatio habita in Astronomico Specula Bononiensis Scientiarum Instituti Die 5 Junii mdcclxi (Bologna: Laelii e Vulpe, 1761), 1.
    [Show full text]
  • The Transit of Venus, 1639 Jeremiah Horrocks and William Crabtree
    THE TRANSIT OF VENUS, 1639 JEREMIAH HORROCKS AND WILLIAM CRABTREE A Selected Bibliography Primary Sources Horrox, Jeremiah., Venus in Sole Visa, reproduced (in English) in Memoir of the Life and Labours of the Reverend Jeremiah Horrox, by Rev. Arundell Blount Whatton, pub. Wertheim, Macintosh and Hunt, 1859, pp.109-216 Secondary Sources Papers and Articles AMC, Horrocks, Jeremiah (1617?-1641), National Dictionary of Biography, pp.1267-1269 Applebaum, W., and Hatch, R.A., Boulliau, Mercator and Horrocks's "Venus in Sole Venus": Three unpublished letters, Journal for the History of Astronomy, Vol.14, part 3, No. 41, pp.174-175 […], October 1983 Applebaum, Wilbur, Horrocks, Jeremiah, Dictionary of Scientific Biography, Vol.6 (1972), pp.514- 516 Bailey, John E., Jeremiah Horrox, The Observatory, 1883, No.79, pp.318-328 Barocas, V., A Country Curate, Quarterly Journal of the Royal Astronomical Society, Vol. 12, 1971, pp.179-182 Bulpit, W.T., Misconceptions concerning Jeremiah Horrocks, the Astronomer, The Observatory, Vol.27, September 1911, No.478, pp.335-337 (illustrations: plate facing p.335 showing Hoole Church, Carr House and stained glass memorial window at Hoole Church) Chapman, Allan, Jeremiah Horrocks, the Transit of Venus, and the 'New Astronomy' in early seventeenth-century England, Quarterly Journal of the Royal Astronomical Society, Vol. 31, 1996, p.333-357 Clark, G.Napier, Sketch of the Life and Works of Rev.Jeremiah Horrox, Journal of the Royal Astronomical Society of Canada, Vol.10, No.10, December 1916, pp.523-536 (illustrations:
    [Show full text]
  • Download This Article (Pdf)
    Percy, JAAVSO Volume 41, 2013 381 Book Review Received August 7, 2013 Meeting Venus—a Collection of Papers Presented at the Venus Transit Conference, Tromsø 2012 Christiaan Sterken and Per Pippin Aspaas, eds., 2013, 256 pages, paperback, ISBN 978-82-8244-094-3, Vrije Universiteit Brussel, and University of Tromsø, available in open access (http://www.vub.ac.be/STER/JAD/JAD19/jad19_1/ jad19_1.htm). On June 6, 2012, the planet Venus passed across the face of the Sun, as seen from the Earth. The brightness of the Sun (if you could measure it precisely) would have decreased by about 0.001 magnitude, adding to the Sun’s status as a variable star. More to the point: a transit of Venus (or Mercury) is a graphic demonstration of what an exoplanet transit would look like, if we had sufficient power to resolve it. Transits of Venus are brief and rare. Kepler’s and Newton’s laws made it possible to predict them. Jeremiah Horrocks was the first to observe one, in 1639, based on Kepler’s prediction, and his own refinement thereof. Edmond Halley, building on a suggestion by James Gregory, showed that it would be possible to measure the absolute size scale of the solar system by observing a transit of Venus from multiple sites across the Earth, and this led to a number of expeditions to observe the 1761 and 1769 transits, notably James Cook’s expedition to Tahiti in 1769. It was the “space race” of its day. Specifically, the project was to measure the solar parallax—the angle subtended at the Sun by the mean radius of the Earth, now known to be 8.794143 arc seconds.
