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Re: {MPML} P100Oms Uranus Trojan?

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  • Alan Harris
    Thoughts: As a rule of thumb, not strict, trojan orbits are more stable with a planet that does not have massive neighbors both inside and outside of it.
    Message 1 of 4 , Jul 27, 2011
      Thoughts: As a rule of thumb, not strict, trojan orbits are more stable
      with a planet that does not have massive neighbors both inside and outside
      of it. Thus, Jupiter, with nothing all the way in to Mars and being the
      most massive planet in the solar system, has a very stable trojan
      zone. Neptune, with no significant mass on the outside, likewise has a
      pretty stable trojan zone (and even a stable 3:2 resonance zone where Pluto
      lives). Uranus is more problematic, with Saturn on the inside and Neptune
      outside, and Saturn likewise, with Jupiter inside and Uranus outside. Mars
      and Earth are marginal. Mars has nothing outside, but is not very massive;
      the Earth has Mars to the outside, but again, it outweighs Mars by a lot so
      it sort of doesn't have much on the outside, all the way to Jupiter.

      Thinking specifically about the claimed Earth trojan, if you have a look at
      the Nature paper, the libration amplitude is almost 180 degrees, that is,
      it librates about the 60-deg L4 point all the way from zero to 180 degrees,
      with a period of about 400 years. In fact, about 1600 years ago, if you
      believe the integrations back that far (you probably shouldn't) it
      "horseshoed", and before that was librating about the L5 point. Now here's
      the problem: the current argument of perihelion is 45 degrees, and the
      eccentricity is substantial. So currently (hundreds to a thousand or so
      years), when the object librates to be almost at the Earth's longitude, it
      doesn't get very close to the Earth because it is far inside or outside of
      the Earth when it is at node, and far above or below the Earth when it is
      at 1 AU. But that doesn't last forever. The period of the trojan
      libration (~400 years) is not commensurate with the period of circulation
      of the argument of perihelion. sooner or later, the libration will carry
      it to the Earth's longitude at a time when the argument of perihelion is
      near 90 (or 270) degrees, and it will make a series of very close passes by
      the Earth, very likely resulting in ejecting it from "trojan"
      configuration. Typically the period of perihelion circulation is some tens
      of thousands of years, so my guess is that this object probably got parked
      in its present configuration some thousands of years ago, and will get
      ejected back out some thousands of years in the future. But as properly
      noted in the Nature paper, the motion is chaotic over only hundreds to a
      thousand years, so one really can't track it 10,000 years and say what will
      actually happen or when. But certainly, this object is not in a stable
      configuration like the current Jupiter Trojan population.

      At 04:32 PM 7/27/2011, Tomas wrote:
      >Could we have a uranus trojan on our hands? The first four sets of
      >observations available on NEOCP currently give the following elements:
      >
      >P100Oms
      > Perihelion 2053 May 26.294451 TT = 7:04:00 (JD 2471048.794451)
      >Epoch 2011 Jul 27.0 TT = JDT 2455769.5 Ur: 0.7678 Find_Orb
      >M 180.00780 (2000.0) P Q
      >n 0.01178013 Peri. 333.53195 -0.73404352 -0.67826697
      >a 19.1294492 Node 163.61868 0.64231709 -0.70952696
      >e 0.1244084 Incl. 6.85767 0.22047418 -0.19111616
      >P 83.67 H 8.5 G 0.15 q 16.7495849 Q 21.5093135
      > From 12 observations 2011 July 25-27; RMS error 0.391 arcseconds
      >
      >Which would place the object into a zone of stability as described by
      >Dvorak, R.; Bazsó, Á.; Zhou, L.-Y. in Where are the Uranus Trojans?
      >
      >http://adsabs.harvard.edu/abs/2010CeMDA.107...51D
      >
      >any thoughts
      >
      >
      >
      >------------------------------------
      >
      >~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
      >
      >Posts to this list or information found within may be freely used, with
      >the stipulation that MPML and the originating author are cited as the
      >source of the information.Yahoo! Groups Links
      >
      >
      >
      *******************************************************************
      Alan W. Harris
      Senior Research Scientist
      Space Science Institute
      4603 Orange Knoll Ave. Phone: 818-790-8291
      La Canada, CA 91011-3364 email: awharris@...
      *******************************************************************
    • Bill J Gray
      Hi Tomas, My apologies; Find_Orb has misled you here. With this short an arc and this great a distance, the orbit is almost completely indeterminate.
      Message 2 of 4 , Jul 27, 2011
        Hi Tomas,

        My apologies; Find_Orb has misled you here.

        With this short an arc and this great a distance, the
        orbit is almost completely indeterminate. (Except to say
        that it's probably pretty darn far off.) In such cases,
        Find_Orb just tries some Vaisala orbits and looks for one
        that has the closest to "reasonable" results. In this
        case, it's putting the object near aphelion (note the
        M=180) at about 21.5 AU.

        This should serve well for finding the object on another
        night, but it's probably not close to the real orbit.

        The current "in development" version of Find_Orb shows
        the U parameter for better-determined orbits. In this case,
        it should probably show "U V", or "U (huge)", just to
        warn you that Find_Orb is guessing.

