A Short History of Astronomy - Arthur Berry (read along books .txt) 📗
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276. Legendre’s other contributions to science were almost entirely to branches of mathematics scarcely affecting astronomy. Gauss, on the other hand, was for nearly half a century head of the observatory of Göttingen, and though his most brilliant and important work was in pure mathematics, while he carried out some researches of first-rate importance in magnetism and other branches of physics, he also made some further contributions of importance to astronomy. These were for the most part processes of calculation of various kinds required for utilising astronomical observations, the best known being a method of calculating the orbit of a planet from three complete observations of its position, which was published in his Theoria Motus (1809). As we have seen (chapter XI., (§ 236), the complete determination of a planet’s orbit depends on six independent elements: any complete observation of the planet’s position in the sky, at any time, gives two quantities, e.g. the right ascension and declination (chapter II., § 33); hence three complete observations give six equations and are theoretically adequate to determine the elements of the orbit; but it had not hitherto been found necessary to deal with the problem in this form. The orbits of all the planets but Uranus had been worked out gradually by the use of a series of observations extending over centuries; and it was feasible to use observations taken at particular times so chosen that certain elements could be determined without any accurate knowledge of the others; even Uranus had been under observation for a considerable time before its path was determined with anything like accuracy; and in the case of comets not only was a considerable series of observations generally available, but the problem was simplified by the fact that the orbit could be taken to be nearly or quite a parabola instead of an ellipse (chapter IX., § 190). The discovery of the new planet Ceres on January 1st, 1801 (§ 294), and its loss when it had only been observed for a few weeks, presented virtually a new problem in the calculation of an orbit. Gauss applied his new methods—including that of least squares—to the observations available, and with complete success, the planet being rediscovered at the end of the year nearly in the position indicated by his calculations.
277. The theory of the “reduction” of observations (chapter X., § 218) was first systematised and very much improved by Friedrich Wilhelm Bessel (1784-1846), who was for more than thirty years the director of the new Prussian observatory at Königsberg. His first great work was the reduction and publication of Bradley’s Greenwich observations (chapter X., § 218). This undertaking involved an elaborate study of such disturbing causes as precession, aberration, and refraction, as well as of the errors of Bradley’s instruments. Allowance was made for these on a uniform and systematic plan, and the result was the publication in 1818, under the title Fundamenta Astronomiae, of a catalogue of the places of 3,222 stars as they were in 1755. A special problem dealt with in the course of the work was that of refraction. Although the complete theoretical solution was then as now unattainable, Bessel succeeded in constructing a table of refractions which agreed very closely with observation and was presented in such a form that the necessary correction for a star in almost any position could be obtained with very little trouble. His general methods of reduction—published finally in his Tabulae Regiomontanae (1830)—also had the great advantage of arranging the necessary calculations in such a way that they could be performed with very little labour and by an almost mechanical process, such as could easily be carried out by a moderately skilled assistant. In addition to editing Bradley’s observations, Bessel undertook a fresh series of observations of his own, executed between the years 1821 and 1833, upon which were based two new catalogues, containing about 62,000 stars, which appeared after his death.
278. The most memorable of Bessel’s special pieces of work was the first definite detection of the parallax of a fixed star. He abandoned the test of brightness as an indication of nearness, and selected a star (61 Cygni) which was barely visible to the naked eye but was remarkable for its large proper motion (about 5″ per annum); evidently if a star is moving at an assigned rate (in miles per hour) through space, the nearer to the observer it is the more rapid does its motion appear to be, so that apparent rapidity of motion, like brightness, is a probable but by no means infallible indication of nearness. A modification of Galilei’s differential method (chapter VI., § 129, and chapter XII., § 263) being adopted, the angular distance of 61 Cygni from two neighbouring stars, the faintness and immovability of which suggested their great distance in space, was measured at frequent intervals during a year. From the changes in these distances σ a, σ b (in fig. 85), the size of the small ellipse described by σ could be calculated. The result, announced at the end of 1838, was that the star had an annual parallax of about 1∕3″ (chapter VIII., § 161), i.e. that the star was at such distance that the greatest angular distance of the earth from the sun viewed from the star (the angle S σ E in fig. 86, where S is the sun and E the earth) was this insignificant angle.160 The result was confirmed, with slight alterations, by a fresh investigation of Bessel’s in 1839-40, but later work seems to shew that the parallax is a little less than 1∕2″.161 With this latter estimate, the apparent size of the earth’s path round the sun as seen from the star is the same as that of a halfpenny at a distance of rather more than three miles. In other words, the distance of the star is about 400,000 times the distance of the sun, which is itself about 93,000,000 miles. A mile is evidently a very small unit by which to measure such a vast distance; and the practice of expressing such distances by means of the time required by light to perform the journey is often convenient. Travelling at the rate of 186,000 miles per second (§ 283), light takes rather more than six years to reach us from 61 Cygni.
279. Bessel’s solution of the great problem which had baffled astronomers ever since the time of Coppernicus was immediately followed by two others. Early in 1839 Thomas Henderson (1798-1844) announced a parallax of nearly 1″ for the bright star α Centauri which he had observed at the Cape, and in the following year Friedrich Georg Wilhelm Struve (1793-1864) obtained from observations made at Pulkowa a parallax of 1∕4″ for Vega; later work has reduced these numbers to 3∕4″ and 1∕10″ respectively.
A number of other parallax determinations have subsequently been made. An interesting variation in method was made by the late Professor Charles Pritchard (1808-1893) of Oxford by photographing the star to be examined and its companions, and subsequently measuring the distances on the photograph, instead of measuring the angular distances directly with a micrometer.
At the present time some 50 stars have been ascertained with some reasonable degree of probability to have measurable, if rather uncertain, parallaxes; α Centauri still holds its own as the nearest star, the light-journey from it being about four years. A considerable number of other stars have been examined with negative or highly uncertain results, indicating that their parallaxes are too small to be measured with our present means, and that their distances are correspondingly great.
280. A number of star catalogues and star maps—too numerous to mention separately—have been constructed during this century, marking steady progress in our knowledge of the position of the stars, and providing fresh materials for ascertaining, by comparison of the state of the sky at different epochs, such quantities as the proper motions of the stars and the amount of precession. Among the most important is the great catalogue of 324,198 stars in the northern hemisphere known as the Bonn Durchmusterung, published in 1859-62 by Bessel’s pupil Friedrich Wilhelm August Argelander (1799-1875); this was extended (1875-85) so as to include 133,659 stars in a portion of the southern hemisphere by Eduard Schönfeld (1828-1891); and more recently Dr. Gill has executed at the Cape photographic observations of the remainder of the southern hemisphere, the reduction to the form of a catalogue (the first instalment of which was published in 1896) having been performed by Professor Kapteyn of Groningen. The star places determined in these catalogues do not profess to be the most accurate attainable, and for many purposes it is important to know with the utmost accuracy the positions of a smaller number of stars. The greatest undertaking
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