{ "export": { "source": "https://urth.darkrealm.vip/thread/urth/3087", "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": "urth", "thread": { "id": 3087, "subject": "Blue moon", "messages": 4, "voices": 2, "first": "2002-03-25T23:19:59+00:00", "last": "2002-03-29T20:04:41+00:00" }, "messages": [ { "message_id": "", "from": { "name": "Roy C. Lackey", "address": "rclackey at stic.net" }, "date": "2002-03-25T23:19:59+00:00", "subject": "(urth) Blue moon", "in_reply_to": null, "reply_link": null, "blocks": [ { "kind": "text", "depth": 0, "text": "This occurred to me last night, and I took it to mantis first today, and he\nsaid to post it all to the list, so here it is:" }, { "kind": "quote", "depth": 1, "text": "You should post this to the list!" }, { "kind": "quote", "depth": 2, "text": "You seem to like to take a sliderule to things, so consider this\nobservation. I'm about 3/4 of the way through IGJ, in my re-read of the SS\nseries. While I am not fond of the idea of Urth=Blue/Lune=Green, and my\nobservation doesn't compel that reading, if I'm correct, then Blue and\nGreen\nare linked in a way that I can only account for if one is orbiting the\nother. In other words, Blue and Green can not be independent bodies\norbiting\nthe sun in the manner of, say, Mars, Earth, and Venus.\n\nIIRC, we are told at the beginning of OBW that conjunction is two years\naway. We are also told that at its closest approach, at conjunction, that\nGreen is some 35,000 leagues (105,000 miles) from Blue. Conjunction took\nplace while Silkhorn was in Gaon. The war between Blanko and Soldo took\nplace only a matter of weeks after Silkhorn left Gaon. During that war,\nSfido told Incanto that Gagliardo had calculated that Green was then over\n80,000 leagues (about 250,000 miles) from Blue. Hide, at about that same\ntime, told Incanto that Horn had been gone for three years. Therefore, at\nthat time, conjunction was one year past. Therefore, in the year since\nconjunction, Green had diverged only about 145,000 miles from Blue. We are\ntold that conjunction occurs every six years.Therefore, at the mid-point\nbetween conjunctions, Green would have to be at its greatest distance from\nBlue. Orbital velocities tend to remain fairly constant, afaik. So, based\non\nthe numbers above, Green would never be more than about 540,000 miles from\nBlue." }, { "kind": "quote", "depth": 1, "text": "Velocities are a little tricky in that they do change: it is \"equal area in\nequal time,\" with the \"area\" in this case being the triangle created by\nplanet at point 1, point 2, and the primary star. Line between point 1 and\npoint 2 being the segment of the orbit. The world does speed up at closest\nencounter and slow down at furthest point.\n\nSo anyway, we are given that the closest is 105,000 miles, and you are\nsaying that based on the movement in one year the maximum separation is\n540,000 miles; the average would be 322,500 miles." }, { "kind": "quote", "depth": 2, "text": "I'm no expert on celestial mechanics, but I find it hard to believe that\ntwo\nplanets, effectively in the same orbital plane and the same distance from\nthe sun, could exist that close together without the planets orbiting each\nother, or one body being a satellite of the other. No? Where am I wrong?" }, { "kind": "text", "depth": 0, "text": "Is" }, { "kind": "quote", "depth": 2, "text": "Green Blue's moon?" }, { "kind": "quote", "depth": 1, "text": "I'm no expert, but I do like to play with these things. In the past I\nwondered online whether it could possibly be that weird \"dosey-do\" trick\nthat some of the Jovian moons do--two worldlets in the same orbit, they\nswing by each other and exchange orbits: the slightly lower/faster one\nchanging places with the higher/slower one. This is a boggling thing in\nthe real world!\n\nIt doesn't seem to match Blue/Green, because it would happen every year or\nless.\n\nToday, with your new numbers, I'm wondering if Green is in a weird orbit\nbetween Blue and Blue's \"trojan point.\" Because otherwise it is very\ndifficult to see how a normal satellite could take six years to come so\nclose and then back off again. (No, the trojan point idea is impossible:\nthe trojan point is where forces are cancelled out--it is not a gravity\npoint, and as such it has no attraction)\n\nIn dealing with satellites it is often handy to use \"planetary radii.\" If\nwe give Blue a radius of 3960 miles (ala Earth), then hey!\n\nRoy's Green Orbit\n105,000 miles = 26.51 radii\n322,500 miles = 81.44 radii\n540,000 miles = 136.36 radii\n\nA large moon is expected to orbit an earthlike planet between 10 and 80\nradii, so this looks quite promising! (FWIW the Roche Limit is around 2.89\nradii: that point where worlds are torn up into confetti.)