        -- Bill
      • andrew_j_walker
        A strange coincidence, here http://www.minorplanetcenter.net/mpec/K11/K11O47.html and here http://www.minorplanetcenter.net/iau/lists/NeptuneTrojans.html 2004
        Message 3 of 4 , Jul 28, 2011
          A strange coincidence, here http://www.minorplanetcenter.net/mpec/K11/K11O47.html

          and here

          http://www.minorplanetcenter.net/iau/lists/NeptuneTrojans.html

          2004 KV18 is the second known Neptune Trojan at L5. There have been
          a number of new TNOs announced by this group over the last few weeks
          based on old observations, maybe they been using better detection
          software?

          Andrew

          --- In mpml@yahoogroups.com, Alan Harris <awharris@...> wrote:
          >
          > Thoughts: As a rule of thumb, not strict, trojan orbits are more stable
          > with a planet that does not have massive neighbors both inside and outside
          > of it. Thus, Jupiter, with nothing all the way in to Mars and being the
          > most massive planet in the solar system, has a very stable trojan
          > zone. Neptune, with no significant mass on the outside, likewise has a
          > pretty stable trojan zone (and even a stable 3:2 resonance zone where Pluto
          > lives). Uranus is more problematic, with Saturn on the inside and Neptune
          > outside, and Saturn likewise, with Jupiter inside and Uranus outside. Mars
          > and Earth are marginal. Mars has nothing outside, but is not very massive;
          > the Earth has Mars to the outside, but again, it outweighs Mars by a lot so
          > it sort of doesn't have much on the outside, all the way to Jupiter.
          >
          > Thinking specifically about the claimed Earth trojan, if you have a look at
          > the Nature paper, the libration amplitude is almost 180 degrees, that is,
          > it librates about the 60-deg L4 point all the way from zero to 180 degrees,
          > with a period of about 400 years. In fact, about 1600 years ago, if you
          > believe the integrations back that far (you probably shouldn't) it
          > "horseshoed", and before that was librating about the L5 point. Now here's
          > the problem: the current argument of perihelion is 45 degrees, and the
          > eccentricity is substantial. So currently (hundreds to a thousand or so
          > years), when the object librates to be almost at the Earth's longitude, it
          > doesn't get very close to the Earth because it is far inside or outside of
          > the Earth when it is at node, and far above or below the Earth when it is
          > at 1 AU. But that doesn't last forever. The period of the trojan
          > libration (~400 years) is not commensurate with the period of circulation
          > of the argument of perihelion. sooner or later, the libration will carry
          > it to the Earth's longitude at a time when the argument of perihelion is
          > near 90 (or 270) degrees, and it will make a series of very close passes by
          > the Earth, very likely resulting in ejecting it from "trojan"
          > configuration. Typically the period of perihelion circulation is some tens
          > of thousands of years, so my guess is that this object probably got parked
          > in its present configuration some thousands of years ago, and will get
          > ejected back out some thousands of years in the future. But as properly
          > noted in the Nature paper, the motion is chaotic over only hundreds to a
          > thousand years, so one really can't track it 10,000 years and say what will
          > actually happen or when. But certainly, this object is not in a stable
          > configuration like the current Jupiter Trojan population.
          >
          > At 04:32 PM 7/27/2011, Tomas wrote:
          > >Could we have a uranus trojan on our hands? The first four sets of
          > >observations available on NEOCP currently give the following elements:
          > >
          > >P100Oms
          > > Perihelion 2053 May 26.294451 TT = 7:04:00 (JD 2471048.794451)
          > >Epoch 2011 Jul 27.0 TT = JDT 2455769.5 Ur: 0.7678 Find_Orb
          > >M 180.00780 (2000.0) P Q
          > >n 0.01178013 Peri. 333.53195 -0.73404352 -0.67826697
          > >a 19.1294492 Node 163.61868 0.64231709 -0.70952696
          > >e 0.1244084 Incl. 6.85767 0.22047418 -0.19111616
          > >P 83.67 H 8.5 G 0.15 q 16.7495849 Q 21.5093135
          > > From 12 observations 2011 July 25-27; RMS error 0.391 arcseconds
          > >
          > >Which would place the object into a zone of stability as described by
          > >Dvorak, R.; Bazsó, Á.; Zhou, L.-Y. in Where are the Uranus Trojans?
          > >
          > >http://adsabs.harvard.edu/abs/2010CeMDA.107...51D
          > >
          > >any thoughts
          > >
          > >
          > >
          > >------------------------------------
          > >
          > >~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
          > >
          > >Posts to this list or information found within may be freely used, with
          > >the stipulation that MPML and the originating author are cited as the
          > >source of the information.Yahoo! Groups Links
          > >
          > >
          > >
          > *******************************************************************
          > Alan W. Harris
          > Senior Research Scientist
          > Space Science Institute
          > 4603 Orange Knoll Ave. Phone: 818-790-8291
          > La Canada, CA 91011-3364 email: awharris@...
          > *******************************************************************
          >
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