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 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 marvellous acumen were necessary consequences of the principle of universal gravitation.

[Plate:  Symbolical representation of the planetary system.]

To appreciate the relations of Kepler and Tycho it is necessary to note the very different way in which these illustrious astronomers viewed the system of the heavens.  It should be observed that Copernicus had already expounded the true system, which located the sun at the centre of the planetary system.  But in the days of Tycho Brahe this doctrine had not as yet commanded universal assent.  In fact, the great observer himself did not accept the new views of Copernicus.  It appeared to Tycho that the earth not only appeared to be the centre of things celestial, but that it actually was the centre.  It is, indeed, not a little remarkable that a student of the heavens so accurate as Tycho should have deliberately rejected the Copernican doctrine in favour of the system which now seems so preposterous.  Throughout his great career, Tycho steadily observed the places of the sun, the moon, and the planets, and as steadily maintained that all those bodies revolved around the earth fixed in the centre.  Kepler, however, had the advantage of belonging to the new school.  He utilised the observations of Tycho in developing the great Copernican theory whose teaching Tycho stoutly resisted.