 Chapter 15 of History of Astronomy This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org. Recording by Justin Ordway. History of Astronomy by George Forbes. Chapter 15 The Fixed Stars and Nebulae Passing now from our solar system, which appears to be subject to the actions of the same forces as those we experience on our globe, there remains an innumerable host of fixed stars, nebulas, and nebulas clusters of stars. To these, the attention of astronomers has been more earnestly directed since telescopes have been so much enlarged. Photography also has enabled a vast amount of work to be covered in a comparatively short period, and the spectroscope has given them the means, not only of studying the chemistry of the heavens, but also of detecting any motion in the line of sight from less than a mile a second and upwards in any star, however distant, provided it be bright enough. In the field of telescopic discovery beyond our solar system, there is no one who has enlarged our knowledge so much as Sir William Herschel, to whom we owe the greatest discovery in dynamical astronomy among the stars. That is, that the law of gravitation extends to the most distant stars and that many of them describe elliptic orbits about each other. W. Herschel was born at Hanover in 1738, came to England in 1758 as a trained musician, and died in 1822. He studied science when he could, and hired a telescope, until he learnt to make his own specula and telescopes. He made 430 parabolic specula in 21 years. He discovered 2,500 nebulae and 806 double stars, counted the stars in 3,400 gauge fields, and compared the principal stars photometrically. Some of the things for which he is best known were results of those accidents that happen only to the indivisible enthusiast. Such was the discovery of Uranus, which led to funds being provided for constructing his 40 feet telescope, after which, in 1786, he settled at Slough. In the same way, while trying to detect the annual parallax of the stars, he failed in that quest, but discovered binary systems of stars revolving in ellipses around each other. Just as Bradley's attack on stellar parallax failed, but led to the discovery of aberration, nutation, and the true velocity of light. Parallax. The absence of stellar parallax was the great objection to any theory of the Earth's motion prior to Kepler's time. It is true that Kepler's theory itself could have been geometrically expressed equally well with the Earth or any other point fixed, but in Kepler's case, the obviously implied physical theory of the planetary motions, even before Newton explained the simplicity of conception involved, made astronomers quite ready to waive the claim for a rigid proof of the Earth's motion by measurement of an annual parallax of stars, which they had insisted on in respect of Copernicus's revival of the idea of the Earth's orbital motion. Still, the desire to measure this parallax was only intensified by the practical certainty of its existence and by repeated failures. The attempts of Bradley failed. The attempts of Piazzi and Brinkley, early in the 19th century, also failed. The first successes afterwards confirmed were by Bessel and Henderson. Both used stars whose proper motion had been found to be large as this argued proximity. Henderson, at the Cape of Good Hope, observed a centauri whose annual proper motion he found to amount to 3 inches, 0.6, in 1832 to 1833, and a few years later, deduced its parallax 1 inch, 0.16. His successor at the Cape, Maclear, reduced this to 0 inches, 0.92. In 1835, Struve assigned a doubtful parallax of 0 inches, 0.261 to Vega, Alire, but Bessel's observations between 1837 and 1840 of 61 Cygni, a star with the large proper motion of over 5 inches, established its annual parallax to be 0 inches, 0.3483. And this was confirmed by Peters, who found the value 0 inches, 0.349. Later determinations for a centauri, by Gill, make its parallax 0 inches, 0.75. This is the nearest known fixed star, and its light takes four and one-third years to reach us. The light year is taken as the unit of measurement in the starry heavens, as the Earth's mean distance is the astronomical unit for the solar system. The proper motions and parallaxes combined tell us the velocity of the motion of these stars across the line of sight. A centauri, 14.4 miles a second, equals 4.2 astronomical units a year. 61 Cygni, 37.9 miles a second, equals 11.2 astronomical units a year. These successes led to renewed zow, and now the distances of many stars are known more or less accurately. Several of the brightest stars, which might be expected to be the nearest, have not shown a parallax amounting to a twentieth of a second of arc. Among these are Canopus, Orionis, Cygni, Centauri, and Cassiopeia. Udman's has published a list of parallaxes observed. Proper Motion In 1718, Halley detected the proper motions of Arcturus and Sirius. In 1738, J. Cassinus showed that the former had moved five minutes of arc since Tycho Bray fixed its position. In 1792, Piazzi noted the motion of 61 Cygni as given above. For a long time, the greatest observed proper motion was that of a small star, 1830 Groombridge, nearly 7 inches a year, but others have since been found reaching as much as 10 inches. Now the spectroscope enables the motion of stars to be detected at a single observation, but only that part of the motion that is in the line of sight. For a complete knowledge of a star's motion, the proper motion and parallax must also be known. When Huggins first applied the Doppler principle to measure velocities in the line of sight, the faintness of star spectra diminished the accuracy, but Vogel in 1888 overcame this to a great extent by long exposures of photographic plates. It has often been noticed that stars would seem to belong to a group of nearly uniform magnitude have the same proper motion. The spectroscope has shown that these have also often the same velocity in the line of sight. Thus in the Great Bear, B, Y, 8, E, L all agree as to angular proper motion. 