Brahe and Kepler

Ok, this is the post I kind of have been putting off. This one is based on the astronomy club lecture, you can check out the topics in the web site. I just wanted to share with you the knowledge. ^_^ I actually knew most of what was in the lecture, but the lecture gave me the idea about what to write. Oh, and I want you to realize that what I am doing is an oversimplification of history. After all, I can’t go on forever. So here I go:

Once upon a time, there was a time when human knowledge made almost no progress at all. I know, it is amazing that at one point, human society actually devolved. I have always thought things kept moving forward. Instead, after the Greeks came around with the first foundations of science (a quiet primitive foundation, I should say) and math, the knowledge were lost with the Muslim, while Europe plungged into the Dark Ages. Indeed, Middle Age Europe was probably the stupidest era in European history, with religion and superstition having dominated the land, and all free inquiry having stopped. In a way, it had to do with the fact that things could only be done to prove the church’s assertion, and when Greek knowledge came their way, Aristotle’s notion of physics seemed very favorable to them. In fact, the church adopted them as their official policy. Some of Aristotle’s assertion included that things go around the Earth in perfect circle, and it had to be circle because it was the perfect shape, the five elements, some elements tending to go either up or down, with aether being the element that composes the heavenly bodies, etc. Ptolemy adepted Aristotle’s theory of geocentrism and made it work by using circles within circles to account for a planetary retrogade action in the sky, like this:

Anyways, progress was difficult because challenging the current view of the universe meant challenging the church. As the Middle Ages ended, the death plague ravaged the land, and the Renaissance rolled through, a more secular, skeptical, and anti authoritarian mode of thinking began to take place. Also, the Reformation afterwards served a great deal to weaken the church. In the wake of these events, three very important people changed the way we thought of the universe. I am talking about Tycho Brahe, Johannes Kepler, and Galileo Galilee. I will only be focusing on the first two.

Firstly, I would like to start with Brahe, and you will see why. Brahe was born a noble in Denmark. And of course, him, being stinky rich, could afford university education. During his travels abroad, he became interested in astronomy and alchemy. His interest in astronomy came from the amazing fact that astronomers were able to predict closely when a solar eclipse would appear. Oh, and get this, he got into a fight, and duelled with another guy in the middle of the night, losing his nose. Yeah, ouch! His nose got replaced with a metal alloy shaped like a nose. After his studies abroad, he returned to Denmark. In 1572, he observed a new, really star being born, which we now know was an exploding star, a supernova. He thought it could have been a comet, but after several observations, seeing that its position relative to the other stars didn’t change, he became convinced it was a star. This was against the conventional wisdom that the sky was never changing and uncorruptible, so it was quiet remarkable that a star suddenly came out of the nothing.

As he went along, he realized the importance of detailed observations in astronomy. An amazing opportunity came when King Frederick II of Denmark asked him to transfer to an island named Hven so that he could do his observations. He went there, and made the peasants in the island work for his fancy observatory:


The disadvantage being, as you can see in the map, that one had to move to the other side of the huge house to observe the other side of the sky. Yeah, I guess he didn’t think of that. Anyways, he did incredibly accurate measurements considering he didn’t have a telescope. He used gigantic instruments like huge quadratns. I will just show you:


I can’t have real pictures from that era, in case you didn’t know. ^_^ Anyways, he left Denmark after some stupid (I don’t really know whether it was stupid, but hey, it’s my bias ^_^) argument with the new king Christian about some chapel falling in disrepair because Tycho wasn’t taking care of it, he was fired (I wonder whether that is the right term) and left. He eventually settled in Prague. This sets the stage for another person to grab his data and make it out into something meaningful. His name is Johannes Kepler.

Kepler was born in Germany (by the way, Germany was a superfragmented state back then, only barely held together by the Holy Roman Empire), with a family whose situations were not really that great. Especially by the horrible fact that his father left him, and his mother was accused of witchcraft. He was interested in astronomy early in his childhood (like me! ^_^), but smallpox crippled some of his vision, so observational astronomy for him was limited. (so sad…) Anyways, he went on to obtain formal education. Under a certain professor Maestlin, he heard about the two views of the Solar System. He chose the Copernican, heliocentric one. His place would have been in theology if it weren’t for the fact that he spoke his mind against the church too much for his own good. Instead, he went on to teach math. He also built up his reputation in astrology (blegh!) after he predicted a cold winter and a Turk invasion, which coincidentally came true.

