galileo, kepler, and brahe -- 1/26/22
Today's selection -- from Great Astronomers: Johannes Kepler by Robert Stawell Ball. The breakthrough theories of Copernicus and Galileo were followed by the breakthrough laws of planetary motion put forward by Johannes Kepler. But Kepler’s work was predicated on the careful--and revolutionary--data collection of the Dane Tycho Brahe. For years, Brahe used precise instruments to painstakingly record the location and movement of the planets, though he did not ever fully grasp the implications of his data. It was Kepler who used this data to not only confirm that the planets orbited the sun, but to reach the stunning conclusion that they travelled in ellipses instead of circles. Without Brahe’s meticulous data collection, Kepler could not have reached any conclusions, much less the powerful laws he articulated in his books Astronomia nova, Harmonice Mundi, and Epitome Astronomiae Copernicanae:
"[Johannes] Kepler must also be remembered as one of the first great astronomers who ever had the privilege of viewing celestial bodies through a telescope. It was in 1610 that he first held in his hands one of those little instruments which had been so recently applied to the heavens by Galileo. It should, however, be borne in mind that the epoch-making achievements of Kepler did not arise from any telescopic observations that he made, or, indeed, that any one else made. They were all elaborately deduced from Tycho [Brahe]’s measurements of the positions of the planets, obtained with his great instruments, which were unprovided with telescopic assistance.
|Kepler's Platonic solid model of the Solar System, from Mysterium Cosmographicum (1596)|
"To realise the tremendous advance which science received from Kepler's great work, it is to be understood that all the astronomers who laboured before him at the difficult subject of the celestial motions, took it for granted that the planets must revolve in circles. If it did not appear that a planet moved in a fixed circle, then the ready answer was provided by Ptolemy's theory that the circle in which the planet did move was itself in motion, so that its centre described another circle.
"When Kepler had before him that wonderful series of observations of the planet Mars, which had been accumulated by the extraordinary skill of Tycho, he proved, after much labour, that the movements of the planet refused to be represented in a circular form. Nor would it do to suppose that Mars revolved in one circle, the centre of which revolved in another circle. On no such supposition could the movements of the planets be made to tally with those which Tycho had actually observed. This led to the astonishing discovery of the true form of a planet’s orbit. For the first time in the history of astronomy the principle was laid down that the movement of a planet could not be represented by a circle, nor even by combinations of circles, but that it could be represented by an elliptic path. In this path the sun is situated at one of those two points in the ellipse which are known as its foci of the curve. If the length of the loop of string is unchanged then the nearer the pins are together, the greater will be the resemblance between the ellipse and the circle, whereas the more the pins are separated the more elongated does the ellipse become. The orbit of a great planet is, in general, one of those ellipses which approaches a nearly circular form. It fortunately happens, however, that the orbit of Mars makes a wider departure from the circular form than any of the other important planets. It is, doubtless, to this circumstance that we must attribute the astonishing success of Kepler in detecting the true shape of a planetary orbit. Tycho's observations would not have been sufficiently accurate to have exhibited the elliptic nature of a planetary orbit which, like that of Venus, differed very little from a circle.
"The more we ponder on this memorable achievement the more striking will it appear. It must be remembered that in these days we know of the physical necessity which requires that a planet shall revolve in an ellipse and not in any other curve. But Kepler had no such knowledge. Even to the last hour of his life he remained in ignorance of the existence of any natural cause which ordained that planets should follow those particular curves which geometers know so well. Kepler’s assignment of the ellipse as the true form of the planetary orbit is to be regarded as a brilliant guess, the truth of which Tycho’s observations enabled him to verify. Kepler also succeeded in pointing out the law according to which the velocity of a planet at different points of its path could be accurately specified. Here, again, we have to admire the sagacity with which this marvelously acute astronomer guessed the deep truth of nature. In this case also he was quite unprovided with any reason for expecting from physical principles that such a law as he discovered must be obeyed. It is quite true that Kepler had some slight knowledge of the existence of what we now know as gravitation. He had even enunciated the remarkable doctrine that the ebb and flow of the tide must be attributed to the attraction of the moon on the waters of the earth. He does not, however, appear to have had any anticipation of those wonderful discoveries which Newton was destined to make a little later, in which he demonstrated that the laws detected by Kepler's marvelous acumen were necessary consequences of the principle of universal gravitation."