8 was too faint for a spectroscopic measurement, but all the others have been shown to be approaching us at a rate of 12 to 20 miles a second. The same has been proved for proper motion and line of sight motion, but in the case of plates and other groups. Masculine measured many proper motions of stars from which W. Herschel came to the conclusion that these apparent motions are for the most part due to a motion of the solar system in space toward a point in the constellation Hercules, This grand discovery has been amply confirmed, and though opinions differ as to the exact direction, it happens that the point first indicated by Herschel from totally insufficient data agrees well with modern estimates. Comparing the proper motions and parallaxes to get the actual velocity of each star relative to our system, C. L. Strouve found the probable velocity of the solar system in space to be 15 miles a second, or 5 astronomical units a year. The work of Herschel in this matter has been checked by comparing spectroscopic velocities in the line of sight, which, so far as the Sun's motion is concerned, would give a maximum rate of approach for stars near Hercules, a maximum rate of recession for stars in the opposite part of the heavens, and no effect for stars halfway between. In this way, the spectroscope has confirmed generally Herschel's view of the direction and makes the velocity 11 miles a second, or nearly 4 astronomical units a year. The average proper motion of a first magnitude star has been found to be 0.25 inches annually, and of a sixth magnitude star, 0.04 inches. But that all bright stars are nearer than all small stars, or that they show greater proper motion for that reason is found to be far from the truth. Many statistical studies have been made in this connection, and interesting results may be expected from this treatment in the hands of Captain of Groningen and others. On analysis of the directions of proper motions of stars in all parts of the heavens, Captain has shown that these indicate, besides the solar motion toward Hercules, two general drifts of stars in nearly opposite directions, which can be detected in any part of the heavens. This result has been confirmed from independent data by Eddington and Dyson. Photography promises to assist in the measurement of parallax and proper motions. Herp Ulfric, of the firm of Carl Zeig, has vastly extended the applications of stereoscopic vision to astronomy. A subject which De La Rue took up in the early days of photography, he has made a stereo comparator of great beauty and convenience for comparing stereoscopically two star photographs taken at different dates. Wolf of Eidelberg has used this for many purposes. His investigations, depending on the solar motion and space, are remarkable. He photographed stars in a direction at right angles to the line of the sun's motion. He has taken photographs of the same region 14 years apart, the two positions of his camera being at the two ends of a baseline over 5 billion miles apart, or 56 astronomical units. On examining these stereoscopically, some of the stars rise out of the general plane of the stars and seem to be much nearer. Many of the stars are thus seen to be suspended in space at different distances corresponding exactly to their real distances from our solar system, except when their proper motion interferes. The effect is most striking. The accuracy of measurement exceeds that of any other method of measuring such displacements, and it seems that with a long interval of time, the advantage of the method increases. The large class of double stars has always been much studied by amateurs, partly for their beauty and color, and partly as a test for telescopic definition. Among the many unexplained stellar problems, there is one noticed in double stars that is thought by some to be likely to throw light on stellar evolution. It is this. There are many instances where one star of the pair is comparatively faint, and the two stars are contrasted in color. In every single case, the general color of the faint companion is invariably to be classed with colors more near to the blue end of the spectrum than that of the principal star. Binary Stars Sir William Herschel began his observations of double stars in the hope of discovering an annual parallax of the stars. In this, he was following a suggestion of Galileo's. The presumption is that, if there be no physical connection between the stars of a pair, the largest is the nearest, and has the greatest parallax. So, by noting the distance between the pair at different times of the year, a delicate test of parallax is provided, unaffected by major instrumental errors. Herschel did