The Rings of Earth, Part II: Implications

What are a long car trip and hosting boring virtual office hours good for? Thinking about how our science and society would be different if the Earth had rings. Science fiction writers, take note.

As I was writing that earlier post, my officemates and I got into a discussion about some of the implications to (at least Western) science and philosophy of such a ring system. One of them suggested that the rings, which would be mostly aligned with the Earth’s equator but would precess with the Moon, would be quite obviously separate from both the purported “celestial spheres” and the Earth, so maybe the ancient Greeks could have dispensed with that destructive Platonic notion much earlier in the history of Western science.

I got thinking and realized that, in addition to their own dynamics, the rings would have a few other obvious effects on the science of those cultures at high enough latitudes to get a good view of the ring system, without seeing them edge-on.

First, the shadows of the Earth and Moon would be visible on the rings. These shadows would be shaped like portions of circles, and would vary in size and shape with time of day, month, and year. From observations of these shadows, easily possible with the naked eye, the Greeks, Egyptians, and Chinese ought to have been able to show without any doubt that the Earth and Moon are spherical. They may have been able to deduce the position of the Earth’s spin axis and axial tilt by comparing the shape of the rings and the shadows on them to the time to year. (These experiments could be quite simple: make a stiff, lightweight circle or hoop, hold it at arm’s length at night, move the circle in and out and tilt it back and forth until its edges line up with the shadow on the ring. Add a little simple geometry, and BAM: I would have just found the axial tilt of the Earth.) They should also have provided some kind of estimate of the distance to the Moon, as observers could compare the size of the Moon with the size of its shadow. And comparing the Earth’s shadow on the rings to the positions of the background stars would have given the ancients an incredibly accurate nighttime clock.

Second, and perhaps most importantly of all, the rings would vary radially in opacity. This would make them beautiful to behold, yes, but it would also give naked-eye astronomers an absolute scale for photometry. Annuli of the rings would block out the light from some stars, but not others. The thicker rings would block more stars than thinner rings, giving a gradation of occultation scales. By comparing which rings block out which stars, observers would have been able to make statements about the relative brightness of the stars with a degree of precision unknown until Christian Huygens arrived on the scene – even surpassing the precision of that experiment. Still more exciting, if the ring was able to occult the Sun, that same method could have been used to measure the light output of the Sun. Now, coupled with the insight that the Sun is a star and a crude estimate of the Earth-Sun distance, an observer should have been able to deduce from naked-eye observations approximate distances to the stars.

I’ll say that again: If the Earth had rings, the ancient Greeks, Chinese, and Egyptians might have had a sense of the scale of the Cosmos. The Romans and Indians might have known what a parsec is.

Furthermore, this photometry could have been used on the visible planets as well as stars. That would have told the ancient astronomers that Mercury, Venus, Mars, Jupiter, and Saturn were a lot closer to the Earth than the stars. In fact, if the ancient photometers tracked the brightness (and, therefore, distance from the Earth) of each planet over time, they would have noticed something interesting: the planets move in circles about a point that is not located within the body of the Earth, but is rather in the Sun. The heliocentric model for the Solar System would have been adopted in ancient times.

Now, knowing that the planets go around the Sun, and the stars are all rather a long way away from the Sun and from each other, ancient astronomers might have realized that other stars could have planets just like the Sun does. Think about what that idea might have done to Western philosophy and religion in their formative years: other Earths? In the sky?! Going around other Suns?

Here’s a possibility I’m not sure about: if the ring was thick enough, it’s possible that it might dim the Sun enough that an observer could safely look at our star with their naked eyes. If so, then sunspots might have been visible to the ancient civilizations. In that case, they might have known that the Sun is not a perfect glowing sphere, and that it rotates. They might have known about the 11-year solar cycle.

And then, imagine what could have happened once Galileo stormed onto the scene with his telescope. When he looked at Saturn, he would have known exactly what he was looking at. “Ears” indeed! By watching Saturn’s rings wax and wane with each Saturnian year, he would have identified the orientation of Saturn’s ringplane to the ecliptic. Knowing that Saturn has rings would have told scientists that Earth’s features are not unique to our own planet.

