Solar Parallax Research Articles

Design and experimental verification on a deformable underwater solar concentrator with bi‐layer film structure

This paper presents a deformable underwater solar concentrator (DUSC) which is innovatively designed to converge underwater radiation. The concentrator is a hollow cylinder-like structure with elastic films covering the two flat ends. When it is put underwater, the elastic films will concave inwards and form spherical convex lenses. The design scheme and concentrating peculiarities of the concentrator were analysed. Optical simulation and experimental verification were carried out on a concentrator sample with diameter of 200 mm. It is found that f-number (the ratio of focal length to radius) and concentration ratio will decrease when enlarge the films' deformation ratio. The effective deformation ratio is found to be less than 0.45 to avoid total reflection. Optical simulation under condition of visible spectrum with considering the solar parallax indicates that the maximum energy density of the focus occurs when deformation ratio is 0.3, and f-number is around 3.5. During the tilt incidence, the shape of focus and energy density value will not vary distinctly until the tilt incident angle is above 10°. The average experimental optical efficiency of the DUSC is about 60% when incident angle is within 10°. This work is likely to provide a new perspective for utilizing solar energy underwater.

An international campaign of the 19th century to determine the solar parallax

In 1847 Christian Ludwig Gerling, Marburg (Germany), suggested the solar parallax to be determined by measuring the position of Venus close to its inferior conjunction, especially at the stationary points, from observatories on nearly the same meridian but widely differing in latitude. James M. Gilliss,astronomer at the newly founded U.S. Naval Observatory, enthusiastically adopted this idea and procured a grant for the young astronomical community of the United States for an expedition to Chile. There they were to observe several conjunctions of Venus and oppositions of Mars, while the accompanying measurements were to be taken at the US Naval Observatory in Washington D.C. and the Harvard College Observatory at Cambridge, USA. This expedition was supported by A. v. Humboldt, C.F. Gau{\ss}, J.F. Encke, S.C. Walker, A.D. Bache, B. Peirce and others. From 1849 to 1852 not only were astronomical, but also meteorological and magnetic observations and measurements recorded, mainly in Santa Lucia close to Santiago, Chile. By comparing these measurements with those taken simultaneously at other observatories around the world the solar parallax could be calculated, although incomplete data from the corresponding northern observatories threatened the project's success. In retrospect this expedition can be recognized as the foundation of the Chilean astronomy. The first director of the new National Astronomical Observatory of Chile was Dr. C.W. Moesta, a Hessian student of Christian Ludwig Gerling's. The exchange of data between German, American and other astronomers during this expedition was well mediated by J.G. Fl\"ugel, consul of the United States of America and representative of the Smithsonian Institution in Europe, who altogether played a major role in nurturing the relationship between the growing scientific community in the U.S. and the well established one in Europe at that time.

Transits in the Seventeenth Century and the Credentialling of Keplerian Astronomy