    [Show full text]
  • A Calendar of Mathematical Dates January
    A CALENDAR OF MATHEMATICAL DATES V. Frederick Rickey Department of Mathematical Sciences United States Military Academy West Point, NY 10996-1786 USA Email: fred-rickey @ usma.edu JANUARY 1 January 4713 B.C. This is Julian day 1 and begins at noon Greenwich or Universal Time (U.T.). It provides a convenient way to keep track of the number of days between events. Noon, January 1, 1984, begins Julian Day 2,445,336. For the use of the Chinese remainder theorem in determining this date, see American Journal of Physics, 49(1981), 658{661. 46 B.C. The first day of the first year of the Julian calendar. It remained in effect until October 4, 1582. The previous year, \the last year of confusion," was the longest year on record|it contained 445 days. [Encyclopedia Brittanica, 13th edition, vol. 4, p. 990] 1618 La Salle's expedition reached the present site of Peoria, Illinois, birthplace of the author of this calendar. 1800 Cauchy's father was elected Secretary of the Senate in France. The young Cauchy used a corner of his father's office in Luxembourg Palace for his own desk. LaGrange and Laplace frequently stopped in on business and so took an interest in the boys mathematical talent. One day, in the presence of numerous dignitaries, Lagrange pointed to the young Cauchy and said \You see that little young man? Well! He will supplant all of us in so far as we are mathematicians." [E. T. Bell, Men of Mathematics, p. 274] 1801 Giuseppe Piazzi (1746{1826) discovered the first asteroid, Ceres, but lost it in the sun 41 days later, after only a few observations.
    [Show full text]
  • Transits of Venus: New Views of the Solar System and Galaxy
    INTERNATIONAL ASTRONOMICAL UNION UNION ASTRONOMIQUE INTERNATIONALE "I TRANSITS OF VENUS: NEW VIEWS OF THE SOLAR SYSTEM AND GALAXY PROCEEDINGS OF THE 196th COLLOQUIUM OF THE INTERNATIONAL ASTRONOMICAL UNION HELD IN PRESTON, LANCASHIRE, UNITED KINGDOM 7-11 JUNE 2004 Edited by D. W. KURTZ Centre for Astrophysics, University of Central Lancashire, Preston, UK CAMBRIDGE UNIVERSITY PRESS V Table of Contents Preface ix Organizing committee xii Conference photograph xiii Conference participants xvi Part 1. TRANSITS OF VENUS: HISTORY, RESULTS AND LEGACY Chairs: Steve Dick & Mary Bru'ck Jeremiah Horrocks, William Crabtree, and the Lancashire observations of the tran- sit of Venus of 1639 [Keynote talk] 3 Allan Chapman ~\ Jeremiah Horrocks's Lancashire 27 John K. Walton William Crabtree's Venus transit observation 34 Nicholas Kollerstrom Venus transits - A French view 41 Suzanne Debarbat James Cook's 1769 transit of Venus expedition to Tahiti 52 Wayne Orchiston v~ Observations of the 1761 and 1769 transits of Venus from Batavia (Dutch East Indies) 67 Robert H. van Gent The 1761 transit of Venus dispute between Audiffredi and Pingre 74 Luisa Pigatto Observations of planetary transits made in Ireland in the 18th Century and the development of astronomy in Ireland 87 C. J. Butler The American transit of Venus expeditions of 1874 and 1882 100 Steven J. Dick The Mexican expedition to observe the 8 December 1874 transit of Venus in Japan 111 Christine Allen Maya observations of 13th-century transits of Venus? 124 Jesus Galindo Trejo and Christine Allen Lord Lindsay's expedition to Mauritius in 1874 138 M. T. Briick ' vi Contents Why did other European astronomers not see the December 1639 transit of Venus? 146 David W.
    [Show full text]
  • Planets Solar System Paper Contents
    Planets Solar system paper Contents 1 Jupiter 1 1.1 Structure ............................................... 1 1.1.1 Composition ......................................... 1 1.1.2 Mass and size ......................................... 2 1.1.3 Internal structure ....................................... 2 1.2 Atmosphere .............................................. 3 1.2.1 Cloud layers ......................................... 3 1.2.2 Great Red Spot and other vortices .............................. 4 1.3 Planetary rings ............................................ 4 1.4 Magnetosphere ............................................ 5 1.5 Orbit and rotation ........................................... 5 1.6 Observation .............................................. 6 1.7 Research and exploration ....................................... 6 1.7.1 Pre-telescopic research .................................... 6 1.7.2 Ground-based telescope research ............................... 7 1.7.3 Radiotelescope research ................................... 8 1.7.4 Exploration with space probes ................................ 8 1.8 Moons ................................................. 9 1.8.1 Galilean moons ........................................ 10 1.8.2 Classification of moons .................................... 10 1.9 Interaction with the Solar System ................................... 10 1.9.1 Impacts ............................................ 11 1.10 Possibility of life ........................................... 12 1.11 Mythology .............................................
