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P100Oms Uranus Trojan?

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  • Tomas
    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
    Message 1 of 4 , Jul 27, 2011
      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
    • 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 2 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 3 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 4 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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