Consider for a moment the problem that the inferior planets posed to early cos- mologists such as Ptolemy or Copernicus. In principle, observations of Mercury or Venus at elongation could establish with fair accuracy the size and eccentricity of their orbits, although in reality the difficulty of observing Mercury at certain critical elongations made this determination somewhat problematic, and the fairly close commensurability of the period of Venus to that of the Earth (5/8) made it almost impossible over extended periods to observe satisfactory configurations. Finding the heliocentric longitude of Mercury or Venus (equivalent to the actual position in the epicycle) was even more difficult, however, because as the planet rounded the curve near elongation it was moving almost directly toward or away from the observer. The angle of elongation gave an excellent fix on the size of the orbit (or epicycle), but the distance from the observer that could have determined the longitude of the planet in its orbit was practically unobtainable. In contrast, an observation of a transit could provide strong leverage for establishing the heliocentric longitude and could furnish a check on the other parameters as well.Transits in the seventeenth century could therefore provide the astronomer with a significant test of planetary theories, and in particular could have revealed that Kepler's astronomy, as expressed in his Tabulae Rudolphinae, was substantially superior to the alternatives.' In principle the Keplerian physics, melded with the large base of Tychonic observations, provide a sophisticated interpolating scheme for the previously unobserved parts of the orbits. One historical fact especially sup- ports the notion that transits played a critical role here. Noel Duret (Natalis Durret), a little-known French astronomer who published a set of ephemerides for 1637 to 1651, started out using the 1632 tables of the Dutch astronomer Philips Lansbergen.2 He was not quite halfway through computing his ephemerides when he noticed that the Lansbergenian-based retro-calculations for the transit of Mercury observed by Gassendi in 1631 were not nearly as satisfactory as those reckoned from Kepler's tables. So, in midstream, Duret switched the basis of his calculations, and when his ephemerides were published in 1641, he prominently explained why Kepler's methods were to be preferred.3Two more publications, from the end of the century, seem to confirm the role of the transits by using and comparing multiple tables for specific transits. Ulrich Junius in Ulm (Figure 1) calculated the circumstances of the Mercury transit of 1697 from eight different tables (including Kepler and Lansbergen), and he also computed the circumstances for earlier transits including the one in 1631 predicted by Kepler and observed by Gassendi.4 Matthew Honold followed suit for the transit of 1721, calculating in advance from six tables, but conspicuously omitting Lansbergen and the Prutenics.5 He dedicated his thesis to Junius.The archives of the Paris Observatory contain the greatest depository of seventeenth-century transit material. These records were systematically collected and arranged by Joseph-Nicolas Delisle in the 1740s during his two decades in St Petersburg. Unlike the majority of his French colleagues, Delisle was a convinced Newtonian, and a fan of Edmond Halley, who had proposed that planetary transits could help determine the solar parallax.6 Delisle hoped that by gathering the data from the Mercury transits of the previous century, he might single-handedly be able to improve the numerical value of the solar parallax. Not only that, but as a Halley disciple he had the advance printed pages of Halley's tables, which would not be finally published until 1752, well after Halley's death. Thus Delisle was not particularly interested in validating Kepler's century-old tables, but in checking out the Halley tables. Nevertheless, his well-organized files showed who had observed the various transits, even if they rarely demonstrated that those observers had any interest in checking up on Kepler. …

From the Transits of Venus to the Birth of Experimental Psychology

I trace the attempts to determine the Earth-Sun distance, which is based on measurements of the solar parallax, from the naked-eye observations of Aristarchus of Samos in antiquity to observations of the transits of Venus in the 18th century, noting the nature of the observational errors involved in them. I then turn to measurements of stellar positions with meridian or transit telescopes in the 17th to 19th centuries using the eye and ear method of observation. I show how an analysis of the observational discrepancies in this method led to the discovery of an observer’s “personal equation,” and ultimately to the birth of experimental psychology.

