Blogs / Bad Astronomy

Tonight at 9:00 (8 central) Penn & Teller will be on Don’t Forget the Lyrics, a music game show… and they’re playing for the JREF! I already know how it turns out (it’s good to be the king) but have no idea how they get there, so I’ll be watching. Even though it’s on Fox.

FOLKS: Please watch the spoilers for this show and Battlestar in the comments! Don’t give anything away for those who still haven’t seen them.

I have been tremendously busy this week with JREF stuff, so I’ve been letting some news and other things slip behind me. I’ll try to put down my thoughts on the gassy Mars news soon, but until then, please feel free to comment on my Pope article, find out how far away the horizon is, or listen to an interview I did with Lab Out Loud, the official podcast of the National Science Teachers Association. Here’s the direct link to the MP3. We talked JREF quite a bit, as well as IYA 2009.

More later. Promise.

I generally don’t write too much about specific religions here on BA, for a lot of reasons. One is because discussing an entire religion is sure to drop the signal to noise ratio in the comments to 0, which is a pain and typically leads to irrational screaming rather than rational discussions based on evidence. But the big reason is that I prefer to attack specific arguments, not the people or establishments who make them. Many religions say the Earth is young, for example, but I don’t worry too much about who they are, but what they’re saying. And many religions do lots of good things, so attacking them en masse can be unfair.

Having said that, what the heck is the Pope thinking lately?

A recent article in the UK’s Daily Mail talks about the Pope creating a guideline to help determine what apparitions of the Virgin Mary are real and which aren’t. As regular readers know, I’m of the opinion — backed by substantial evidence — that at the very best the vast majority of these sightings are not real. They are, so far as I can tell, cases of pareidolia (seeing familiar patterns like faces in random noise) or mass hallucination. Some, of course, are simply hoaxes, and the Pope acknowledges this. His guidelines include having the claimant not go public, since that is highly suspicious behavior.

Some are just silly, like seeing the Virgin in your lava lamp (bonus: the skeptical viewpoint in that article is given by my friend Richard Saunders). I sometimes wonder: don’t people ever take into account the likelihood that an event will spawn a Virgin-shaped object? Oil dripping down, wax solidifying, grain patterns, folds: all of these can easily make a simple oval shape, reminiscent of how Mary is generally depicted. Seeing that pattern in them is hardly a miracle; I’d expect it to occur given enough examples. If someone shows me a demure cloaked Virgin in a quartz crystal, then maybe you’ll have something.

But that announcement pales in comparisons to the next: the Vatican has released a previously secret list of sins. The list itself is not terribly surprising, of course. What shocked me was the way it listed relative importance of these sins: desecrating a Eucharist (the cracker Catholics believe is the transubstantiated body of Christ) is considered a worse sin than murder or even genocide.

I had to read that part twice to make sure I had understood it, but the meaning is pretty clear. What PZ Myers did was worse, according to this doctrine, than what Stalin, Hitler, and Pol Pot did.

I understand that if you are a devout Catholic, you truly and fervently believe the cracker has become the actual body of Christ. But honestly, is spitting it out — an example specifically stated in the article — or even driving a rusty nail through it a worse sin than actually murdering millions of living people? I’ve read the Bible, and from the Sermon on the Mount it doesn’t sound to me that Jesus was someone who would think that way.

Now, having dealt with the media many times before, I understand how things get distorted in articles like these. Also, I was not raised Catholic, so perhaps I am missing important information here. I would be very interested in getting the opinions and viewpoints of other people in the comments. There are well over a billion Catholics on the planet, so whether you agree or disagree with the tenets of the religion, it’s a force with which to be dealt.

So let’s talk. Keep it polite, folks, and if you make claims, please try to include links. I am seriously interested in learning here — I always am — so let’s keep this dialogue respectful of people’s feelings, if not their ideas.

The Hubble Space Telescope folks just released a spectacular and surprising picture:

Hubble picture of the planetary nebula NGC 2818. Click to way embiggen. Credit: NASA, ESA, and the Hubble Heritage Team (STScI/AURA).

