Kepler

Forgive, then, please, any slights that have been offered you in ignorance by

your friend, K

Wenzel House Prague Christmastide 1606

Hans Georg Herwart von Hohenburg: at München

Salve. This will, I fear, be but the briefest of scribbles, to wish you amp; your family all happiness of the season. The court is busy with preparations for the festivities, and consequently I am forgotten for the moment, and hence am allowed a little time to pursue my private studies undisturbed. Is it not strange, how, at the most unexpected of moments, the speculative faculty, having just alighted from a long amp; wearisome flight, will suddenly take wing again immediately, and soar to even loftier heights? Having lately completed my Astronomia nova, and looking forward to a year or two of much needed rest amp; recuperation, here I am now launching out again, with renewed fervour, upon those studies of world harmony, which I interrupted seven years ago in order to clear away the little task of founding a new astronomy!

Since, as I believe, the mind from the first contains within it the basic amp; essential forms of reality, it is not surprising that, before I have any clear knowledge of what the contents will be, I have already conceived the form of my projected book. It is ever thus with me: in the begi

I have taken as my motto that phrase from Copernicus, in which he speaks of the marvellous symmetry of the world, and the harmony in the relationships of the motion amp; size of the planetary orbits. I ask, in what does this symmetry consist? How is it that man can perceive these relationships? The latter question is, I think, quickly solved-I have given the answer just a moment ago. The soul contains in its own i

These, then, are some of my present concerns. I shall have much to say of them in the future. For now, my lady wife desires that the great astronomer issue forth into the town to purchase a fat goose.

Fröhliche Weihnachten! Joha

Loretoplatz Hradcany Hill Prague Easter Day 1605

David Fabricius: in Friesland

As I have delayed long in my promise of a further letter, so it is right all the same that I should sit down now, on this festival of redemption, to tell you of my triumph. As, my dear Fabricius, what a foolish bird I had been! All along the solution to the mystery of the Mars orbit was in my hands, had I but looked at things correctly. Four long years had elapsed, from the time I acknowledged defeat because of that error of 8 minutes of arc, to my coming back on the problem again. In the meantime, to be sure, I had gained much skill in geometry, and had invented many new mathematical methods which were to prove invaluable in the renewed Martian campaign. The final assault took two, nearly three more years. Had my circumstances been better, perhaps I would have done it more quickly, but I was ill with an infection of the gall, and busy with the Nova of 1604, and the birth of a son. Still, the real cause of the delay was my own foolishness amp; shortness of sight. It pains me to admit, that even when I had solved the problem, I did not recognise the solution for what it was. Thus we do progress, my dear Doctor, blunderingly, in a dream, like wise but undeveloped children!

I began again by trying once more to attribute a circular orbit to Mars. I failed. The conclusion was, simply, that the planet's path curves inwards on both sides, and outwards again at opposite ends. This oval figure, I readily admit, terrified me. It went against that dogma of circular motion, to which astronomers have held since the first begi

After some preliminary work, I arrived at the notion that the oval was an egg shape. Certainly, this conclusion involved some geometrical sleight of hand, but I could not think of any other means of imposing an oval orbit on the planets. It all seemed to me wonderfully plausible. To find the area of this doubtful egg, I computed 180 sun-Mars distances, and added them together. This operation I repeated 40 times. And still I failed. Next, I decided that the true orbit must be somewhere between the egg shape amp; the circular, just as if it were a perfect ellipse. By this time, of course, I was growing frantic, and grasping at any straw.

And then a strange amp; wonderful thing occurred. The two sickle shapes, or moonlets, lying between the flattened sides of the oval and the ideal circular orbit, had a width at their thickest points amounting to 0.00429 of the radius of the circle. This value was oddly familiar (I ca

You think that was the end of it? There is a final act to this comedy. Having tried to construct the orbit by using the equation I had just discovered, I made an error in geometry, and failed again. In despair, I threw out the formula, in order to try a new hypothesis, namely, that the orbit might be an ellipse. When I had constructed such a figure, by means of geometry, I saw of course that the two methods produced the same result, and that my equations was, in fact, the mathematical expression of an ellipse. Imagine, Doctor, my amazement, joy amp; embarrassment. I had been staring at the solution, without recognising it! Now I was able to express the thing as a law, simple, elegant, and true: The planets move in ellipses with the sun at one focus. God is great, and I am his servant; as I am also,