Kepler's Archetypes: How They Increased the Scale of the Universe

(ProQuest: ... denotes formulae omitted.)In work1 of Kepler (1 57 1-1630), an archetype meant some pattern or structure that was ordained by God, or, that was in accordance with divine plan. Kepler's belief that astronomy depended above all on primacy of observations is well-known and has been frequently applauded - notably when he abandoned an especially promising solution on his way to finding path of Mars just because it did not match level of accuracy of best available observations.2 By contrast, Kepler's cosmologica! principles often depended on archetypes, which were proposed in circumstances when observations were not feasible or measurements were impractical.The purpose of this Note is to draw attention to an investigation in Kepler's Epitome Book IV (1620) in which reasoning was entirely founded on archetypes, in a situation in which it has always been natural to suppose that Kepler had relied on observation - natural, because all his predecessors had attempted to derive similar results using observational methods (however inadequate). These attempts had arisen in connection with sizing of Sun-Earth-Moon system. It was only after Kepler's era, simply as a result of technical improvement of instruments, that problem indeed became amenable to observation, and later astronomers were able to determine correct value for solar parallax.3 This value was single measurement that provided foundation for accurate determination of Earth-Sun distance (and eventually for dimensions of universe itself).The reasoning that we present here was set out in a self-contained sub-section in Epitome IV, I, 4 (KGW, vii, p. 276 line 40 - p. 281 line 26). Kepler's own diagram of KGW, vii, p. 278 (repeated p. 280), is reproduced in Figure 1, using solid lines. We can appropriately describe it as 'Eclipse Diagram', since it represents situation in which Moon exactly eclipses Sun, viewed from Earth - so that radii of Sun and Moon appear precisely equal.It may not previously have been appreciated that Eclipse Diagram had two separate functions, as an archetype, as well as being an observational tool. For Kepler, though diagram was indeed drawn in accordance with observations, its archetypal significance was over-riding consideration: he believed that universe was embodiment of divine principles, incorporating observations that agreed with archetype ordained by God. Kepler set out many arguments to explain underlying plan of universe (KGW, vii, p. 276 line 41 - p. 277 line 28). Compellingly, it seemed to him self-evident that positions of Sun and Moon relative to Earth had been arranged by Creator for benefit of humankind, so that the contemplative creature (or alternatively, the measuring creature) would be able to calculate dimensions of universe (KGW, vii, p. 280 lines 1-2). Kepler set out to do just this - and results, with citations of his own words, are collected for ease of reference in Table 1.During this limited investigation Kepler avoided discussion of detailed measurements and concerned himself with considerations of relative size alone (KGW, vii, p. 277 lines 13-17). For instance, question of whether distances of Sun or Moon from Earth were apogeal, or perigeal, or intermediate, was irrelevant; instead, Kepler stated what they ought to be, implying a (subsidiary) archetypal reason (KGW, vii, p. 280 lines 2-4).Throughout, we refer to the distance between bodies rather than the semidiameter of sphere and to the radius (a term that was seldom, if ever, used by Kepler) instead of the semidiameter [of body]. This is simply to avoid inaccuracies that have been found in translations and commentaries when 'semidiameter' is mistyped in haste as 'diameter' .4For convenience of modern readers we shall use symbolic notation (as Kepler did not) to write proportions as fractions, and to express Kepler's intentions more concisely by using indices to replace his extended verbal descriptions involving powers and roots. …

The 1874 transit of Venus: New Zealand's first foray into international astronomy

The nineteenth century transits of Venus provided astronomers with the opportunity to use these rare events to calculate the solar parallax, and New Zealand played a vital role. Apart from activities by local astronomers, international expeditions from England, France, Germany and the USA were based in New Zealand for the 1874 transit. Although many observing sites were clouded out on the vital day, New Zealand-based observations contributed to the determination of the solar parallax and led to further local observations during the 1882 transit of Venus.

ROMANIAN ASTRONOMY AND THE 1874 TRANSIT OF VENUS

The 1874 transit was an event that attracted world-wide attention, and many nations arranged observing stations within their own territories or organized international expeditions in order to try and contribute to one of the most challenging problems in astronomy at the time: the value of the solar parallax (and hence the 'astronomical unit'). Romania was also involved in these exploits when two Austrian astronomers, Edmund Weiss and Theodor von Oppolzer, came to Jassy to observe the transit, with assistance from two Romanian astronomers, Stefan Micle and Neculai Culianu. In this paper I describe the state of Romanian astronomy at this time before providing an account of the transit observations.

Sensational Differences: the Case of the Transit of Venus

In the nineteenth century, astronomers, physiologists and experimental psychologists noticed that different individuals timed simultaneous phenomena differently. These small “sensational differences”, sometimes referred to as personal equations, augmented considerably in astronomical measurements, in perceptions of movement, and in measurements of rapid phenomena, such as the speed of light. Alarmingly, these differences affected science beyond determinations of time and simultaneity. They appeared in elementary perceptions of lengths, angles, color, and sound. Unlike well-known random errors, they persisted even when observations were repeated and averaged. This paper examines various attempts by scientists to overcome these differences in the determination of the most important constant of celestial mechanics: the solar parallax. It takes us from the famous transit of Venus observations of 1874 to later speed-of-light measurements, tracking fundamental changes in the establishment of measurement-based science.