    [Show full text]
  • 78. Don't Miss the Transit of Venus in 2012: It's Your Last Chance Until
    © 2011, Astronomical Society of the Pacific No. 78 • Fall 2011 www.astrosociety.org/uitc 390 Ashton Avenue, San Francisco, CA 94112 Don’t Miss the Transit of Venus in 2012: It’s Your Last Chance Until 2117 by Chuck Bueter (www.transitofvenus.org) The Travails of Le Gentil Imagine your country is sending you on a quest to resolve one of the era’s biggest questions in science. At this moment in history, the solution, the technology, and the alignment of planets have come together. For your part of the mission, all you have to do is record the instant when the edge of one small circle touches the edge of a second larger circle. Such were the fortunate circumstances of Guilliame Hyacinthe Jean Baptiste Le Gentil. The French astronomer eagerly set sail for India to witness the 1761 transit of Venus, a rare celestial alignment in which the silhouette of Venus appears to pass directly across the sun. A fleet of astronomers spread out across the globe in response to Edmund Halley’s call to time the event from diverse locations, from which the distance to the sun—the highly valuable Astronomical Unit—could be mathematically derived. Expeditions were sent around the world to observe the transit of Venus. Image courtesy of Chuck Bueter Upon Le Gentil’s arrival, the intended destination was occupied by hostile English troops, so his ship turned Johannes Kepler showed the relationship between a planet’s back to sea, where he could not effectively use a telescope. orbital period and its distance from the sun.
    [Show full text]
  • The 1761 Transit of Venus and Hell's Transition to Fame
    Chapter 3 A New Node of Science in Action: The 1761 Transit of Venus and Hell’s Transition to Fame I reckon there is no one interested in astronomy who does not wait impa- tiently to learn what was observed during the recent meeting of Venus with the Sun, especially since there is no other encounter between celes- tial bodies from which we are able to ascertain with a greater degree of exactness the still unknown, or not yet sufficiently well defined, paral- laxes of the Sun and Venus. Eustachio Zanotti 17611 1 A Golden Opportunity The above assessment of Hell’s Bolognese colleague Eustachio Zanotti could hardly have been more to the point. The passage (or transit) of Venus in front of the Sun as seen from the Earth is a rare astronomical phenomenon: it comes in pairs separated by eight years, after which it does not take place for more than a whole century. The first transit of Venus observed by means of astro- nomical equipment was in 1639. Since then, transits of Venus have occurred in the years 1761 and 1769, 1874 and 1882, and 2004 and 2012—but they will not happen again until 2117 and 2125. The 1639 transit of Venus made no immediate impact and (as far is known) was only observed by two amateur astronomers in the English countryside.2 By contrast, the pre-calculated transits of 1761 and 1 Eustachio Zanotti, De Veneris ac Solis Congressu Observatio habita in Astronomico Specula Bononiensis Scientiarum Instituti Die 5 Junii mdcclxi (Bologna: Laelii e Vulpe, 1761), 1.
    [Show full text]
  • The 1761'S Transit of Venus : an International Transfer of Mathematical Knowledge…
    The 1761's transit of Venus : an international transfer of mathematical knowledge…. Isabelle Lémonon (EHESS- CAK Paris) Novembertagung 2015, Turin, November, 26th-28th The 1761's transit of Venus : an international transfer of mathematical knowledge…. ...out of women's reach ? Isabelle Lémonon (EHESS- CAK Paris) Novembertagung 2015, Turin, November, 26th-28th • What is a transit of Venus ? • What for ? • How ? • Historical context • Who ? Where ? When ? • Transfer of mathematical knowledge • Transit of Venus and “eclipse of a Savante” • Conclusion What is a transit of Venus ? • Transit = one celestial body appears to move across the face of another celestial body (different apparent diameter) • Conjunction= apparent close approach between the objects as seen on the sky Diagram of transit of Venus Image of the 2012 transit taken by4 NASA's 3,4° Solar Dynamics Observatory spacecraft What is a transit of Venus ? • Predictable astronomical phenomenon • One of the rarest of these phenomena • Every 243 years, with pairs of transits eight years apart separated by long gaps of 121,5 years and 105,5 years ( orbital periods of Earth and Venus are close to 8:13 and 243:395 commensurabilities) 5 What for ? • Measurement of the distance Sun/Earth A (E.Halley 1716, Royal Society) : solar parallax a “a clarion call for scientists everywhere to prepare for the rare opportunity presented by the forthcoming transits of 1761 and 1769. […] I recommend it to the curious strenuously to apply themselves to this observation. By this means, the Sun's parallax
    [Show full text]
  • Orozco-Echeverri2020.Pdf (3.437Mb)
    This thesis has been submitted in fulfilment of the requirements for a postgraduate degree (e.g. PhD, MPhil, DClinPsychol) at the University of Edinburgh. Please note the following terms and conditions of use: This work is protected by copyright and other intellectual property rights, which are retained by the thesis author, unless otherwise stated. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This thesis cannot be reproduced or quoted extensively from without first obtaining permission in writing from the author. The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the author. When referring to this work, full bibliographic details including the author, title, awarding institution and date of the thesis must be given. How do planets find their way? Laws of nature and the transformations of knowledge in the Scientific Revolution Sergio Orozco-Echeverri Doctor of Philosophy in Science and Technology Studies University of Edinburgh 2019 To Uğur In his own handwriting, he set down a concise synthesis of the studies by Monk Hermann, which he left José Arcadio so that he would be able to make use of the astrolabe, the compass, and the sextant. José Arcadio Buendía spent the long months of the rainy season shut up in a small room that he had built in the rear of the house so that no one would disturb his experiments. Having completely abandoned his domestic obligations, he spent entire nights in the courtyard watching the course of the stars and he almost contracted sunstroke from trying to establish an exact method to ascertain noon.
