Via a link from New Scientist, I got to a page about Neptune's Trojan asteroids. According to the author, a handful are known, all found in the last five years. One of them, newly discovered, is in an orbit tilted 25° from the ecliptic. Which is to say, 25° from the orbit of Neptune.

As I understand it, all five of Lagrange's special-case solutions to the three-body problem involve two co-planar orbits. In the real world, there's a little slack, just as not all of Jupiter's Trojan asteroids are exactly 60° ahead or behind the planet. But 25 degrees inclination seems like a lot to count as at the Lagrangian points. Does anyone know if someone has done the math for that set of orbits? I can't see how this geometry is stable: right now, 2005 TO74 is at or near Neptune's L4 point, but eventually it's going to be 25 degrees north or south of the ecliptic; with Neptune staying in the ecliptic, and at that orbital radius, we're looking at a couple of hundred millions of kilometers north or south of the L4 point. I thought the reason the Lagrange points are interesting and potentially important is that they're small areas: a body at L4 will be consistently in the same direction, and distance, from the primary.
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Via a link from New Scientist, I got to a page about Neptune's Trojan asteroids. According to the author, a handful are known, all found in the last five years. One of them, newly discovered, is in an orbit tilted 25° from the ecliptic. Which is to say, 25° from the orbit of Neptune.

As I understand it, all five of Lagrange's special-case solutions to the three-body problem involve two co-planar orbits. In the real world, there's a little slack, just as not all of Jupiter's Trojan asteroids are exactly 60° ahead or behind the planet. But 25 degrees inclination seems like a lot to count as at the Lagrangian points. Does anyone know if someone has done the math for that set of orbits? I can't see how this geometry is stable: right now, 2005 TO74 is at or near Neptune's L4 point, but eventually it's going to be 25 degrees north or south of the ecliptic; with Neptune staying in the ecliptic, and at that orbital radius, we're looking at a couple of hundred millions of kilometers north or south of the L4 point. I thought the reason the Lagrange points are interesting and potentially important is that they're small areas: a body at L4 will be consistently in the same direction, and distance, from the primary.
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I got myself over to Metalliferous today. I now have a couple of simple silver necklace chains, suited for wearing pendants and such on. I have some sterling silver ear wires and pins. And I have beads.

I have a half dozen pretty glass beads, selected individually from a large tray of different sorts. I have a string of amethysts. I have a string of malachite, and one of green aventurine. I have two strings of garnets (they were the last each of two slightly different styles, and she gave me a discount to avoid having to hang a single string.

I have spent quite a bit of money, and suspect that when I sit down to earring-making (which may wait until the June BotMo arrive) it's going to be heavy on green and purple. (The garnets are quite small.) I'll have spares, because I don't want everything I make to look the same, but I wanted these colors and shapes.
I got myself over to Metalliferous today. I now have a couple of simple silver necklace chains, suited for wearing pendants and such on. I have some sterling silver ear wires and pins. And I have beads.

I have a half dozen pretty glass beads, selected individually from a large tray of different sorts. I have a string of amethysts. I have a string of malachite, and one of green aventurine. I have two strings of garnets (they were the last each of two slightly different styles, and she gave me a discount to avoid having to hang a single string.

I have spent quite a bit of money, and suspect that when I sit down to earring-making (which may wait until the June BotMo arrive) it's going to be heavy on green and purple. (The garnets are quite small.) I'll have spares, because I don't want everything I make to look the same, but I wanted these colors and shapes.
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