Early telescopes might have been powerful enough to identify some of the larger rocky chunks making up the Terrestrial rings. Observing their orbits at different radii within the ring could have lent a lot more data to scientists like Kepler and Newton, who were trying to figure out what forces kept the planets in orbit. Armed with data on the orbits of ring particles and Kepler’s Laws, early scientists might have been able to get a pretty good estimate for the mass of the Earth and fix the Earth-Sun and Earth-Moon distances pretty accurately.

I’m thinking that, given how great a dynamical laboratory the Saturnian ring system is, rings around the Earth would have allowed the progress of science to advance much more rapidly, as the rings would provide a precise tool for measurements of position, time, and distance of celestial bodies. If the laws governing those bodies had been puzzled out, say, before Christianity dominated Europe, imagine what society would have resulted….

I know what I’m doing the last week of December

I’m home for Thanksgiving, and at my mom’s suggestion, I just listened to storyteller Jay O’Callahan perform part of his work about NASA, “Forged in the Stars,” on the “Living on Earth” program for NPR. If you’re at all interested in space exploration, NASA, or just hearing a good story, it is well worth listening to this performance, which you can do by clicking the download link on this web page.

NPR will air the full performance of “Forged in the Stars” during the last week of December. O’Callahan has performed the piece at JPL and JSC, and received standing ovations for it. Here’s to him for doing a little bit to capture the public interest once again.

a nifty thought experiment: the Earth with rings

One of the most majestic and awe-inspiring structures in the Solar System is the Saturnian ring system. My sister sent me this video, which imagines what that same ring system would look like around the Earth – and what it would look like in our sky when viewed from the surface. The result is pretty wonderful to imagine:

However, sciency guy that I am, my very first thought on seeing this video translocate the Saturnian rings around the planet Earth was, “Hey! The Cassini Division’s still there!”

The significance of that gap between Saturn’s A and B rings is that it’s one of the most clear markers of the interaction between Saturn’s moons and the rings. All of the various gaps and spaces between the rings come from orbital resonances between the rings particles and various moons. If, for example, a ring particle orbits twice around Saturn for every orbit of the moon Mimas, then Mimas will pump energy into the orbiting particle and it will move into a higher-energy orbit with a larger semimajor axis – thus clearing a space in the rings (for the 2:1 Mimas resonance, the Huygens Gap).

That made me wonder just what a Terrestrial ring system would look like. We have only one moon, but it’s incredibly massive compared to the Earth. In fact, the Earth/Moon system has the largest moon-to-planet size ratio, by any measure, in the Solar System. (Sorry, Pluto/Charon!) Our single moon compared to Saturn’s dozens means that our ring system would be much more orderly, with many fewer and much more regularly spaced gaps. However, the huge size of the Moon means that the weaker resonances would have a stronger effect. The Saturnian rings show evidence of weak resonances all the way out to the double digits – like, say, 9:14 resonances – so I’d argue that weaker-still resonances would still be visible in the Earth-Moon system.

So, I wrote a little Matlab script. Clearly, this was more important today than getting my work done.

As in that video, I placed the outer limit of my hypothetical Terrestrial ring system at the Roche Limit, ~2.86 Earth radii from the center of the orbit. This is the innermost limit at which a fluid satellite could hold itself together, by its own self-gravity, against being ripped apart by tidal forces fromt he Earth. Outside this limit, the rings could start to aggregate together into moonlets. I bounded the inside of the ring at 1.59 Earth radii on the inside, coinciding with the definition of the outer limit of the exosphere. Even in low Earth orbit, atmospheric drag would eventually cause ring particles to fall into the deeper atmosphere, so I felt this would be a good value to pick to ensure that the ring would have a long enough lifetime to persist for millions or billions of years.

I started my script with a ring opacity of 100% at all radii and put a fuzzy boundary on the ring system at either end. Then I had Matlab calculate the orbital radii of every ring-Moon resonance from 1:1 to 100:100 using Kepler’s Third Law. For each resonant semimajor axis that fell between the Roche limit and drag limit, I subtracted a narrow Gaussian from the ring opacity as a function of radius. Since my big 100×100 matrix of resonances had some repeats (like 3:4 and 6:8), several of these Gaussian functions would add together and decrease the ring opacity further, crudely estimating the effect of stronger resonances. Finally, I lowered the albedo and tweaked the color of the rings from what they are at Saturn, to make them look more like they’re made of rock rather than ice, which sublimes away in space at our distance from the Sun. This is what I got:

THe Earth's hypothetical rings
The Earth's hypothetical rings

Earth's Rings in a more Moon-like color
Earth's Rings in a more Moon-like color

The rings in this image go around the Earth’s equator, inclined 22 degrees with respect to the field of view because of the Earth’s obliquity. Sadly, my Matlab graphics cannot handle casting the shadow of the rings onto the Earth, and I had to Photoshop in the shadow of Earth on the rings for effect. Still, pretty cool looking. Here’s the punchline: the ring system viewed from directly above the ring plane, with a white background so you can easily see the pattern:

From directly above the ring plane and backlit
From directly above the ring plane and backlit

You can see that the lunar resonances don’t start to have a major effect until about halfway through the ring system. This pattern, and the coloration, are mainly what that video was missing.

Of course, I don’t have the complete story, either. Again, our Moon is huge and that will do even more to the rings’ shape. The Moon’s orbit is inclined 5 degrees to the Earth’s equator, so the tidal torques from the Moon should make the rings precess around the Earth with a one-month period. (That precession would lag the Moon, so we wouldn’t always see the rings piercing the Moon in our night sky.) In addition, I suspect that the lunar tides would twist the rings a bit, pulling them into a spoked configuration like Cassini has seen at Saturn.

It’s definitely fun to think about how these rings would look from vantage points on the Earth. Actually, since my ring system starts well above low Earth orbit, I have to wonder what they would look like to spacewalking astronauts…

Why isn’t America sick of Sarah Palin yet?

More importantly, why does a recent Gallup poll, as reported by Newsweek, say that 58% of Republicans believe that Palin is qualified for the job of being President, but 65% of them would vote for her. For those of you who know that probabilities must add up to 100% and possess the skill of subtraction, this means that at least 7% of Republicans think that Palin is unqualified to be President but would still vote for her. does not report the actual intersection between these sets, so keep in mind that 7% is a lower bound on that figure.

Um, hi, Republicans? Just FYI, no cause for alarm, but… There is something wrong with your brains.

diabetes blows

This is somewhat of a personal note, but every now and then being a type 1 diabetic really frustrates me and I just have to unload a bit.

Don’t get me wrong, medicine has made great strides in managing diabetes. If you observe me for a randomly selected 1% of every day, I will seem fine. And I can for the most part do anything that a healthy human being can do. I can go hiking, or waterskiing, or kayaking. I can go out in the heat and out in the cold. I can fly or ride in airplanes.

But catch me during the wrong 1%-of-the-day sample, and this crap can be really annoying to me.

I’m on an Animas IR1250 insulin pump. Every three days, give or take, the reservoir in the pump runs out of insulin and needs to be replenished. I also have to replace the infusion set where the pump’s tubing goes into a subcutaneous cannula, to avoid picking up any infections where the cannula pierces my skin. This process usually takes me 15-30 minutes, and involves sticking myself in the abdomen or hip with a 1″-long needle. This needle goes in at an angle and is supposed to end up just below the skin; then I take out the needle and leave the cannula in place. Sometimes this is fine and simple.

Saturday I go to do a normal change, and encounter a couple problems that I have to deal with on a regular basis. First, I weigh 142 pounds. I don’t have a lot of padding or extra skin. The infusion sites aren’t supposed to get clustered up too densely, so I kind of end up struggling to find a place to put them sometimes. Second, this injection isn’t exactly like going to a nurse and having her stick a needle in your arm; she doesn’t feel what you feel, she just goes ahead and pokes you. In, out, bam, done. It’s better that way, at least, on an intellectual level. But when I’m doing this to myself, I tend to go really slowly sometimes. Especially on those occasions when I don’t miss all the nerve clusters on the way in. When something hurts, reflex tells me to either stop what I’m doing or pull back, not keep going.

So anyway, on Saturday I’m looking at my hip for a place to put this infusion set, and I ended up choosing wrong or going in at too steep an angle, because pretty quickly I get this really weird twinge and all my reflexes scream HALT. But I try to override that, because that’s what I have to do, and I end up with HALTHALTHALTSTOPOUCH and my hand practically jerks away on its own. I figure I was probably getting into muscle tissue rather than skin and fat. So I yank the needle out and SURPRISE out comes a bunch of blood. Great for improving my disposition, you know. Standing with my weight on one leg, twisting around to see my hip better, holding a needle that I have just used to wound myself, looking around for some kleenex and neosporin, and knowing that I have to do it again in order to stay alive.