    [Show full text]
  • And the Ends of Jesuit Science in Enlightenment Europe
    Maximilian Hell (1720–92) and the Ends of Jesuit Science in Enlightenment Europe <UN> Jesuit Studies Modernity through the Prism of Jesuit History Editor Robert A. Maryks (Independent Scholar) Editorial Board James Bernauer, S.J. (Boston College) Louis Caruana, S.J. (Pontificia Università Gregoriana, Rome) Emanuele Colombo (DePaul University) Paul Grendler (University of Toronto, emeritus) Yasmin Haskell (University of Western Australia) Ronnie Po-chia Hsia (Pennsylvania State University) Thomas M. McCoog, S.J. (Loyola University Maryland) Mia Mochizuki (Independent Scholar) Sabina Pavone (Università degli Studi di Macerata) Moshe Sluhovsky (The Hebrew University of Jerusalem) Jeffrey Chipps Smith (The University of Texas at Austin) volume 27 The titles published in this series are listed at brill.com/js <UN> Maximilian Hell (1720–92) and the Ends of Jesuit Science in Enlightenment Europe By Per Pippin Aspaas László Kontler leiden | boston <UN> This is an open access title distributed under the terms of the CC-BY-NC-Nd 4.0 License, which permits any non-commercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. The publication of this book in Open Access has been made possible with the support of the Central European University and the publication fund of UiT The Arctic University of Norway. Cover illustration: Silhouette of Maximilian Hell by unknown artist, probably dating from the early 1780s. (In a letter to Johann III Bernoulli in Berlin, dated Vienna March 25, 1780, Hell states that he is trying to have his silhouette made by “a person who is proficient in this.” The silhouette reproduced here is probably the outcome.) © Österreichische Nationalbibliothek.
    [Show full text]
  • The Black-Drop Effect Explained
    Transits of Venus: New Views of the Solar System and Galaxy Proceedings IAU Colloquium No. 196, 2004 c 2004 International Astronomical Union D.W. Kurtz & G.E. Bromage, eds. DOI: 00.0000/X000000000000000X The black-drop effect explained Jay M. Pasachoff1, Glenn Schneider2, and Leon Golub3 1Williams College-Hopkins Observatory, Williamstown, MA 01267, USA email: jay.m.pasachoff@williams.edu 2Steward Observatory, University of Arizona, Tucson, Arizona 85721, USA 3Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA Abstract. The black-drop effect bedeviled attempts to determine the Astronomical Unit from the time of the transit of Venus of 1761, until dynamical determinations of the AU obviated the need for transit measurements. By studying the 1999 transit of Mercury, using observations taken from space with NASA's Transition Region and Coronal Explorer (TRACE), we have fully explained Mercury's black-drop effect, with contributions from not only the telescope's point-spread function but also the solar limb darkening. Since Mercury has no atmosphere, we have thus verified the previous understanding, often overlooked, that the black-drop effect does not necessarily correspond to the detection of an atmosphere. We continued our studies with observations of the 2004 transit of Venus with the TRACE spacecraft in orbit and with ground- based imagery from Thessaloniki, Greece. We report on preliminary reduction of those data; see http://www.transitofvenus.info for updated results. Such studies are expected to contribute to the understanding of transits of exoplanets. Though the determination of the Astronomical Unit from studies of transit of Venus has been undertaken only rarely, it was for centuries expected to be the best method.
    [Show full text]