Models, Metaphors, and the Transit of Venus at Victorian Greenwich

During the nineteenth century, the Royal Observatory Greenwich underwent a remarkable transformation, which has been described by historians as like an industrial revolution in observatory science. George Biddell Airy (Astronomer Royal from 1835 to 1881) was a leading figure in this period. The effort to measure the distance to the sun (solar parallax) using observations of the 1874 transit of Venus was one of the most ambitious enterprises of his career. In many ways the transit program became a proving ground for the new methods of “industrial” astronomy that had been developing over the previous half-century. In order for the plan to succeed, multiple geographically-separated observations of a particular moment in the transit’s passage would have to be made. The problem was that no one alive had ever witnessed a transit or knew what this moment would look like. The response was to build simulation transits of Venus-mechanical models-to be used for experimentation and training. The design of these models was driven in part by calculations and in part by the astronomical reports from previous transits of Venus in the eighteenth century. Some of these reports evoked metaphorical descriptions of a “black drop effect” at the crucial moment to be observed. When it was found that some models also produced a black drop effect, the phenomenon came to be thought of by Airy and his assistants as real and reliable. This belief would turn out to be false.

The American transit of Venus expeditions of 1874 and 1882

When in 1874 and 1882 Venus passed in front of the face of the Sun, most countries with a scientific reputation to keep or to gain made plans to observe the great event. The United States was no exception. The purpose was primarily to measure the solar parallax, and thereby determine the astronomical unit, the distance between the Earth and the Sun. With a 0059, yielding an Earth-Sun distance of 92797000 miles, with a probable error of 59700 miles. This was a significant improvement over previous estimates. How important were the transit of Venus observations? In the end it was Newcomb who had the final say, for it was his system of astronomical constants that was adopted internationally at a Paris conference in 1896. Ironically, just at this time other methods were proving more accurate than Venus transits. In determining a final value for the solar parallax from all methods, Newcomb gave all photographic observations of the 1874 and 1882 transit a weight of 2, compared to a weight of 40 for Pulkovo Observatory's determination of solar parallax from the constant of aberration. Thus the Venus transit observations played little role in the official value used for the astronomical unit in the 20th century.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

The 1882 Belgian transit of Venus expeditions to Texas and Chile - a reappraisal

In 1871, the Belgian astronomer Houzeau suggested applying a new heliometric device to measure the position of Venus transiting the solar disc. This "heliometer with unequal focal lengths" produces a large and a small solar image, as well as a large and a small image of Venus. Making the small solar and the large Venus image coincide would yield a measure of the distance of the centres of both objects. Two separate stations equipped with similar instruments may provide a value for the solar parallax. After being appointed Director of the Royal Observatory of Belgium in 1876, Houzeau obtained support to organize two Belgian expeditions to observe the 1882 December 6 transit of Venus: one to San Antonio (Texas) and the other to Santiago (Chile). The observations were quite successful, but it took some time to take into account the effects that influenced the measurements, in order to determine the parallactic displacement. While the result was not overwhelmingly convincing, the experiment nevertheless was a fresh approach to determining the solar parallax. This enterprise was the first major expedition in the history of Belgian science.

'The Grange', Tasmania: survival of a unique suite of 1874 transit of Venus relics

One of the two US expeditions in Australia for the 1874 transit of Venus was based in Campbell Town, Tasmania. While the transit was observed from this site and some of the photographs taken were used in the subsequent investigation of the solar parallax, its main claim to fame is the physical vestiges of the transit programme that have survived there through to the present day. These comprise foundations for instruments, two piers associated with the photographic telescope, and one of the prefabricated observatory buildings. In addition, a copy of a photograph of the transit is preserved in the Queen Victoria Museum and Art Gallery in nearby Launceston. Collectively these form a unique suite of 1874 transit of Venus relics, and arc of international importance.