Well, after stomping around my room in consternation for a bit to cool off, and developing a bit of ache in some hip muscles, I decided to move to a different site in my rotation and put a new infusion set in my abdomen, instead. This one seemed to go okay, so I pack things up and go do whatever it was I thought I would be doing an hour previously, before this happened.

Today, that infusion set totally failed. My blood sugars had been running in the high 200’s (yours is probably 100, maybe 120 if you just ate) and wouldn’t come down in response to extra insulin. So I watch the infusion site while I’m trying to give myself a correction bolus and find that, hey, look, insulin is just pumping out and pooling on the surface of my skin. Fat lot of good that does. This sometimes happens, and someone explained to me that it’s because insulin can act like a growth hormone, so sometimes a little knot of tissue forms right at the end of the cannula where insulin is going into my body, and that knot can plug up the cannula and the insulin from a bolus just ends up forcing its way back out the hole in my skin and onto the surface. Anyway, this is supremely annoying, because then I have to change the infusion set again. This wastes insulin (which is expensive), pump cartridges (which are highly specialized and therefore expensive), and infusion sets (which are also highly specialized and therefore expensive). It also causes physical pain and emotional stress, for obvious reasons. Did I mention that I hate needles? IV’s make me squeamish. It is for this reason, basically, that an anomalous high blood sugar is a way to make me instantly aggravated. It’s more effective at that than a bad grade, or a rejection letter, or Fox News.

So today it was time to leave work and change the infusion set early. This one also seemed to go okay, except that when I pulled the needle out of the cannula, it hurt like CRAP. And when I gave myself the first bolus a minute ago, it burned. So now I might have fixed the previous problem, but I face the prospect of burning pain every time I want to eat any carbohydrates and have to bolus again.

FML. I’d like some stem cells, please.

I’m going to rail against Apple ads for a minute

Here’s a quick paraphrase of how a typical Apple Mac ad goes:

Cut to a white background. John Hodgeman, dressed in a suit nobody’s worn since the 90’s, is on the left. Justin Long, looking like he’s about to audition for the guy in ‘Best in Show’ who met his wife when they were in adjacent Starbucks, is on the right.

Hodgeman: I’m a PC, and Windows 7 just came out.

Long: Well, I’m a Mac. Wait a minute, PC, isn’t Windows 7 a kind of Windows?

Hodgeman: Uh – you – uh – yes, Mac. I suppose so.

Long: And isn’t Windows inherently bad?

Hodgeman: I guess you’re right. That means Windows 7 is inherently bad.

I can’t begin to tell you how sick I am of these TV spots. They are just so…spiteful. They rarely ever have anything positive to say about Macs, and they never have anything substantive to say about PCs. They just say, over and over again, “Macs GOOD, PCs BAD!”

Particularly the Win7 ads. The whole campaign seems to revolve around the assertion that Windows is just bad in general, and therefore Win7 is bad. So far as I can tell, the writers and directors of these ads never laid their hands on Win7. I’ve been using it since early October, and I have yet to even press Ctrl-Alt-Delete, let alone see it crash or even bog down.

It’s really telling to compare this style of advertising to Microsoft’s Win7 ad campaign. First, they showed cute kids, unicorns, and puppies, played over glowing quotes from reviews. (Wait – you mean they showed evidence for their claims?!) Then, they showed short TV spots focusing on some new feature on Win7 and how it’s useful, presented by a normal, average-looking person. It just shows how militant Mac is, iwth their tiny minority market share.

I think this mirrors the contrast between Steve Jobs’ and Bill Gates’ characters perfectly. Apple hasn’t produced anything new in years (Apple today = OSX + iPods), while MS has been evolving new features and putting forward new services. MS has even been opening up a bit, while Apple’s business practices are all about locking their devices down to prevent anyone from doing anything that rubs their snootily discerning noses the wrong way. While Jobs is just full of vitriol at his competitors and tries to survive on hero worship from his devoted minority, Gates just doesn’t care. He’s off filling impoverished schools with computers and trying to cure AIDS in Africa.

Fortunately, one of the Discovery Channel “Boom-dee-atta” ads came on immediately thereafter and made me feel better!