{
  "export": {
    "source": "https://urth.darkrealm.vip/thread/whorl/816",
    "note": "Exported from an unofficial mirror of a public mailing list. Copyright in each message remains with the person who wrote it.  Email addresses are obscured as `user at host`, the form the original archive published. This file was rebuilt from parsed fields rather than retained headers, so it is faithful in content but not byte-exact.",
    "addresses": "obscured as 'user at host'"
  },
  "archive": "whorl",
  "thread": {
    "id": 816,
    "subject": "Green's orbit",
    "messages": 1,
    "voices": 1,
    "first": "2000-04-09T17:47:12+00:00",
    "last": "2000-04-09T17:47:12+00:00"
  },
  "messages": [
    {
      "message_id": "<whorl-v0010-0311@digest.urth.net>",
      "from": {
        "name": "Adam Stephanides",
        "address": "adamsteph at earthlink.net"
      },
      "date": "2000-04-09T17:47:12+00:00",
      "subject": "(whorl) Re: Green's orbit",
      "in_reply_to": null,
      "reply_link": null,
      "blocks": [
        {
          "kind": "text",
          "depth": 0,
          "text": "Apologies in advance to those bored by \"techie stuff\"; you can just skip\nthis message.\n\nKieran Mullen wrote:\n\n[I wrote:] "
        },
        {
          "kind": "quote",
          "depth": 2,
          "text": "Furthermore, as someone\nelse once pointed out, if Blue and Green's orbits brought them into\nconjunction as frequently as every six years, they would not be stable:\nthe repeated perturberations from each other's gravity would pull them\ninto new orbits."
        },
        {
          "kind": "quote",
          "depth": 1,
          "text": "    Hmm... I don't think this is correct.  It is true that if their periods were\nexactly integer multiples, you would have a problem (like the Shepherd Moons and\nthe Cassini divisions of Saturn's rings).  But if they are not integer multiples\nyou should be ok, I think.  (After all, the gaps in Saturn's rings do not deny\nthe existence of the rings themselves!)"
        },
        {
          "kind": "text",
          "depth": 0,
          "text": "After reading your reply, I realized I didn't really know why\n\"resonances\" (to use the technical term) had the effects they did.  So I\ndid a little research, beginning with _Newton's Clock: Chaos in the\nSolar System_ by Ivars Peterson, and going on to what non-technical\narticles dealing with the gaps in the asteroid belt (which seem to be\nbetter understood, and are a better analogy to our hypothetical\nsituation) I could find in my local academic library.  What I found out\nis that the situation is much more complex than I had realized.\n\nIn the first place, the picture I had in my head of repeated\ngravitational tugs gradually pulling the asteroid out of orbit is\ncompletely wrong.  In the case of the 3/1 gap in the asteroid belt\n(where the period of the asteroid is a third that of Jupiter's), where\nthe dynamics are the simplest and best understood, in numerical\nsimulations an asteroid can spend up to a million years in a\nnear-circular orbit and then jump to an eccentric orbit crossing\nMars's.  Moreover, to explain why there is a gap at the 2/1 resonance,\nyou need to take into account the gravitational effects of Saturn as\nwell.  And at the 3/2 resonance, there is actually a cluster of\nasteroids, not a gap.  So resonances with small numbers don't\nautomatically imply unstable orbits.\n\nOn the other hand, there are no asteroids with periods equal or near to\nsix-sevenths of Blue's (which Green's is most likely to be if it has an\n\"ordinary\" orbit).  And a numerical simulation of 3000 randomly chosen\norbits between the 2/1 gap and Jupiter's orbit yielded no surviving\norbits in that region.  On the other other hand, the fact that in OBW we\nhave two bodies of comparable sizes, rather than an asteroid and\nJupiter, may make a difference.  \n\nSo I would sum up the findings of my research as follows:\n\n1) The fact that Blue and Green reach conjunction every few years does\nnot, in itself, imply that their orbits are unstable; but\n\n2) The fact that Green's period would have to be close to six-seventh of\nBlue's probably means that its orbit would be unstable; but\n\n3) I don't really know.\n\nDoes anybody know a good celestial mechanic?  If not, I may make\ninquiries on sci.astro.\n\nFinally, a minor point.  If Blue and Green do have conjunctions every\nsix years, it has to be exactly every six years, for reasons given in my\nreply to mantis below.  But, as I said earlier, they may not."
        },
        {
          "kind": "quote",
          "depth": 1,
          "text": "mantis wrote:\nModel 1: Two Planets (Earth and Venus), with standard Bode-Titus style\norbits and a comparatively wide separation (significant fraction of an\nAstronomical Unit).  (Problems: to see one as a looming disk from the\nsurface of the other, the world has to be much closer than this suggests.\nPossible solution: ditch Bode-Titus! <g>)"
        },
        {
          "kind": "text",
          "depth": 0,
          "text": "Not just the appearance argues against Bode-Titus, but the tides: after\nall, Earth gets no tides from Venus.  So Green has to be quite a bit\ncloser.  But ditching Bode-Titus shouldn't be a problem: it's just a\nnumerical regularity with no known theoretical explanation, and it\ndoesn't even work for Nepture (or Pluto either, but there are arguments\nthat Pluto isn't really a planet).\n\nAt first I thought Kepler's Third Law would be a problem, but when you\ndo the calculations, it isn't (at least I don't think so).  Kepler's\nThird Law says that the ratio of the square of a planet's period to the\ncube of its semimajor axis (the average of its closest distance to the\nsun and its furthest distance away from the sun) is constant for the\nplanets in a given system.  Green seems to be hotter than Blue (the\njungles), so its orbit is inside Blue's and its period is smaller.  If\nits period is six-seventh of Blue's, then its semimajor axis is about .9\nas long as Blue's.  If the distance between Blue and Green at\nconjunction is insignificant compared to the distance between Blue and\nthe Short Sun, and if we assume that blue's orbit is nearly circular,\nthen Green's distance when closest to the Short Sun is about .8 its\ndistance when furthest from the Short Sun, which doesn't seem too\neccentric to allow life to evolve on Green (by comparison, Venus's\naverage distance from the Sun is .72 times Earth's distance from the\nSun).  On the other hand, if Green's period is five-seventh that of\nBlue's, then under the same assumptions its closest approach to the\nShort Sun must be .6 times its furthest distance, which does seem\nexcessive to me (though again, I'm not an expert).\n\nSo neither Bode-Titus nor Kepler argue against \"ordinary\" planetary\norbits for Blue and Green.  Stability may or may not, as I discuss\nabove; and I still think that Horn's narrative implies that Green moves\nvisibly across the sky, which is another problem for this model.\n\n--Adam\n\n*This is WHORL, for discussion of Gene Wolfe's Book of the Long Sun."
        }
      ]
    }
  ]
}