\n\nOrbital period (in days) for moon = .0074 * sqrt (R^3/M)\n\nWhere R = orbit in thousands of miles\nWhere M = sum of planet and moon in Earth masses.\n\nFiguring that Green is equal to Blue, then let M = 2.\n\nThis gives an answer of . . .\n\n30 days.\n\n6 years = 2191.5 days\n\nWe can solve this for M, which would then give us the mass of Green!\n\nShot in the dark: M = 1.5 . . . 35 days.\n\nShot in the dark: M = 1.16 (like Earth + Mars) . . . 40 days.\n\nThird shot: M = 1 . . . 42.86 days\n\nWell, there's that old problem again! If Green is a satellite of Blue,\norbiting at 322,500 miles, it should complete an orbit in 43 days!\n\nMaybe you should post all of this to the list--I didn't think I'd get so\nwrapped up in it so quickly.\n\n=M=" }, { "kind": "text", "depth": 0, "text": "-Roy" } ] }, { "message_id": "", "from": { "name": "Adam Stephanides", "address": "adamsteph at earthlink.net" }, "date": "2002-03-28T21:20:38+00:00", "subject": "Re: (urth) Blue moon", "in_reply_to": "", "reply_link": "subject", "blocks": [ { "kind": "text", "depth": 0, "text": "on 3/25/02 5:19 PM, Roy C. Lackey at rclackey at stic.net wrote:\n\nThanks for digging these figures up! They indeed present serious\ndifficulties. " }, { "kind": "quote", "depth": 3, "text": "IIRC, we are told at the beginning of OBW that conjunction is two years\naway. We are also told that at its closest approach, at conjunction, that\nGreen is some 35,000 leagues (105,000 miles) from Blue. Conjunction took\nplace while Silkhorn was in Gaon. The war between Blanko and Soldo took\nplace only a matter of weeks after Silkhorn left Gaon. During that war,\nSfido told Incanto that Gagliardo had calculated that Green was then over\n80,000 leagues (about 250,000 miles) from Blue. Hide, at about that same\ntime, told Incanto that Horn had been gone for three years. Therefore, at\nthat time, conjunction was one year past. Therefore, in the year since\nconjunction, Green had diverged only about 145,000 miles from Blue. We are\ntold that conjunction occurs every six years.Therefore, at the mid-point\nbetween conjunctions, Green would have to be at its greatest distance from\nBlue. Orbital velocities tend to remain fairly constant, afaik. So, based\non\nthe numbers above, Green would never be more than about 540,000 miles from\nBlue." }, { "kind": "text", "depth": 0, "text": "This last bit doesn't follow. It's true that orbital velocities tend to\nremain fairly constant if the orbit is approximately circular. But it\ndoesn't follow that the rate at which the distance between two planets\nchanges remains fairly constant (and indeed, it doesn't). But still, your\nnumbers do indeed rule out the idea of Blue and Green having independent\norbits around the Short Sun, I think.\n\nSuppose that they do have independent orbits. Conjunction is every six\nyears, so six Blue years equal either five or seven Green years. Hence the\ntime between conjunction and Gagliardo's observation is either five-sixth or\nseven-sixth of a Green year. In either case, the distance between\nconjunction and the position Green is in at Gagliardo's observation (call it\nposition A) is the distance Green travels in one-sixth of a Green year.\n\nNow at conjunction Green is 105,000 miles from Blue. At position A Green is\n250,000 miles from Blue. Hence position A cannot be more than 355,000 miles\nfrom conjunction (actually, we could get an even better estimate, but it's\nnot necessary). If Green's orbit is approximately circular, then simple\ngeometry (think a regular hexagon) shows that Green's distance from the\nShort Sun itself can't be more than 355,000 miles, with Blue's distance not\nmuch more: that is, less than twice the distance from the Earth to the Moon.\n\nThis is impossible. Even if we posit that the Short Sun is a very small,\ndim star, the numbers don't work. Mantis's formula for the orbital period\nof a satellite was:\n\nOrbital period (in days) for moon = .0074 * sqrt (R^3/M), where M is the\ncombined mass of the two bodies in Earth masses.\n\nApplying this to Blue and the Short Sun, and assuming Blue's year to be\nclose in length to an Earth year, we find that for Blue to be less than\ntwice the distance from the Short Sun that the Moon is from the Earth, and\nyet have an orbital period twelve times as long, the total mass of Blue and\nthe Short Sun would have to be a small fraction of the Earth's mass.