First off, whoa. It’s gorgeous. What you’re looking at is a planetary nebula (it doesn’t have much to do with planets; these objects were named thus because they looked like planets through small telescopes). It was a star something like the Sun that reached the end of its life and blew off a strong wind of gas. Eventually, as more material left the star, deeper layers of the star got exposed. Eventually, the core was all that was left: a hot, small, dense object called a white dwarf. It flooded the nebula with UV light, ionizing the gas and lighting it up. The complex interaction of the gas and the radiation produced the shape and the different colors.

But NGC 2818, as it’s called, is an oddball. When I first saw this picture I didn’t even think it was a planetary nebula, I thought it was a much larger gas cloud that forms stars. The shape is not much like other planetaries! Usually they are round, or hourglass shaped. This one is squashed and weird. The colors are pretty much normal: the outer parts are loaded with nitrogen and are reddish, while the inner region is hotter, less dense (because late in the game the wind from the star got hotter and less dense), and glows blue due to oxygen. The fingers or towers pointing toward the center are due to the light and wind slamming into denser blobs of material. They’re a bit like sandbars that form in a current.

In fact, NGC 2818 does appear to be a bit different. I think the star that formed it (which should be right smack in the middle, but I don’t see much there; it might be hidden by one of the fingers) was more massive than the Sun. The wind speed is higher, indicative of a more massive star. The nebula itself is much larger than other planetaries; they are usually a light year or so across, and this one is well over three. The amount of different elements in the cloud also seem to say that this was a bigger and hotter star than usual, too.

What makes this guy most unusual, though, is that it appears to be inside an open cluster, a loose aggregation of stars about 10,000 light years from Earth. Most planetaries are loners, since they come from old, dying stars. The Sun has a ten billion year lifespan, enough time that were it born in a cluster it would have long ago drifted away. But NGC 2818 is located in a cluster, and the safe assumption is that this was where it was born. That means it must be from a relatively young star (or else it would have left the cluster)… and massive stars age faster and die younger than low mass stars.

So I think the star that formed this beautiful and intricate web of gas was a big one, maybe even close to the limit between where stars die this way, and explode as spectacular supernovae. I had never heard of this particular object before, and I’m glad astronomers got this image so that it can be studied more carefully. You can learn a lot looking at things that are up against the edge of two different behaviors, and investigating stars like this give us a lot of insight into what happens at that limit between going gentle into that good night, and raging against the the dying of the light.

I fly a lot. Talks, meetings, whatever. I usually prefer an aisle seat, because then the rude guy who smells funny and spreads over 1.8 seats only irritates me on one side, and I’m not wedged up against the window.

However, sometimes I do like to grab a window seat, especially if I’m flying near sunset, or over a particularly interesting landscape (flying over southern Utah near sunset will change your life). But even then, the landscape blows past, and eventually you wind up flying over eastern Colorado, and there’s nothing to see but flat, flat land, extending all the way to the horizon.

And as I gaze over the amber waves of grain to the line that divides land and sky, I sometimes wonder how far away that line is. The horizon is a semi-mythical distance, used in poetry as a metaphor for a philosophical division of some kind. But in fact it’s a real thing, and the distance to it can be determined. All it takes is a little knowledge of geometry, and a diagram to show you the way.

Follow along with me here. We’re going to find the lost horizon.

So you’re standing on the Earth. Let’s assume the Earth is a perfect sphere, because that makes things a lot easier. What does our situation look like? Well, it looks something like this:

In this diagram, the circle is the surface of the Earth, which has a radius of R. The Earth’s radius varies with latitude, but I’ll just use 6365 kilometers as a decent average. The dude standing on the Earth is a human of height h (not to scale, huge duh there). The line-of-sight to the horizon is the red line, labeled d. Finding the value of d is the goal here. Note that the radius of the Earth is a constant, but that d will vary as h goes up or down.

