His autobiography from “Mecanica”:
DE IIS QUÆ HACTENUS IN ASTRONOMICIS DEI DONO, EXANTLAVIMUS, QUEQUE POSTHAC EODEM FAVENTE, EXEQUENDA RESTANT
ON THAT WHICH WE HAVE HITHERTO ACCOMPLISHED IN ASTRONOMY WITH GOD’S HELP, AND ON THAT WHICH WITH HIS GRACIOUS AID HAS YET TO BE COMPLETED IN THE FUTURE
All this shows that I have observed the stars continuously from my sixteenth year, and that I have continued these observations for nearly 35 years, up to the present day; yet they were not all of equal accuracy and importance. For those that I made in Leipzig in my youth and up to my 21st year, I usually call childish and of doubtful value. Those that I took later until my 28th year I call juvenile and fairly serviceable. The third group however, which I made at Uraniborg during approximately the last 21 years with the greatest care and with very accurate instruments at a more mature age, until I was fifty years of age, those I call the observations of my manhood, completely valid and absolutely certain, and this is my opinion of them. It is particularly upon these observations that I build when I strive by energetic labours to lay the foundations of and develop a renewed Astronomy, although some of the observations of the previous years contribute considerably. But that which I have hitherto carried out and prepared in this field with God’s help and that which I have yet, with the help of the same gracious God, to do and bring to a conclusion during days to come, I shall now describe.
First of all we determined the course of the sun by very careful observations during several years. We not only investigated with great care its entrance into the equinoctial points, but we also considered the positions lying in between these and the solstitial points, particularly in the northern semicircle of the ecliptic since the sun there is not affected by refraction at noon. Observations were made in both cases and repeatedly confirmed, and from these I calculated mathematically both the apogee and the eccentricity corresponding to these times. With regard to the apogee as well as the eccentricity an obvious error has crept into both the Alphonsine tables and Copernicus’ work, so that the apogee of the sun is almost three degrees ahead of Copernicus’ value. The eccentricity amounts to about 2% when the radius of the eccentric orbit is put equal to 60, while the value of Copernicus is too small by almost a quarter [Copernicus’ value of the eccentricity is 0.0323, or 1.938 when the radius of the eccentric orbit is put equal to 60. The corresponding maximum inequality of the longitude is 1° 51′. Tycho Brahe’s values of these quantities are 0.0359, 2.156, and 2° 3′]. He also commits an error in the determination of the sun’s motus simplex during these years which amounts to about a quarter of a degree. From this the Alphonsine determinations may be judged comparing them with those of Copernicus. From these data I derived the rules of the sun’s uniform motion, as well as those of its prostaphaeresis [inequality] and established them by accurate values. As a consequence there can no longer be any doubt that the orbit of the sun is accurately determined and explained by suitable numbers. This work on the sun was of necessity the first thing that had to be done, since it is on the sun that the motions of the celestial bodies depend, and since it moves in the ecliptic, to which the other motions are referred. I also determined the obliquity of the ecliptic relative to the equator and found a value differing from that of Copernicus and his contemporaries, namely 23 degrees and 31½ minutes, that is 3½ minutes greater than the value they found. I took the refraction of. the sun in its winter position into account, a quantity which they had thoughtlessly overlooked. We also provided tables for the various revolutions of the sun, and we also added tables of declinations and right ascensions, based on our observations. We furthermore took its parallax and refraction into account, by means of special tables.