\n\nAs mantis points out, when orbits are not circular orbital velocity is not\nconstant, so by assuming that Green's orbit is eccentric we can push Green\nand Blue farther out. But doing so raises other, insuperable problems. Say\nwe want to push Green at conjunction, and hence Blue, out to 35 million\nmiles. This is probably still too close, assuming the Short Sun is\napproximately like our own (Earth is 83 million miles from the sun, iirc),\nbut it's convenient to work with, and more than sufficient for our purposes.\nIf Green is 35 million miles from the Short Sun at its farthest point, its\norbit must be at least 70 million miles in length. Since Green goes 355,000\nmiles in a sixth of a year, it is covering 1/200 of its orbit during this\nperiod. In other words, Green's orbital velocity near conjunction is about\n1/33 of its average velocity. As mantis says, planets sweep out equal areas\nin equal times. This means, if I'm not mistaken, that\n\norbital velocity at perihelion distance from sun at apohelion\n------------------------------ = ------------------------------\norbital velocity at apohelion distance from sun at perihelion\n\nHence, Green's distance from the Short Sun at perihelion can be no more than\n1/33 of its distance at apohelion, or approximately one million miles. The\ncomplex flora on Green could not possibly survive such an eccentric orbit.\n\nWhat about combining a reasonably eccentric orbit with a small, dim, Short\nSun? Some very rough calculations (which I won't bother to write down)\nsuggest that that won't work either. Even if Green is twice as far at\napohelion as it is at perihelion, this gets the Short Sun's mass up to more\nthan Earth's mass, if that. (It might be objected that if Blue were Ushas,\nthan the Short Sun might be the \"bare\" White Fountain. But what would have\ncaused the sun to shed over 99% of its mass, without rendering Ushas and\nLune uninhabitable?)\n\nMantis's outer Green can't help us either. That would mean that Green was\nnearest to the Short Sun at conjunction, meaning that it was going fastest\nat that point, not slowest, which just makes things worse.\n\nSo if these figures are correct, Green and Blue can't have independent\norbits. But I still don't see how it's possible for Green to be a satellite\nof Blue and have \"conjunction\" every six years: i.e. a six-year \"month.\"\nFor that matter, if Green's \"orbital period\" around Blue is six times as\nlong as Blue's orbital period around the Short Sun, in what sense can Green\nbe said to be a satellite of Blue at all?\n\nI see four possibilities:\n\n1) Green is in one of the \"strange orbits\" me and mantis discussed some time\nback (the discussion should be in the archives somewhere).\n\n2) The time indications are only approximate, and the time between\nconjunction and Gagliardo's observation was really much less than a year.\nAre there any mentions of the seasons? Or has somebody put together a\nchronology for TBOTSS? If one was posted here, I've forgotten.\n\n3) Gagliardo was talking through his hat, and his distances bear no\nrelationship to reality.\n\n4) Wolfe didn't care about the astronomical plausibility of his \"solar\nsystem,\" any more than he did about the physiological plausibility of his\ninhumi reaching escape velocity unaided.\n\nI'm leaning more and more towards 4).\n\n--Adam" } ] }, { "message_id": "", "from": { "name": "Roy C. Lackey", "address": "rclackey at stic.net" }, "date": "2002-03-29T05:44:31+00:00", "subject": "Re: (urth) Blue moon", "in_reply_to": "", "reply_link": "subject", "blocks": [ { "kind": "quote", "depth": 1, "text": "From: Adam Stephanides \nDate: Thursday, March 28, 2002 3:19 PM\nSuppose that they do have independent orbits. Conjunction is every six\nyears, so six Blue years equal either five or seven Green years. Hence the\ntime between conjunction and Gagliardo's observation is either five-sixth\nor\nseven-sixth of a Green year. In either case, the distance between\nconjunction and the position Green is in at Gagliardo's observation (call\nit\nposition A) is the distance Green travels in one-sixth of a Green year.\n\nNow at conjunction Green is 105,000 miles from Blue. At position A Green\nis\n250,000 miles from Blue. Hence position A cannot be more than 355,000\nmiles\nfrom conjunction (actually, we could get an even better estimate, but it's\nnot necessary). If Green's orbit is approximately circular, then simple\ngeometry (think a regular hexagon) shows that Green's distance from the\nShort Sun itself can't be more than 355,000 miles, with Blue's distance not\nmuch more: that is, less than twice the distance from the Earth to the\nMoon.