indeed discover changes of distance, but not of the character to indicate parallax. Following this by further observation, he found that the motions were not uniform nor rectilinear. And by a clear analysis of the movements, he established the remarkable and wholly unexpected fact that, in all these cases, the motion is due to a revolution about their common center of gravity. He gave the approximate period of revolution of some of these. Castor 342 years Serpentis 375 years Leonis 1200 years Boutis 1681 years Twenty years later, Sir John Herschel and Sir James South, after re-examination of these stars, confirmed and extended the results. One pair of coronet, having, in the interval, completed more than a whole revolution. It is, then, to Sir William Herschel, that we owe the extension of the law of gravitation, beyond the limits of the solar system, to the whole universe. His observations were confirmed by FGW Shroove, born 1793, died 1864, who carried on the work at Dorpat. But it was first to savoury, and later to Anke and Sir John Herschel, that we owe the computation of the elliptic elements of these stars, also the resulting identification of their law of force with Newton's force of gravitation applied to the solar system, and the force that makes an apple fall to the ground. As Grant Well says in his history, This may be justly asserted to be one of the most sublime truths which astronomical science has hitherto disclosed to the researches of the human mind. Laterally, the best work on double stars has been done by SW Burnham, at the Lick Observatory. The shortest period he found was eleven years, Pegasi. In the case of some of these binaries, the parallax has been measured, from which it appears that in four of the surest cases, the orbits are about the size of the orbit of Uranus, these being probably among the smallest stellar orbits. The law of gravitation, having been proved to extend to the stars a discovery like that of Neptune in its origin, though unlike it in the labour and originality involved in the calculation, that entrances the imagination became possible, and was realised by Bessel, the discovery of an unknown body by its gravitational disturbance on one that was visible. In 1834 and 1840, he began to suspect a want of uniformity in the proper motion of Sirius and Procyon, respectively. In 1844, in a letter to Sir John Herschel, he attributed these irregularities in each case to the attraction of an invisible companion, the period of revolution of Sirius being about half a century. Later, he said, I adhere to the conviction that Procyon and Sirius form real binary systems, consisting of a visible and an invisible star. There is no reason to suppose luminosity in essential quality of cosmic bodies. The visibility of countless stars is no argument against the invisibility of countless others. This grand conception led Peters to compute more accurately the orbit and to assign the place of the invisible companion of Sirius. In 1862, Alvin G. Clarke was testing a new 18 inch object glass, now at Chicago. Upon Sirius, and knowing nothing of these predictions, actually found the companion in the very place assigned to it. In 1896, the companion of Procyon was discovered by Professor Shabrily at the Lick Observatory. Now, by the refined parallax determinations of Gil at the Cape, we know that of Sirius to be 0.38 inches. From this, it has been calculated that the mass of Sirius equals two of our suns, and its intrinsic brightness equals 20 suns. But the companion, having a mass equal to our sun, has only a 500th part of the sun's brightness. On measuring the velocity of a star in the line of sight at frequent intervals, periodic variations have been found leading to a belief in motion round an invisible companion. Vogel, in 1889, discovered this in the case of Spica, virginus, whose period is 4 days, 0 hours, 19 minutes, and the diameter of whose orbit is 6 million miles. Great numbers of binaries of this type have since then been discovered, all of short period. Also, in 1889, Pickering found that at regular intervals of 52 days, the lines in the spectrum of the Great Bear are duplicated, indicating a relative velocity equal to 100 miles a second of two components revolving round each other, of which that apparently single star must be composed. It would be interesting, no doubt, to follow and detail the accumulating knowledge about the distances, proper motions, and orbits of the stars, but this must be done elsewhere. Enough has been said to show how results are accumulating, which must in time unfold to us the various stellar systems in their mutual relationships. Variable Stars It has often happened in the history of different branches of physical science that observation and experiment were so far ahead of theory that hopeless confusion appeared to reign, and then one chance result has given a clue, and from that time all differences and difficulties in the previous researches have stood forth as natural consequences, explaining one another in a rational sequence. So we find parallax, proper motion, double stars, binary systems, variable stars, and new stars all bound together. The logical and necessary explanation given of the cause of ordinary spectroscopic binaries, and of irregular proper motions of Sirius and Procyon, leads to the interference that if ever the plane of such