With regard to the moon we used no less diligence in order to explain its intricate path, which in so many ways is complicated and not so simple and easy to make out as the ancients and Copernicus thought. For it presents another inequality with regard to the longitude, which these astronomers did not notice; nor have they determined the ratios of its revolution with sufficient accuracy. Moreover the limits of its maximum latitude differ from the value determined by Ptolemy, who with regard to this point was too confidently followed by all subsequent astronomers. In fact, this inequality of the moon even varies in a non-uniform way, the deviations amounting to a third of a degree. Nor are the nodes, which are the points of intersection of its orbit and the ecliptic, moving uniformly as was previously assumed; every revolution of the moon in its orbit makes them move to and fro, and the difference is quite considerable, amounting on both sides to somewhat more than one and a half degrees. This is all apparent from our most careful observations and calculations, among which are some pertaining to 18 eclipses of the moon that were accurately observed by us. For three lunar eclipses are not sufficient for the study of the first inequality as Ptolemy, Albategnius and Copernicus thought. In addition six solar eclipses were employed, in so far as they could contribute to the purpose. Further the moon was investigated in its quadratures, and at the greatest elongation from its mean motion, near the apogee as well as near the perigee, and also at the intermediate points. This was done in many ways and very often in order that its intricate course might be properly determined, and it has caused us many years of incredible effort. Finally, however, we found methods by which it was possible to make its non-uniform and multifarious wanderings subject to rules expressed by circles and numbers. Therefore, having established a new hypothesis that was in agreement with the phenomena [i. e. the observations], we adjusted the numbers representing the uniform as well as the non-uniform motions, not only in longitude, but also in latitude, and we took account of its parallax by a method differing from that of Ptolemy and Copernicus, but which agreed with experience, and also with the hypothesis itself. We also took account of the moon’s refraction, since it is impossible without this accurately to distinguish the rest. All this and several other relations regarding the moon we put into concise tables, the purpose being the derivation, by calculation, of the motions thereby described. [An account of Tycho Brahe’s theory of the motion of the moon is given in Dreyer, Planetary Systems, p. 368]. After the orbits of both celestial bodies [the sun and the moon] have thus been determined in such a way that they agree with the celestial phenomena, it follows that it will be possible to determine with absolute correctness their eclipses, their relative positions, and their motions and places, the need for which has been long felt. What we have said so far about the course of the sun and the moon, and the question of agreement with celestial phenomena, is clearly presented together with other subjects, in the first chapter of our Astronomiae instauratae Progymnasmata [Opera Omnia II, p. 13 f.]. Anybody interested in the subject will there find what he wants. With regard to the further investigation of these celestial bodies, the only thing that is still lacking is an adjustment valid for many centuries, and a presentation in greater generality. This would not involve a very great effort, if only the observations of the ancients and of our predecessors, on which the investigation would have to be based, could be trusted. This full and comprehensive account we reserve for our work Theatrum Astronomicum. For the present anybody interested in Astronomy, will benefit by reading our exposition in the part of the Progymnasmata referred to above, and there he will find what he wants.
Further, as far as time and circumstances permitted, we very carefully determined the positions of all fixed stars visible to the naked eye, even those that are denoted as stars of the sixth magnitude, the longitude as well as the latitude. The accuracy was one minute of arc, in some cases even half a minute of arc. In this way we determined the positions of one thousand stars. The ancients were only able to count 22 more in spite of the fact that they lived at a lower geographical latitude where they ought to be able to see as many more as would correspond to the 200 stars that are always hidden from us here. Instead of these we determined a number of others which are very small, and which they did not include on this account. This immense task occupied us for almost 20 years, as we wished to investigate the whole problem carefully with different instruments. Since however the very small stars are only visible during the winter, when the nights are sufficiently dark, and even then only when the moon is not in the sky, it took many years of patient work before this task was fully completed in a satisfactory way. Add to this that at the time of the new moon, when this work is best carried out, the sky was seldom clear. The method we used for the accurate determination of the longitudes of the fixed stars from the equinoctial point is set forth sufficiently clearly in the second chapter of the Progymnasmata mentioned [Opera Omnia II, p. 159 f.]. It consists in using Venus, both as a morning star and as an evening star, as a connecting link between the sun and the fixed stars. The connection is carried out with several stars and these are all referred to the brightest star above the head of the Ram, which is denoted as the third [a Arietis]. (We preferred this star to the others, because the two preceding stars are fainter). From the exposition in the Progymnasmata it will also be clear how we determined the positions of the others relative to this star, and in particular how we used a triple procedure comprising certain selected stars located along the zodiac and the equator all around the sky, and succeeded in making the intervals accurately fill the entire circumference [cf. Opera Omnia II, p. 198 f.]. I have also noticed that the irregularity of the rate of change of their longitudes [trepidation] is not so considerable as Copernicus assumed. His erroneous ideas on this matter are a consequence of the incorrect observations of the ancients, as well as those of more recent times. Consequently the precession of the equinoctial point during these years is not so slow as he asserted. For in our times the fixed stars do not take a hundred years to move one degree, as indicated in his table, but only 71½ years. This has practically always been the case, as appears when the observations of our predecessors are carefully checked. In fact only a small irregularity appears, which is due to accidental causes. This we shall, God willing, explain in more detail in due course.
