Tycho

One of the most famous stories in astronomy surrounds the development of the Keplerian model of the planets. Kepler’s model (the one we use today) has three laws:

  1. Planets travel in an ellipse with the sun at one focus. This is the revolutionary part, since it puts the sun at the “center” (or focus, but close enough).


  2. The area swept out by a planet (the various shaded regions) is equal for equal times. This basically means that planets travel faster as they’re nearer the sun.
  3. P^2=a^3, where P is the period of the orbit (in years) of any planet in the solar system, and a is the semi-major axis (roughly the radius) in Astronomical Units. It’s a perfect fit.

Johannes Kepler was the assistant of Tycho Brahe (or “Tycho” as he as almost always known), who died in 1601, at which point Kepler “inherited” all of Tycho’s data, and came up with his model of the solar system. That’s the short version, but the long version has some very weird twists and turns.

Tycho was the greatest observational astronomer of his day, but since his death predated the invention of the astronomical telescope by about 8 years or so, and a 16th century observatory has almost now similarity to those of more recent vintage. After all, naked eye observations are limited by the resolution of our eye (roughly an arcminute) rather than by the “seeing” of the atmosphere (about an arcsecond, 60 times finer) which limits ground-based telescopes.

How were observations made in the days before telescopes?

Well, it helped if you were as outsized and influential as Tycho was. Tycho was a Danish Nobleman, incredibly eccentric, and incredibly influential with the king (not least because his uncle had saved the king from drowning). To give you an idea of the sort astronomical badassery of the day, he lost his nose in a duel with the fancifully named nobleman Manderup Parsberg. The (almost certainly apocryphal) story was that they argued about who was better in math and decided to settle it with swords. Tycho had his nose replaced with a prosthetic made of silver and gold.

Or to give another example, Tycho managed to acquire a pet moose, apparently just to satisfy his curiosity about the animal. It met an even worse end than Kepler’s nose:

It had been transported to the castle of Landskrona, a city close to Hven, to entertain a nobleman there. But it had happened that during the dinner, the moose had ascended the castle stairs and drunk of the beer in such amounts, that it had fallen down the stairs, and broken a leg. Despite the best care, the moose had died shortly thereafter.

All of which is to say that when Tycho decided that he wanted to model the heavens, the construction of the world’s premier observatory on the private island of Hven (map at the top of the page) was apparently a simple task. His goal was to prove a sort of hybrid Ptolemaic–Copernican model wherein the sun orbits the earth, but the rest of the planets orbited the sun.

Construction on the temple of Urania (the muse of astronomy, and the ultimate origin of countless infantile jokes about the 7th planet) — the Uraniborg — began in 1576. Most of the structure was living and guest quarters, along with the library. What made this a real observatory, however, were large mounted sextants and other angular devices positioned on the roof, some of which were aligned permanently with the meridian.



In astronomy, you see, all that matters are angles on the sky. If you can record those with great accuracy, then it’s a simple matter of very complicated math to try to reconstruct what’s going on in 3-d (the task that Kepler tried his hand at a few decades later).

As it happens, placing unprotected giant metal instruments on the roof is not the best idea in the world. It became apparent almost immediately that the wind would shake them too much to be effective. As a result, construction was begun almost immediately on the Sjerneborg (the temple of the stars) right next door.

The Sjerneborg was built below ground with a retractable cover — kind of like modern telescopes, and was completed by 1581. For the next 20 years, Tycho took some of the best astronomical observations ever taken, especially of Mars. Not only were the positions of the stars and planets meticulously recorded, but the baseline of observations was so long that several orbits of many of the planets were observed.

Besides providing the basis for Kepler’s work, Brahe independently concluded that either the earth (and sun) are at the center of the universe, or the other stars are so far away that they appear perfectly stationary.

The stories of Tycho’s death were as outsized as those of his life. Most famously, he was supposed to have died when out of politeness, he refused to excuse himself from a banquet to use the facilities, and got a fatal bladder infection:

The 13th of October 1601 Tycho Brahes was invides together with a nobleman called Minckwitz to a supper at Baron von Rosenberg. Before they sat down at the table, Tycho did not let his water, as he otherwise usually did. During the dinner lots of wine was consumed, and Tycho noticed that his bladder was tense, and he realised that he soon would have to get up. Out of respect for the host, he waited however, but finally he had to get up from the table and get home.

He died 11 days later.

More recent evidence points (rather prosaically) to him dying from mercury poisoning, a rather more common cause of death at the time. Then again, it may have been murder.

After his death, Kepler decided to strike. By all accounts, Kepler went into Tycho’s service essentially just to get his hands on the data. Upon Tycho’s death in 1601, Kepler went to work. As he later described it:

I confess that when Tycho died, I quickly took advantage of the absence, or lack of circumspection, of the heirs, by taking the observations under my care, or perhaps usurping them.

Even with the data in hand, it wasn’t obvious what to do with it. Kepler didn’t immediately come up with the elliptical orbit model that we use today, and that Newton derived later in the century.

Instead, he first came up with a model of symmetry and bizarre elegance, the awesomely named Mysterium Cosmographicum, in which he proposed that the orbits of all of the planets were determined by inscribing each of the Platonic solids in one another like an astronomical turducken:

The orbits of the six known planets (everything out to Saturn) could be approximately fit by putting a cube inside of a tetrahedron inside of a dodecahedron inside of an icosahedron inside of an octahedron inside of a sphere. This is a great example of scientific inspiration coming from symmetry. It’s also an example of a symmetry that turns out to be completely irrelevant. He was lucky that the fit was even close.

In the end, the reason it took Kepler so long (8 years after stealing Tycho’s data) to come up with what is now known as the Keplerian model is that Kepler assumed that for something as simple as an ellipse, somebody surely must have come up with it already. But you know what happens when you assume, right?

-Dave

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