Wapsi Square Forum

Long ago, I remember a discussion of Bode's Law in astronomy class, and the issue was why ratio relationships didn't pull the related orbits apart. The thinking was a orbital relation like 1:2, 3:4, 5:17 and so on would "tug" on each other and change the orbits, so why did the ratio endure?

It's now seems that tons of asteroids, moon systems like Jupiter and Saturn, all have tightly stable orbital resonances of (mostly) small whole numbers. The thinking has changed to where eccentric orbits become stabilized when two bodies approach some integral resonance. The "Shepard Moons" of Saturn bear this out.

Just wanted to mention this as a change of science thinking as taught since the 70's.

And there's another weird stable solution to the three-body problem, called the horseshoe orbit.

Unlike LaGrange's solution, for a horseshoe orbit the secondary and tertiary objects can be of ANY relative size - even the same size, in fact that's the classical case (and makes the terms "secondary" and "tertiary" interchangeable). They just need to be in orbits of near-identical period and eccentricity around the primary.

The "horseshoe" is the orbit of the tertiary relative to the secondary. As such, the period of the "horseshoe" bears no particular relationship to their orbital periods around the primary.

Assume we start with the tertiary moving faster than the secondary - which also means it's on an orbit slightly closer to the primary. Eventually, it will start to catch up to the secondary, and the two will start having significant gravitational effect on each other. This causes the tertiary to speed up and move OUT to a slower orbit around the primary, and simultaneously the secondary slows down and moves IN to a faster orbit. If they are identical in size, they will fairly precisely swap orbits. If one is quite a bit larger (e.g. a planet versus an asteroid), the effect on it will be nigh-indetectable while the smaller one will do nearly all the shifting.

With the secondary moving to a faster orbit and the tertiary to a slower one, now the secondary is moving faster than the secondary. The separation between the two bodies starts to increase... and eventually, probably after quite a few revolutions around the primary, the secondary starts to catch up with the tertiary.

Neither body will ever pass the other - there's a gap. Like between the ends of a horseshoe.

There are known pairs of asteroids in such orbits. There are asteroids in horseshoe orbits with Earth as the secondary.

Now for even more fun... imagine three objects in such an orbital arrangement.

And then use the Jupiter-Sun L4 and L5 points as two of those objects.

There are asteroids in horseshoe orbits with said LaGrange points as the secondaries. (And there are others with sufficiently different orbits that they don't bounce off the LaGrange points, but sufficiently similar orbits that they do bounce off Jupiter itself.)

Space spirograph!

chicgeek wrote:Space spirograph!

That was, in fact, how the site i found it at described it.

Rest In Peace, Casey Sledge, A.K.A. Bearhugger McClain. Was mowing his lawn, and had a heart attack. Viewing is tomorrow.

Most of you probably have never heard of him. Those who did the Filk circuit or frequented the convention circuit in Texas probably are familiar with him. In addition to doing plenty of solo work, he also was in a group called October Country. He was to play this fall at FenCon IX this year. They'll probably have a wake for him in lieu, but things are understandably up in the air at the moment.

He was a mentor of mine, and not only introduced me to the wonderful world of filk but was also another father figure during a very difficult time in my life.

You can see him performing the title song October Country here.

He will be sorely missed.

I suspect that my ex-wife (very into filk) would know of him.

I'm sorry to hear that Shneeky ...

My grandfather is running short on time. He was diagnosed with lung cancer earlier this year, and we already weren't expecting him to make it to Christmas this year.

However, I'm not expecting him to make it past spring. I found out last night that his kidneys are failing, and he's not really concerned about trying to put much more time behind him. He'd been preaching since the early 60s, so he hasn't really been worried about dying, as far as I've ever noticed.

I'm more worried about my grandmother and my dad. Dad was sounding pretty upset last night when he got home from work, and didn't get home from the hospital until 3 this morning.

I'm not really sure what to say, since there isn't much to really do about it at this point.

Alkarii wrote:I'm not really sure what to say, since there isn't much to really do about it at this point.

"I'll be there for you" is perhaps the most important thing to say.

You can't change the basic situation, but you can be with your grandfather as he says good-bye and lets go, and you can be there when your grandmother and your father go through their grieving.

Just quietly let them know (by your words and by your actions and attitude) that you love them.

As Spider Robinson has written, "Shared pain is lessened. Shared joy is increased."

As Dave said. And do not be concerned if the care is only palliative. Morphine is our friend at these times.

((hugs)), Alkarii. Wishing you and your family strength in this difficult time.

Apparently my grandfather has been falling a lot, because the cancer may have reached his spine. My dad had to go all the way to their house, about half an hour away, to help him up again, because apparently my aunt, who lives there, is unable to pick him up (not surprising, as she has let herself get to more than 300 pounds, and is incredibly lazy), and was unwilling to do as my dad told her, and call 911 and tell them she needed lift assistance.

I had my gallbladder yanked out sunday! Apparently it was both highly infected and full of stones, so they took it out right away. When I went in saturday night, I was thinking heart attack. Because women have different symptoms-my back, chest, and arm hurt, and I started puking as soon as I got there. Fun. They sent me home monday afternoon, yay laproscopic surgery.
One of my sisters tried to get the surgeon to save the stones, but no go. Not that I wanted them.
Been doing okay. I'll need to be on restrictions at work when I go back, no lifing immensly heavy totes of books.
Aaand this weekend is when I have a table at the local sci fi con. I'm not supposed to lift. My helpers? Kiddo has the hyper mobile joint syndrome, where if she isn't careful, her joints pop out (as well as get hurty), and other half can't walk very far without hurting-he's also got dialysis to get through tomorrow morning before we go. I can probably grab a con volunteer to help.
Hopefully I'll sell a few rayguns and such to make it worth it. Ah, it's just fun to hang out there. Wish me luck.

Break a leg! and best of luck in your recovery! I'm glad they got to it before the problem spread further than it did!

Well... I'm at my grandparents' house, and I overheard my grandfather say that the doctor said six months to a year, which is beyond the predictions I had been making.

Article here

I survived the con! It's nice, seeing the same geeky family crowd every year. Had fun, sold stuff, kiddo made a decent minion, went to a talk by a NASA rocket scientist, bought books. The usual. I was in a corner next to a photography booth, and too late we had the bright idea of them using my stuff for props. Next year. Right now they have cheap generic toy guns, and other things. I figure, someone chooses a badass raygun for their shoot, they just might buy it, for a small discount. And I get publicity.
I still crapped out too early to get much time in the game room, and didn't join a larp. Next year. And I'm healing splendidly.