The fact that the latitudes of the fixed stars are also undergoing changes as a consequence of the change in the obliquity of the ecliptic, was first discovered by me. In the chapter mentioned above I have proved it by various examples. Thus we can maintain with ample certainty, and this is confirmed by actual experience, that the positions of the fixed stars have been determined by us with perfect and infallible accuracy. We have even determined a great many of them several times, and with different instruments, too, each leading to the same result. We have not in carrying out this work made use of mechanical devices, although the great brass globe was at our disposal, but every star has been assigned its proper position by cumbersome trigonometrical calculations. This will already be clear from what has been said towards the end of the chapter mentioned on the subject of the constellation of Cassiopeia (in which we count 26 stars, twice as many as the ancients), but for other, and yet other stars we have developed the trigonometrical measurements and calculations even further, when it appeared expedient. Had the ancients and our predecessors spent as much labour in determining the positions of the stars, their catalogue, handed down to us from the time of Hipparchus, would not have been so full of errors. In fact it is not even correct within a sixth of a degree – that being the accuracy to which the positions are given – but contains far greater errors, often quite intolerable. In order to see this clearly it suffices to consider the angular distances between the stars, which remain forever the same. For a great number of stars there is a considerable deviation from what is required by the values of the ancients. That all fixed stars always keep their relative positions is, however, made sufficiently clear by the stars which according to Hipparchus and Ptolemy are in a straight line; for this is still the case without any change. We shall in due course present a catalogue of all the stars for which we determined longitudes and latitudes with an accuracy of a minute of arc, or in certain cases, as already mentioned, of half a minute of arc.
We have not only striven to determine carefully longitudes and latitudes of the fixed stars, but for some particularly important stars, 100 altogether, we have also by trigonometrical calculation derived the right ascensions and declinations, and referred these to two secular years (namely 1600 and 1700), so that it is possible by a proportional calculation to derive values valid for epochs in between. The refraction of the stars can be taken into account with the help of a special table that has been prepared on the basis of long and multitudinous experiments. For if refraction be neglected, it is not possible to derive accurate positions of the fixed stars, particularly when they are near the horizon at an altitude of less than twenty degrees. Therefore it was always our custom to take the error of refraction into account whenever it was necessary for determining the improved position of the stars. This refraction in the case of the fixed stars differs slightly from that of the sun (let me here make this statement also). It also differs somewhat from that valid for the moon, as was disclosed and explained by us a long time ago.
The only thing which is yet wanting with regard to the stars is to indicate their general motion through all the centuries during which the world has existed. It would not be so difficult to do this carefully, had the observations of the ancients in this field not been accepted, as they actually were. Yet I am convinced that I shall, by suitable corrections, be able to satisfy astronomers in this respect also, as far as that is possible.
One might have wished that the other stars which were catalogued by the ancients, but which are invisible in our latitudes, could have been added to the first thousand that I determined. Further, there are all the others, which were invisible even to the ancients who lived in the regions of Egypt, namely those that are located around the south Pole of the sky. For from the narratives of people who have sailed across the equator we know that there, too, the most beautiful stars are shining. With regard to the first proposition, it would be necessary to go to Egypt or some other similar place in Africa, and there industriously to note all the stars visible from that part of the world. But in order to attain the second goal it would be necessary to sail to South America, or to some other country beyond the equator, whence all the stars around the southern pole are visible, and observe them from there. So, if some mighty noblemen would care to fulfil our own and others’ wishes in both these respects, they would do a very good deed that would be ever gloriously remembered. Up to now no one has even tried to do a thing like this in the right way, let alone carried it out, as far as is known. I would be willing to provide the necessary instruments and tools if somebody could organize the work and get the right people for such a deserving enterprise.
