Wednesday, March 26, 2014

Cosmos "When Knowledge Conquered Fear": Nitpicks, Nods, and News

A young Edmond Halley is more curious than frightened. (
Missed this episode? Check it out for free here!
This week, Cosmos took us on a journey from our childlike fear of the unknown to the edge of the Solar System, from astrology to astronomy, and from what we thought was an ad hoc chaos, to the law-abiding cosmos. The story of comets begins with our inchoate understanding of the night sky as a divine gift to aid us in knowing when to sow and when to reap. Any disturbance in such a wondrous and orderly display was certain to foretell some disturbance on Earth, just as the rising of Orion foretells the coming of winter. The Chinese had even worked out a relationship between the kind of disaster and the number of cometary tails!

Kepler's laws of planetary motion implied something simpler was going on, though. The planets didn't move in perfect circles, but rather ellipses with the Sun at one focus. What a peculiar arrangement for God, the ultimate clock-maker, to use—Every good horologist knows that circles are simpler. There had to be a reason, some force that pulls the planets towards the Sun, but no one could think of what it could depend on. After a few interesting speed bumps (like the History of Fish eating up the Royal Society's annual budget), Edmond Halley was able to convince Isaac Newton to publish his Philosophiae Naturalis Principia Mathematica, and are we ever glad he did. Not only did it propose the correct form of the gravitational force (it was considered just a force then, fellow nitpickers), but it detailed the mathematical relationship between the force and the motion of the planets, and introduced us to Newton's Laws of Motion, still the backbone of engineering mechanics over 300 years after their discovery.

The last link in the chain comes with Halley's use of the new gravitational laws to compute the period of the comet which we now call his. He predicted its return 16 years after his death, and when it was confirmed it became the first object known to orbit the Sun apart from the planets. So returning to the original model of comets as harbingers of doom, either God had something nasty in mind every 76 years, or the ancients were a tad oversure of the correlation between disasters and bad stars.

Let's take a look at some of this week's notables:


This isn't what a comet looks like up close. (
I was a bit confused at the way Cosmos decided to animate the coma (that's the fuzzy cloud around the nucleus) and tail (that's the... tail part). The picture above isn't the right shot, but it looks basically the same. The comet appears to leave behind a pretty, blue trail of smoky-looking gas in the show, immediately floating back away from the Sun within a few meters of being ejected from the surface. In reality, pictures of comets close up, specifically Halley's Comet, look completely different. Take a look at this string of images from the Giotto probe that (using the laws in Newton's Principia!) flew by Halley's Comet in 1986:

If you look to the top left, you'll see a green arrow (hiding behind the ESA logo) indicating the direction of the Sun. With the jets of gas shooting towards the Sun, it looks like the opposite of the Cosmos comet! It turns out that it takes a while for radiation pressure and the solar wind to turn the emitted gas and dust around to form the tail, and on the scale of the tiny nucleus (about 10 km), the gas just looks like it shoots straight off into space. Only on much larger scales do comets look "right", with the tail streaming away from the Sun.

How large? Some comets can form truly enormous comas and tails. The Great Comet of 1811 was really spectacular, with a coma that may have been about 1.5 times the size of the Sun. The comet's tail was observed to be 25 degrees long (as visible from Earth). That's about two and a half times the size your fist appears at arm's length. This thing was pretty noticeable, even though the nucleus was only perhaps 40 km across (by comparison, at a distance of 1 au, the nucleus would appear as a single point of light even to the Hubble Telescope).

So Cosmos was showing us more of the process of how the tail forms from gas ejected from the nucleus as opposed to the actual look of a comet, but it's hard to blame them when you consider the scales involved.


I'm always impressed with just how nutty Newton was. He was searching for coded messages in the Bible, trying to recreate ancient recipes to turn lead into gold and grant eternal life, and just generally being a woo-woo when he wasn't busy with the whole inventing-calculus, solving-the-problem-of-planetary-motion, developing-the-foundations-of-modern-physics-thing. His feud with Hooke was interesting to see in the cartoon-style. "Put up or shut up" probably wasn't Halley's phrasing, but it stays out of my nitpicks section because it was pretty funny. One interesting thing is that Newton had more than one of these feuds over primacy regarding his ideas. There was also his famous dispute with Leibniz over calculus, which appears to be a case of independent arrival at similar ideas by different routes. Wikipedia has a whole list of these kinds of arguments if you like reading about scientists fighting over credit.


Charted the southern sky, called his shots 76 years in advance, perfected the diving bell.
Halley was... The most interesting man in the Enlightenment. (
So apparently, Edmond Halley was a total badass. Apart from his own amazing achievements, he also was the key player in publishing Newton's Principia, so we owe this guy a lot. Some people make much of Einstein's General Relativity, but the fact is that Newton's laws (as Halley showed) are good enough for government work (and by government work I mean exploring the Solar System, flying past Halley's own comet, and landing men on the Moon). By helping to ensure that Newton didn't let his brilliant achievements die with him, Halley gave us all the tools we needed to design the Industrial Revolution and leave the planet for the first time.

Halley's story exemplified the "moral" in this episode: That with science guiding our investigations, our fear of the unknown is rapidly transformed into our understanding. We've turned comets from prophets of destruction to beautiful proof of the elegance and predictive power of simple natural laws, and all we had to do was be curious. We should all look at the unknown as a new frontier to explore and, instead of simplifying our maps with "here be dragons", find pride in having discovered a new patch to explore. We have the means to enter unknown realms, let's not waste them because we didn't have the courage.