The key thing here is that at the visible horizon, the angle between your line-of-sight and the radius line of the Earth is a right angle (marked in the diagram). That means we have a right triangle, and — reach back into the dim, dusty memory of high school — that means we can use the Pythagorean Theorem to get d. The square of the hypotenuse is equal to the sum of the squares of the other two sides. One side is d, the other is R, and the hypotenuse is the Earth’s radius plus your height above the surface, R+h. This gives us the following algebraic formula:

OK. Now what? Well, let’s expand that last term using FOIL:

Substitute that back into the first equation to get

Hey, we have a factor of R² on both sides, so they cancel! That leaves us with:

Now, take the square root of both sides, and voila! You get d.

So now we have an equation that tells us how far away the horizon is depending on where we are above the surface. We can use this to put in different values for h, our height, and see how far away the edge of the Earth is. I put this into an Excel spreadsheet, and the numbers are below.

In the table, the first column is your height in meters above the Earth’s surface (really the height of your eyes) and the second column is the horizon distance in kilometers. Columns three and four are the same, but in feet and miles for you Amurcans.

Sanity check: if you are 0 meters off the surface of the Earth (lying down really really flat), the horizon is 0 kilometers away. That makes sense — you’re tangent to the surface! So the first line sounds right.

Now imagine you are standing on a beach, lookig out over the ocean to the horizon. Most people aren’t two meters tall, and your eyes are several centimeters below the top of your head. But let’s just say your eyes are two meters off the ground (maybe you’re standing on a small sand dune). In that case, your horizon is 5.1 km (3 miles) away. That also sounds about right to me.

But now let’s say you are in your hotel overlooking the beach, and on your floor your eyes are 20 meters off the ground. The horizon is then 16 km away, much farther than before. Good: the higher you are, the farther away the horizon should be.

What if you’re a lot higher up, like in an airplane? At a cruising altitude of 39,000 feet (12,000 meters; typical for a cross-country flight) the horizon is 391 km (235 miles) away! That’s a surprisingly long way; in general that means you could be looking across one or more states in the US. This commonly fools me; seeing something even a little bit out from directly underneath the plane means it’s miles away.

What if you go up even higher? The Space Shuttle can reach a maximum height of about 500 km (actually a little more, but close enough). That’s 500,000 meters, or the second-to-last line of the table. For them, the horizon is almost 2600 km away! That means they can see almost the entire US by looking from one side of the Shuttle to the other. Cool.

And what if you’re really far away? From an infinite distance, you should see the horizon as being one Earth radius farther away than your height (draw a diagram if you want). In reality that’s impossible, so in the last line I put our poor observer floating in space one million kilometers away (more than twice the distance to the Moon). The horizon is then 1,006,344 km away, which is just about (but not quite) the Earth’s radius plus the observer’s distance over the surface. They are seeing almost — but not quite — half the Earth all at once.

So there you go. The next time you’re on a beach, or the next time you’re flying, take a look out to the horizon. Like the end of a rainbow, it’s impossible to reach. But it’s not impossible — it’s not even all that hard — to know how far away it is.

If you liked this, take a look at Mooey’s Top Ten ways to know the Earth isn’t flat. There’s even more geometric nerdity there. [Update: I had no idea, but Erik Rasmussen also has a writeup on this from last March, and it’s eerily similar to what I wrote. I swear I never saw his; but I guess great minds and all that!]

I just read that we lost another Star Trek great: Ricardo Montalban passed away at the age of 88. You can say what you want about Fantasy Island, or any other role he ever had, but his portrayal of Khan Noonian Singh will go down as one of the great scenery-chewers of all time, one of the only characters able to hold his own against the overly-amplified James Kirk. Trek has never — and the way things look, will never — have a greater movie than the second one. It’s the classic example of a sequel being better than the original. A lot of that was due to Montalban’s portrayal of Singh.

The newest Carnival of Space — #86, which I find smart — is at CollectSPACE. Lots of cool posts, including one on how the incredible artist Chesley Bonestell got his famous Saturn painting wrong. Since I love Bonestell’s stuff, I was kicking myself I hadn’t thought of it.