With regard finally to the investigations of the intricate course of the five other planets, and attempts at explaining them, I have done all I could. For in this whole field we have assembled, first of all, the apogees as well as the eccentricities, and further the angular motions and the ratios of their orbits and periods, so that they no longer contain all the numerous errors of previous investigations. We have shown that the very apogees of the planets are subject to yet another inequality that had not previously been noted. Further, we have made the discovery that the annual period, which Copernicus explained by a motion of the earth in a large circle, while the ancients explained it by epicycles, is subject to a variation. All this and other matters connected with it we have remedied by means of a special hypothesis [the Tychonic System] that we invented and worked out 14 years ago, basing it on the phenomena. There are certain persons, of whom I know three with distinguished names, who have not been ashamed to appropriate this hypothesis and present it as their own invention. In due course I shall, God willing, point out the occasions on which they did it, and repudiate and refute their immense impudence, and I shall demonstrate that the fact of the matter is as I say, and that so clearly that it will be impossible for impartial men to doubt or contradict me. But if they honestly admit their error, and give that back to me which is mine, then I shall bear with them, and therefore I now willingly refrain from mentioning their names. [Reymers, Liddel, and Röslin].
Nor have we left the latitudes unchanged, but revised the results given by our predecessors from Ptolemy onwards. For the five planets we carefully noted the latitudes during the whole of the revolution, and from these observations we determined revised values of the maximum latitudes and of their transits over the ecliptic, in such a way that everything was in accordance with the sky. Hereby we made the clear observation that the nodes and the maximum latitudes of the three upper planets do not depend in a regular way on the motions of their apogees, but have a special motion, at any rate if it can be assumed that the results of Ptolemy regarding this subject are correct, those which both the Alphonsine tables and Copernicus use without any correction by observations of their own. As a consequence it may happen that the planets have a southern latitude in the sky, while the tables indicate a northern latitude, or vice versa. [Cf. Opera Omnia V, p. 254 f.].
With regard to all five planets there remains only one thing to do, namely to construct new and correct tables expressing by numbers all that has been established by more than 25 years of careful celestial observations (without mentioning the observations of the previous 10 years), thereby demonstrating the inaccuracy of the usual tables. We began this work and laid its foundations. It will not be difficult to complete it with the help of a few computers, and the results will then serve as a basis for the calculation of ephemerides for the coming years, as many as desired. The same can be done for the sun and the moon, for which we already have tables. In this way it will be possible with the greatest ease to demonstrate to posterity that the course of the celestial bodies as determined by us agrees with the phenomena, and is correctly given in every respect.
Finally it would be of great importance to the perfection of Astronomy in all directions, if it were possible to determine correctly not only geographical latitudes, but also geographical longitudes of localities on the earth. We investigated this problem industriously as far as this was possible, and we are convinced that we made determinations for various places that are more nearly correct than the previous ones. However, it is impossible to attend to this problem without having recourse to observations of the times of several lunar eclipses made with equal accuracy in various widely separated localities by different observers. Therefore, as before, if kings and princes and other mighty noblemen in widely separated parts of the world would generously make suitable preparations, then they would really be doing a good deed, and ill this way Astronomy, which is in need of widely different terrestrial horizons, would develop towards greater perfection.
While we thus with untiring industry through many years observed these eternal celestial bodies which are as old as the world itself, we studied with equal care all new celestial bodies in the ethereal regions that appeared during this time, above all the new and very admirable star that was first seen towards the end of the year 1572 and stayed for 16 months before it became completely invisible. On the subject of this star we wrote a small book describing its appearance, while it was still visible, as I have already indicated. When we resumed this work a few years later, we prepared a whole volume on this same star on account of the wonderful nature of the phenomenon, and we found it suitable to incorporate it in the first volume of the Progymnasmata for certain reasons that are indicated there [Opera Omnia II, pp. 305-435 and III, pp. 1-319]. In this volume I am not content to present clearly our own observations with regard to this marvellous star, and to elucidate them geometrically, but I discuss, too, the opinions of others about the same star, in so far as it was possible for me to get them and become acquainted with them. This I do with scientific liberty, examining them and making it clear whether they were in accordance with the truth, or not.