a binary orbit were edge on to us, there ought to be an eclipse of the luminous partner whenever the non-luminous one is interposed between us. This should give rise either to intermittence in the star's light, or else to variability. It was by supposing the existence of a dark companion to Algol that its discoverer, Goodrich of York, in 1783, explained variable stars of this type. Algol, per sigh, completes the period of variable brightness in 68.8 hours. It loses three-fifths of its light and regains it in twelve hours. In 1889, Vogel, with the Potsdam Spectrograph, actually found that the luminous star is receding before each eclipse and approaching us after each eclipse, thus entirely supporting Goodrich's opinion. There are many variables of the Algol type, and information is steadily accumulating. But all variable stars do not suffer the sudden variations of Algol. There are many types, and the explanations of others have not proved so easy. The Harvard College photographs have disclosed the very great prevalence of variability, and this is certainly one of the lines in which modern discovery must progress. Roberts, in South Africa, has done splendid work on the periods of variables of the Algol type. New Stars Extreme instances of variable stars are the new stars such as those detected by Hipparchus, Tycho Bray, and Kepler, of which many have been found in the last half-century. One of the latest great nove, was discovered in Aurega, by a Scotsman, Dr. Anderson, on February 1st, 1892, and, with the modesty of his race, he communicated the fact to his Majesty's astronomer for Scotland on an unsigned postcard. Its spectrum was observed and photographed by Huggins and many others. It was full of bright lines of hydrogen, calcium, helium, and others not identified. The astounding fact was that lines were shown in pairs, bright and dark, on a faint continuous spectrum, indicating apparently that a dark body approaching us at the rate of 550 miles a second was traversing a cold nebulous atmosphere, and was heated to incandescence by friction, like a meteor in our atmosphere, leaving a luminous train behind it. It almost disappeared, and on April 26th it was of the 16th magnitude. But on August 17th it brightened to the 10th, showing the principal nebular band in its spectrum, and no sign of approach or recession. It was as if it emerged from one part of the nebula, cooled down, and rushed through another part of the nebula, rendering the nebular gas more luminous than itself. Since 1892, one nova after another has shown a spectrum as described above, like a meteor rushing toward us and leaving a train behind, for this seems to be the obvious meaning of the spectra. The same may be said of the brilliant nova parsae, brighter at its best than Capella, and discovered also by Dr. Anderson on February 22, 1901. It increased in brightness as it reached the densest part of the nebula, then it varied for some weeks by a couple of magnitudes, up and down, as if passing through separate nebular condensations. In February 1902 it could still be seen with an opera glass. As with other novae, when it first dashed into the nebula, it was vaporized and gave a continuous spectrum with dark lines of hydrogen and helium. It showed no bright lines paired with dark ones to indicate a train left behind, but in the end its own luminosity died out and the nebular spectrum predominated. The nebular illumination, as seen in photographs taken from August to November, seemed to spread out slowly in a gradually increasing circle at the rate of 90 inches in 48 days. Captain, put this down to the velocity of light, the original opera sending its illumination to the nebulous gas and illuminating a spherical shell whose radius increased at the velocity of light. This supposition seems correct, in which case it can easily be shown from the above figures that the distance of this nova was 300 light years. Star Catalogs Since the days of very accurate observations, numerous star catalogs have been produced by individuals or by observatories. Bradley's monumental work may be said to head the list. Wakai's in the Southern Hemisphere was complimentary. Then Piazzi, Laland, Groombridge, and Bessel were followed by AgriLander with his 324,000 stars, Rumker's Paramata Catalog of the Southern Hemisphere, and the frequent catalogs of national observatories. Later, the Astronomish, Gellishaft, started their great catalog, the combined work of many observatories. Other Southern ones were golds at Cordova and stones at the Cape. After this we have a new departure. Gil at the Cape, having the comet in 1882, all to himself in those latitudes, wished his friends in Europe to see it and employed a local photographer to strap his camera to the observatory equatorial driven by clockwork and adjusted on the comet by the eye. The result with half an hour's exposure was good, so he tried 3 hours. The result was such a display of sharp star images that he resolved on the Cape photographic Dermastrum, which after 14 years, with captain's aid and reducing, was completed. Meanwhile, the brothers Henry of Paris were engaged in going over cacornax, zodiacal stars, were about to catalog the Milky Way portion, a serious labor. When they saw Gil's comet photograph and conceived the idea of doing the rest of their work by photography, Gil had previously written to