While lecturing mathematics one day, he had a “wonderful” insight. He realized that the ration between the orbit of the planets had to do with the platonic solids. His basic idea was like this:

The spheres represented the orbit. Poor guy, he really tried to make this one work. I want you to realize, though, that in that era, that was the normal mode of thinking. It had to be that way because there had to be some sort of harmony in the universe based on ancient Greek ideas of ratio, and the Christian idea that God was perfect, which is the same reason why orbits had to be perfectly circular. Anyways, Brahe invited Kepler as his assistant based on the work above. See, told you their path would intersect! At that time, Brahe worked on a Solar System model that said that the planets circled the sun which circled the Earth! The crazy looked like this:

During Kepler’s assistance to Brahe, he tried to get his data, but Brahe, being suspicious of Kepler’s motive, didn’t give it to him. In fact, Kepler didn’t get it until Brahe’s death. Supposedly, he died of a burst bladder after he held his bladder for so long after a party, since it was etiquette. A recent new studies says mercury poisoning. I don’t know which one, and I won’t even try to choose.

Once Kepler got hold of them, he spent years working them out. He made a really accurate table of stars for Holy Roman Emperor Rudolf II, which was extremely tedious to do it, so he kind of procrasinated, and finished it after around 20 years. He also made works on optics, and corresponded with Galileo. Apparently, Kepler was one of the few who believed him, but Galileo, who had a large ego above all, did not respond to a single letter by Kepler after the first one. It is quiet sad. If both of them would have worked together, a complete law of inertia (Newton’s 1st law), and they could have made some sense on gravity. Instead, Galileo thought that the pull of a planet causing tides was silly, and each one had different ideas of motion. that if united, could have completed the laws of motion. Galileo didn’t even bother to send him a telescope after a few requests. Or maybe they just would have quarreled ’til the world’s end. It is also interesting to note Kepler wrote the first sci-fi, which was about a bunch of explorers who went to the moon. In it, he imagined that the moon had seas in it, and that the Earth caused tides.

His most important works, though, were in his books he published about planetary motion. Now, from what I heard, Kepler loved to write a bit too much, and useful stuffs were interspaced between useless garbage which included every detail of how he failed or succeded in getting to his theories. Now, he first discovered the 1st and 2nd law of planetary motion together, which basically says that a planet orbits the sun elliptically (if you thought it was circular, you were very wrong), with the sun at its focus, and that if a planet orbits in different parts of an orbit, and you measure how much it travels in equal time, the planet will sweep out equal area in both cases. You have to realize that this is amazing thing to be discovered considering that Kepler employed a medieval mindset. In this very theory, he discarded his precious platonic solid model and the widespread belief in circular orbit. He shattered his very own wishes of how a universe should be. Because of this, and in it, the work contained one of the very first scientific mindset. You see, when he tried to use Mars for his circular orbits, Brahe’s data just didn’t fit. Instead of ignoring the error, he tried an ellipse, and it worked! He overcame mideaval thought and instead, thought scientifically. The data didn’t fit his hypothesis, so he discarded it with a new one that worked. He let data tell the story, instead of trying to make data fit his own assumption. He was still mostly mideaval in thought, though. Now that I finished with that bit of hero worship, here is how both laws look like visually:

(1st law, star is at one focus)

They can be explained in the following ways: As the planet approaches the star, the gravity pulls on it, making it go faster, and go around it. That makes the area under it fatter, but shorter. The higher speed makes the object makes the object go slightly away from, and the pull of the star makes it slower. The slower speed makes the area under it thinner, but the distance from the star makes it longer. See? In the long run, it makes sense.

As for the third law, it is a ratio between the time a planet takes to orbit a star and its distance. Basically, it states that the squared of the time is proportional to the cubed of the distance. The table at the end of this page shows how closely they coincide, look at the final column. This is the basic equation:

 or  (k means constant, squigly thing means directly proportional)

By the way, I just want you to know that at Kepler’s time, there was no equal sign or any thing similar, and that this is the modern form. Kepler wrote it in words, and they showed it in the astronomy club, which was hard to understand, so this math thing makes things easier.

After all that, though, Kepler didn’t live a good life at the end. His grandma was accused of witchcraft, and the thirty year’s war was bringing destruction around him. In the end, he ended up without a salary or postition. Such a sad end to a somewhat productive life…

So, you see, these men were important.  Brahe kept bringing in better and more accurate instruments for better observations, while Kepler used the data to understand how the planets move, and used math to describe them.


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