We also prepared a special book on the immense comet that appeared live years later [Opera Omnia IV, pp. 1-378]. In this we discuss it fully, including in the discussion our own observations and determinations as well as the opinions of others. We add a few pamphlets on this same subject, which elucidate this cometary problem more fully, and it was our plan to include all this ill the first part of the second volume of the Progymnasmata. In the second part we shall, God willing, deal with the remaining six smaller comets that we observed with equal care in some of the
subsequent years. Although all this has not yet been quite completed, the more important parts, and most of the demonstration, has been prepared. For the constant stars have not left us with sufficient time to dwell too long on these fading and quickly passing celestial bodies. Yet I hope that I shall soon, with the help of the gracious God, complete the second part of the second volume also. In this volume I shall clearly demonstrate that all the comets observed by me moved in the ethereal regions of the world and never in the air below the moon as Aristotle and his followers have tried without reason to make us believe for so many centuries; and the demonstration will be clearest for some of the comets, while for others it will be according to the opportunity I had. The reason why I treat the comets in the second volume of the Progymnasmata before I set about the other five planets, which I intend to discuss in the third volume, are given in the same place in the preface [Opera Omnia IV, pp. 6-8]. But the principal reason is that the results pertaining to the comets, the true ethereal nature of which I prove conclusively, show that the entire sky is transparent and clear, and cannot contain any solid and real spheres. For the comets as a rule follow orbits of a kind that no celestial sphere whatever would permit, and consequently it is a settled thing that there is nothing unreasonable in the hypothesis invented by us [the Tychonic System], since we have found that there is no such thing as penetration of spheres and limits of distance, as the solid spheres do not really exist.
With regard to that which we have until now accomplished in Astronomy, and to that which has yet to be done, this brief account must now suffice.
In the field of Astrology, too, we carried out work that should not be looked down upon by those who study the influences of the stars. Our purpose was to rid this field of mistakes and superstition, and to obtain the best possible agreement with the experience on which it is based. For I think that it will hardly be possible to find in this field a perfectly accurate theory that can come up to mathematical and astronomical truth. Having in my youth been more interested in this foretelling part of Astronomy that deals with prophesying and builds on conjectures, I later on, feeling that the courses of the stars upon which it builds were insufficiently known, put it aside until I should have remedied this want. After I at length obtained more accurate knowledge of the orbits of the celestial bodies, I took Astrology up again from time to time, and I arrived at the conclusion that this science, although it is considered idle and meaningless not only by laymen but also by most scholars, among which are even several astronomers, is really more reliable than one would think; and this is true not only with regard to meteorological influences and predictions of the weather [natural astrology], but also concerning the predictions by nativities [judicial astrology], provided that the times are determined correctly, and that the courses of the stars and their entrances into definite sections of the sky are utilized in accordance with the actual sky, and that their directions of motion and revolutions are correctly worked tip. With regard to these two points we have developed a method, based on experience, which differs from those used up to now. But we are not inclined to communicate this kind of astrological knowledge to others, since not a little has been made out by us in this field. For it is not given to everybody to know how to use it on their own, without superstition or excessive confidence, which it is not wise to show towards created things. Therefore we shall not publish any, or at least very little, of the things that we have found out in this field. What I have now briefly and in all generality stated here about the subject in question, must therefore suffice.
I also made with much care alchemical investigations, or chemical experiments. This subject too, I shall occasionally mention here, as the substances treated are somewhat analogous to the celestial bodies and their influences, for which reason I usually call this science terrestrial Astronomy. I have been occupied by this subject as much as by the celestial studies from my 23rd year, trying to gain knowledge and to prepare it, and up to now I have with much labour and at great expense made a great many findings with regard to the metals and minerals as well as the precious stones and plants, and other similar substances. I shall be willing to discuss these questions frankly with princes and noblemen, and other distinguished and learned people, who are interested in this subject and know something about it, and I shall occasionally give them information, as long as I feel sure, of their good intentions and that they will keep it secret. For it serves no useful purpose, and is unreasonable, to make such things generally known. For although many people pretend to understand them, it is not given to everybody to treat these mysteries properly according to the demands of nature, and in an honest and beneficial way.