Lord Lindsay's expedition to Mauritius in 1874

An account is given of Lord Lindsay's lavishly equipped independent expedition to the Island of Mauritius in the Indian Ocean to observe the 1874 Transit of Venus. The expedition's secondary programme, the deriving of the solar parallax from observations of the minor planet Juno, is also described. This work proved a positive outcome of a generally disappointing event and brought about an important shift in the approach to the parallax challenge. The site on Mauritius where Lord Lindsay observed the Transit in 1874, now preserved as a National Monument, was the centre of celebrations during the Transit of 2004.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

The 1761 transit of Venus dispute between Audiffredi and Pingré

On 6 June 1761 the Dominican Giovanni Battista Audiffredi observed the transit of Venus in his little observatory at the Monastery of Santa Maria sopra Minerva in Rome. Soon after, he published an anonymous short report in Italian, and in the first months of 1762 he published a complete Latin essay about his transit observations. Late in 1762, and in 1765, the French abbé Alexandre-Gui Pingré, who had observed the transit at the Rodriguez Isle, to the south of the equator, presented to the French Royal Academy of Sciences the results of the solar parallax determination derived from comparison of observations made in different geographic places. He had excluded the Roman data because – he said – of the lack of a fundamental quantity, the longitude of the Monastery, concluding that the Roman observations were imperfect. In order to defend his scientific reputation, Audiffredi published two Latin essays concerning the solar parallax determination, the Investigatio parallaxis solaris in 1765, and the De Solis parallaxis Commentarius in 1766.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

James Cook's 1769 transit of Venus expedition to Tahiti

After the failure of the 1761 transit to provide a reliable value for the astronomical unit, the focus shifted to the 1769 event, and Britain mounted an ambitious program, with overseas observing parties dispatched to North Cape (Norway), Hudson Bay (Canada) and newly-discovered Tahiti in the Pacific. Lieutenant James Cook was in charge of the Tahitian expedition, ably assisted by fellow-astronomer, Charles Green, and they were supplied by the Royal Society and the Royal Observatory at Greenwich with telescopes and other scientific instruments. The main observing site was set up at Fort Venus, and supplementary transit stations were established on Irioa Island (Moorea) and Taaupiri Island (off the east coast of Tahiti). June 3 was warm and clear, and all observers successfully recorded the transit, but on the journey home ‘the curse of the transit’ prevailed and more than half of them fell ill and died. Back in England, Cook wrote up the transit observations for the Philosophical Transactions of the Royal Society, but for some inexplicable reason only used data obtained at Fort Venus. It was left to Oxford astronomer, Professor Thomas Hornsby, to derive a meaningful figure for the solar parallax, and he utilized the Tahitian data and observations made at four other sites to arrive at a figure of 8794148, thereby discrediting Beaglehole's oft-quoted claim that the Tahitian observations were a failure. Although more than a dozen men were involved in the Tahitian transit program, most of their records have been lost, and remarkably few of the instruments they employed can now be identified. Yet for those of us with Pacific affiliations, Cook's first voyage to the South Seas occupies a special place in transit of Venus history.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Shades of the goddess: Venus in transit

I review the talks given during IAU Colloquium 196, sometimes in a revised order to suggest certain connexions. The AU now, its definition, value and uncertainty, and its modern determination are contrasted with the situation in 1640. While there are differences, not least in the value of the AU and its error, some things have not changed. As an enduring constant we require: a correct theoretical framework, precise observations, and accurate calculations. The history and context of Horrocks' transit observations are set against the backdrop of our own sightings during the 2004 event, and our journeys to Carr House and other sites in Much Hoole.The apparent success of the subsequent 1769 world-wide effort belied the limitations imposed by the ‘black drop’ effect, now said to have two causes: finite resolution and limb darkening. Some mysteries surrounding Henderson's determination of the parallax of Centauri were dispelled, which led to a discussion of modern astrometry, both from the ground and in space. A passionate plea for continuing ground-based astrometry was followed by results from satellite observatories, in particular discordant values for the parallax of the Pleiades. A graph of parallax determinations since 1769 illustrates the steadily increasing precision reminiscent of a ‘Livingston curve,’ with improvement by an order of magnitude every 50 years. This progression is expected to continue, as the next space missions (Gaia, JASMINE) should better Hipparcos by large factors. Time on the Earth and our very definition of the second are quite naturally related to motion of the planets, and the dynamical history of the solar system.The 19th-century transit efforts were the last gasp in a 250-year endeavour linking Kepler with his Victorian heirs: From the viewpoint of determining solar parallax the Venus transit must have had its day. Discussion of its history, though, can be expected to continue. Finally, I trace the progress in determining the value of the AU over nearly 400 years, and suggest that more rapid advancement could have been facilitated by the introduction of other techniques. The danger of sticking to one strategy for too long is perhaps the best lesson which the Venus transits have to offer.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