\n\nThis is impossible. [snip]" }, { "kind": "text", "depth": 0, "text": "Huh? I don't follow that. Gagliardo's numbers don't say anything about the\nlength of either body's solar orbit that I can see. His numbers indicate\nthat at your position A the two bodies have _diverged_ by about 145,000\nmiles since conjunction. In that one year interval both bodies have also\ncircumnavigated the sun. Two years later Blue and Green will have attained\nmaximum separation, a distance af about 540,000 miles, then start gradually\ngetting closer together until the next conjunction.\n\nIn other words, for the two bodies to be in independent orbits, those orbits\nwould have to be almost congruent--almost, but not quite. Think of the two\nbodies as twin planets, traveling almost in tandem around the sun. The\nattraction of one body for the other causes minor changes in their orbital\nvelocities, which average out over a six-year cycle, but account for the\nfluctuation in distance between the two bodies during the cycle. Or am I\nmissing something so obvious I can't see it?" }, { "kind": "quote", "depth": 1, "text": "So if these figures are correct, Green and Blue can't have independent\norbits. But I still don't see how it's possible for Green to be a\nsatellite\nof Blue and have \"conjunction\" every six years: i.e. a six-year \"month.\"" }, { "kind": "quote", "depth": 1, "text": "4) Wolfe didn't care about the astronomical plausibility of his \"solar\nsystem,\" any more than he did about the physiological plausibility of his\ninhumi reaching escape velocity unaided.\n\nI'm leaning more and more towards 4)." }, { "kind": "text", "depth": 0, "text": "That seems to be where most here who have an opinion about it are leaning. I\nwould tend to agree--but, Wolfe could have avoided the whole thing by\ninvoking some kind \"magic\" and just left out those numbers, which certainly\nweren't necessary to the plot.\n\n-Roy" } ] }, { "message_id": "", "from": { "name": "Adam Stephanides", "address": "adamsteph at earthlink.net" }, "date": "2002-03-29T20:04:41+00:00", "subject": "Re: (urth) Blue moon", "in_reply_to": "", "reply_link": "subject", "blocks": [ { "kind": "quote", "depth": 1, "text": "on 3/28/02 11:44 PM, Roy C. Lackey at rclackey at stic.net wrote:\nFrom: Adam Stephanides \nDate: Thursday, March 28, 2002 3:19 PM\nSuppose that they do have independent orbits. Conjunction is every six\nyears, so six Blue years equal either five or seven Green years. Hence the\ntime between conjunction and Gagliardo's observation is either five-sixth\nor\nseven-sixth of a Green year. In either case, the distance between\nconjunction and the position Green is in at Gagliardo's observation (call\nit\nposition A) is the distance Green travels in one-sixth of a Green year." }, { "kind": "quote", "depth": 2, "text": "Now at conjunction Green is 105,000 miles from Blue. At position A Green\nis\n250,000 miles from Blue. Hence position A cannot be more than 355,000\nmiles\nfrom conjunction (actually, we could get an even better estimate, but it's\nnot necessary). If Green's orbit is approximately circular, then simple\ngeometry (think a regular hexagon) shows that Green's distance from the\nShort Sun itself can't be more than 355,000 miles, with Blue's distance not\nmuch more: that is, less than twice the distance from the Earth to the\nMoon.\n\nThis is impossible. [snip]" }, { "kind": "quote", "depth": 1, "text": "Huh? I don't follow that. Gagliardo's numbers don't say anything about the\nlength of either body's solar orbit that I can see. His numbers indicate\nthat at your position A the two bodies have _diverged_ by about 145,000\nmiles since conjunction. In that one year interval both bodies have also\ncircumnavigated the sun. Two years later Blue and Green will have attained\nmaximum separation, a distance af about 540,000 miles, then start gradually\ngetting closer together until the next conjunction.\n\nIn other words, for the two bodies to be in independent orbits, those orbits\nwould have to be almost congruent--almost, but not quite. Think of the two\nbodies as twin planets, traveling almost in tandem around the sun. The\nattraction of one body for the other causes minor changes in their orbital\nvelocities, which average out over a six-year cycle, but account for the\nfluctuation in distance between the two bodies during the cycle. Or am I\nmissing something so obvious I can't see it?" }, { "kind": "text", "depth": 0, "text": "I was treating Blue and Green as analogous to Earth and Venus: completely\nindependent orbits which remain fixed (i. e. don't oscillate). What you\ndescribe is more like mantis's twin moons chasing each other.\n\nBut I think it's probably hopeless to try and figure out what, if anything,\nWolfe had in mind.\n\n--Adam" } ] } ] }