Admiral Mouchet of the Paris Observatory and explained to him his project for charting the heavens photographically by combining the work of many observatories. This led Admiral Mouchet to support the brothers Henry in their scheme. Gil, having got his own photographic work underway, suggested an international astrographic chart, the materials for different zones to be supplied by observatories of all nations, each equipped with similar photographic telescopes at a conference in Paris, 1887. This was decided on. The stars in the charts going down to the 14th magnitude and the catalogs to the 11th. This monumental work is near in completion. The labor involved was immense and the highest skill was required for devising instruments and methods to read off the star positions from the plates. Then we have the Harvard College collection of photographic plates always being automatically added to and their annex at the Arequipa in Peru. Such catalogs vary in their degree of accuracy and fundamental catalogs of standard stars have been compiled. These require extension because the differential methods of the heliometer and the camera cannot otherwise be made absolute. The number of stars down to the 14th magnitude may be taken at about 30 million and that of all the stars visible in the greatest modern telescopes is probably about 100 million. Nebulae and star clusters. Our knowledge of Nebulae really dates from the time of W. Herschel. In his great sweeps of the heavens with his giant telescopes he opened in this direction a new branch of astronomy. At one time he held that all Nebulae might be clusters of innumerable minute stars at a great distance. Then he recognized the different classes of Nebulae and became convinced that there is a widely diffused shining fluid in space though many so-called Nebulae could be resolved by large telescopes into stars. He considered that the Milky Way is a great star cluster whose form may be conjectured from numerous stargazings. He supposed that the compact planetary Nebulae might show a stage of evolution from the diffused Nebulae and that his classifications actually indicate various stages of development. Such speculations like those of the ancients about the solar system are apt to be harmful to true progress of knowledge unless in the hands of the ableist mathematical physicists. And Herschel violated their principles in other directions. But here his speculations have attracted a great deal of attention and with modifications are accepted at least as a working hypothesis by a fair number of people. When Sir John Herschel had extended his father's researches into the southern hemisphere he was also led to the belief that some Nebulae were a phosphorescent material spread through space like fog or mist. Then his views were changed by the revelations due to the great discoveries of Lord Ross with his gigantic refractor when one Nebula after another was resolved into a cluster of minute stars. At that time the opinion gained ground that with increase of telescopic power this would prove to be the case with all Nebulae. In 1864 all doubt was dispelled by Huggins in his first examination of the spectrum of a Nebula and the subsequent extension of this observation to other Nebulae. Thus providing a certain test which increase in the size of the telescopes could never have given. In 1864 Huggins found that all true Nebulae give a spectrum of bright lines. Three are due to Hydrogen. Two discovered by Copeland are Helium lines. Others are unknown. Fifty-five lines have been photographed in the spectrum of the Orion Nebulae. It seems to be pretty certain that all true Nebulae are gaseous and show almost exactly the same spectrum. Other Nebulae, and especially the white ones like that in Andromeda, which have not yet been resolved into stars, show a continuous spectrum. Others are greenish and give no lines. A great deal has to be done by the chemist before the astronomer can be on sure ground in drawing conclusions from certain portions of his spectroscopic evidence. The light of the Nebulas is remarkably actinic, so the photography has a specially fine field in revealing details imperceptible in the telescope. In 1885 the Brothers Henry photographed round the star maya in the play-eds a spiral Nebula three feet long as bright on the plate as that star itself, but quite invisible in the telescope. And an exposure of four hours revealed other new Nebulae in the same district. That painstaking and most careful observer, Barnard, with ten and a quarter hours exposure extended this Nebulosity for several degrees and discovered to the north of the play-ads a huge diffused Nebulosity in a region almost destitute of stars. By establishing a ten inch instrument at an altitude of 6000 feet, Barnard has revealed the wide distribution of Nebulae matter in the constellation Scorpio over a space of four degrees or five degrees square. Barnard asserts that the Nebulae hypothesis would have been killed at its birth by a knowledge of these photographs. Later he has used still more powerful instruments and extended his discoveries. The association of stars with planetary Nebulae and the distribution of Nebulae in the heavens, especially in relation to the Milky Way, are striking facts, which will certainly bear fruit when the time arrives for discarding vague speculations and learning to