The 1900-1 opposition of 433 Eros, the solar parallax, and the contribution of Padova Observatory

In 1898 a new asteroid, 433 Eros, was discovered. As the opposition of 1900 October 30, would bring this asteroid very close to Earth, the <italic>Comité International Permanent pour l'Exécution Photographique de La Carte du Ciel</italic> instituted a special temporary Commission with the task of co-ordinating micrometric, heliometric, and photographic observations from different places on Earth, in order to determine the solar parallax. Fifty-one astronomical observatories, including the Italian Observatories of Arcetri, Padova, and Teramo, took part in this project with visual and photographic observations. Antonio Maria Antoniazzi, astronomer at the Padova Observatory, observed the new asteroid from 1900 October to 1901 February. The 122 observations made in Padova from October to December, formed part of the data set used by Arthur Hinks of the Cambridge Observatory, who had the task of reducing all of the observations. In addition to discussing the final outcome of the 1900-1 programme, this paper briefly examines the solar parallax investigations associated with the Eros opposition of 1930-1.

Photogenic Venus

During the late nineteenth century, scientists around the world disagreed as to the types of instruments and methods that should be used for determining the most important constant of celestial mechanics: the solar parallax. Venus's 1874 transit across the sun was seen as the best opportunity for ending decades of debate. However, a mysterious black drop that appeared between Venus and the sun and individual differences in observations of the phenomenon brought traditional methods into disrepute. To combat these difficulties, the astronomer Jules Janssen devised a controversial new instrument, the photographic revolver, that photographed Venus at regular intervals. Another solution came from physicists, who rivaled the astronomers' dominance in precision measurements by deducing the solar parallax from physical measurements of the speed of light. Yet other astronomers relied on drawings and well-trained observers. The new space emerging from this debate was characterized by a decline in faith in (nonstandardized, nonreproducible) photography and in (pure) geometry and by the growing realization of the importance of alternative elements needed for establishing scientific truths: power and authority, skill and discipline, standardization, mechanical reproducibility, and theatricality. By examining the cinematographic turn in science and its alternatives, this essay brings to light unexplored multidisciplinary connections that contribute to the histories of psychology, philosophy, physics, and film studies.

Mason &amp; Dixon &amp; the Ampersand

Research Article| September 01 2002 Mason & Dixon & the Ampersand Samuel Cohen Samuel Cohen Search for other works by this author on: This Site Google Twentieth-Century Literature (2002) 48 (3): 264–291. https://doi.org/10.1215/0041462X-2002-4004 Cite Icon Cite Share Icon Share Twitter Permissions Search Site Citation Samuel Cohen; Mason & Dixon & the Ampersand. Twentieth-Century Literature 1 September 2002; 48 (3): 264–291. doi: https://doi.org/10.1215/0041462X-2002-4004 Download citation file: Zotero Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search Books & JournalsAll JournalsTwentieth-Century Literature Search Advanced Search The text of this article is only available as a PDF. Copyright © Hofstra University2002 Article PDF first page preview Close Modal Issue Section: Articles You do not currently have access to this content.

The transits of Venus

The transits of Venus across the solar disk in 1761 and 1769 were two of the most momentous events in the history of astronomy. For, in the wake of Newton's theory of universal gravitation, the correct determination of the solar parallax (and the ensuing distance of the Sun) had become of the greatest significance in establishing the proportions of the solar system. And, following a suggestion first made by Edmond Halley in 1677, a Venus transit could provide the key to an accurate parallax value. In both 1761 and 1769, astronomers from Britain, France and many other countries sent expeditions across the world to establish the longest possible base lines. The expeditions produced a host of scientific adventures, especially as in 1761 Britain and France were at war. And it was the 1769 British expedition to Tahiti which launched the career of Captain James Cook.