Great Astronomers [35]
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's measurements of the positions of the planets, obtained with his great instruments, which were unprovided with telescopic assistance.
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.
[PLATE: KEPLER.]
Very simple apparatus is needed for the drawing of one of those ellipses which Kepler has shown to possess such astonishing astronomical significance. Two pins are stuck through a sheet of paper on a board, the point of a pencil is inserted in a loop of string which passes over the pins, and as the pencil is moved round in such a way as to keep the string stretched, that beautiful curve known as the ellipse is delineated, while the positions of the pins indicate the two 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 marvellously 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
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.
[PLATE: KEPLER.]
Very simple apparatus is needed for the drawing of one of those ellipses which Kepler has shown to possess such astonishing astronomical significance. Two pins are stuck through a sheet of paper on a board, the point of a pencil is inserted in a loop of string which passes over the pins, and as the pencil is moved round in such a way as to keep the string stretched, that beautiful curve known as the ellipse is delineated, while the positions of the pins indicate the two 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 marvellously 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