Exoplanets, MIT, Mathematics, and Thinking With a Cold

It's almost two months since I've done a post here. There's some excuse - or explanation, at any rate. A busted pipe in the laundry room created something a distraction, for one thing. ("Busted Water Pipe, Day 32: Plumbing Progress and Regress," Through One Dad's Eye (October 18, 2010))

Now, back to the general topic of this blog.

You've heard of writer's block? I've got something more like writer's fog. I've heard that I'm recovering from a cold - and that may be so. I don't feel sick, which is nice. I don't even feel tired. But it's been one of those Mondays where I can't seem to think all that well.

Like I said, I'm recovering from a cold. Or so I've heard.

'Creative' work being off the table, I decided to do a little - wait a minute. "Off the table?" What does that mean? Did 'creative' work fall onto the floor? Maybe I should look there. No. Wait. It's a term from parliamentary procedure. Not 'creative' work. The other thing.

And that's the way it's been today.

Anyway, I decided to do a little research. Like the animated Jackie Chan's Adventure's Uncle: "MORE RESEARCH!" I like that series. Don't watch it much now.

Anyway, I decided to do a little more research.

About exoplanets. There's quite a bit out there: everything from (fairly) hard data; to serious research; to stuff that may or may not have been intended as a practical joke. Don't get me wrong: some of the more solid resources haven't been 'real' academic or government outfits - dedicated, intelligent amateurs - - - and I'm drifting off-topic again.

The again, sometimes an old-school academic institution gets it right.

CalTech had some interesting pages - some of which I eventually found. They'd done a more-than-usually-creative rehash of their website. Sort of like dropping an encyclopedia into a food processor, hitting 'puree,' pouring out the results and telling folks that they've reorganized the information - please browse our new-and-improved website.

It wasn't that bad, actually, although the data I was looking for wasn't - quite - there. Like I said, they'd 'improved' the website.

I had a little better 'luck' at MIT, finding a 19-page paper about exoplanets by Seager and others. It's in PDF format, and starts with:

"We use new interior models of cold planets to investigate the mass-radius relationships of solid exoplanets, considering planets made primarily of iron, silicates, water, and carbon compounds. We find that the mass-radius relationships for cold terrestrial mass planets of all compositions we considered follow a generic functional form that is not a simple power law:..."
(Seager and others, via MIT)

That "simple power law" uses symbols that aren't in all character code sets, ASCII or otherwise, so I'm not quoting more from that paper here.

Besides, anything that gets into mathspeak after the first 55 words isn't something I want to tackle right now.

On the other hand, it's an excellent resource.

So, in case someone at MIT gets the bright idea of handing their website over to a caffeinated intern for "improvement," I dropped a copy of the PDF file into a server I trust:

• "MASS-RADIUS RELATIONSHIPS FOR SOLID EXOPLANETS"
  The Astrophysical Journal, The American Astronomical Society (November 10, 2007)
  S. Seager, Kuchner, C. A. Hier-Majumder, B. Militzer (Received 2006 December 25; accepted 2007 June 21)

Please note: The AJ of the AAS seems to own the copyright to this paper. A bunch of folks who know a whole lot more math than I do created the paper's content. All I'm doing is putting a copy where I'm reasonably sure I can find it, a week or a month from now.

That disclaimer out of the way, the paper is a pretty good discussion of how mass and size (diameter) are related - or should be - for differentiated and undifferentiated planets. In other words, for planets that are pretty much the same material all the way through, and those with onion-like layers, like Earth.

Mostly, it's a fascinating look at what researchers are doing, making sense of what's being learned about planets circling other suns.

From the point of view of this blog, it's also a pretty good resource for working out plausible fictional planets.