read the true physical structure and history of the starry universe. Stellar Spectra When the spectroscope was first available for stellar research, the leaders in this branch of astronomy were Huggins and Father Secchi of Rome. The former began by devoting years of work principally to the most accurate study of a few stars. The latter devoted the years from 1863 to 1867 to a general survey of the whole heavens, including 4000 stars. He divided these into four principal classes, which have been of the greatest service. Half of his stars belong to the first class, including Sirius, Vega, Regulus, Altair. The characteristic feature of their spectra is the strength and breadth of the hydrogen lines in the extreme faintness of the metallic lines. This class of star is white to the eye and rich in ultraviolet light. The second class includes about three eighths of his stars, including Capella, Pollux, and Arcturus. These stars give a spectrum like that of our sun and appear yellowish to the eye. The third class includes Hercules, Orionis, Batelligio, Miraceti, and about 500 red and variable stars. The spectrum has fluted bands shaded from blue to red and sharply defined at the more refrangeable edge. The fourth class is a small one containing no stars over fifth magnitude, of which 152 Skelsruppe in Canes Venatici is a good example. This spectrum also has bands, but these are shaded on the violet side and sharp on the red side. They are due to carbon in some form. These stars are ruby red in the telescope. It would appear then that all stars are suns with continuous spectra and the classes are differentiated by the character of the absorbent vapors of their atmospheres. It is very likely that, after the chemists have taught us how to interpret all the varieties of spectrum, it will be possible to ascribe the different spectrum classes to different stages in the life history of every star. Already, there are plenty of people ready to lay down arbitrary assumptions about the lessons to be drawn from stellar spectra. Some say that they know with certainty that each star begins by being a nebula, and is condensed and heated by condensation until it begins to shine as a star. That it attains a climax of temperature, then cools down and eventually becomes extinct. They go so far as to declare that they know what class of spectrum belongs to each stage of a star's life and how to distinguish between one that is increasing and another that is decreasing in temperature. The more cautious astronomers believe that chemistry is not sufficiently advanced to justify all of these deductions. That, until chemists have settled the lately raised question of the transmutation of elements, no theory can be sure. It is also held that, until they have explained, without room for doubt, the reasons for the presence of some lines in the absence of others of any element in a stellar spectrum, why the arc spectrum of each element differs from its spark spectrum, and what are all the various changes produced in the spectrum of a gas by all possible concomitant variations of pressure and temperature. Also, the meanings of all the flutings in the spectra of metalloids and compounds, and other equally pertinent matters. Until that time arrives, the part to be played by the astronomer is one of observation. By all means, they say, make use of working hypotheses to add an interest to years of laborious research and to serve as a guide to the direction of further labors. But be sure not to fall into the error of calling any mere hypothesis a theory. Nebula Hypothesis The nebular hypothesis, which was first, as it were, tentatively put forward by Laplace in a note in his System du Monde, supposes the solar system to have been a flat, disc-shaped nebula at a high temperature in rapid rotation. In cooling, it condensed, leaving revolving rings at different distances from the center. These themselves were supposed to condense into the nucleus for a rotating planet, which might, in contracting, again throw off rings to form satellites. The speculation can be put in a really attractive form, but is in direct opposition to many of the actual facts, so long as it is not favored by those who wish to maintain the position of astronomy as the most exact of the sciences, exact in its facts, exact in its logic. This speculation must be recorded by the historian, only as he records the guesses of the ancient Greeks, as an interesting phase in the history of human thought. Other hypotheses, having the same end in view, are the meteoritic hypothesis of Locklear and the planetysmal hypothesis that has been largely developed in the United States. These can best be read in the original papers to various journals, references to which may be found in the footnotes of Miss Clerk's History of Astronomy during the 19th century. The same can be said of Bredician's hypothesis of Comet's Tales, Orenius's book on the applications of the theory of light repulsion, the speculations on radium, the origin of the sun's heat and the age of the earth, the electron hypothesis of terrestrial magnetism, and a host of similar speculations, all combining to throw an interesting light on the evolution of a modern strain of thought that seems to delight in conjecture, while rebelling against that strict mathematical logic which has crowned astronomy as the Queen of the Sciences.