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Re: R: {MPML} NASA's Wise Mission Finds First Trojan Asteroid Sharing Earth's Orbit

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  • Aldo
    Just an update: I keep the integration going, and I m finding that the stability of this Trojan does not last for long. Around 12000 years from present, some
    Message 1 of 10 , Jul 28, 2011
      Just an update:

      I keep the integration going, and I'm finding that the stability of this Trojan does not last for long.
      Around 12000 years from present, some clones step over the L3 point, switching to a "horseshoe" path, and some are even captured on the opposite side, becoming L5 trojans ...

      Aldo Vitagliano
    • Alan Harris
      Aldo, This is consistent with what I suggested yesterday regarding the precession of the perihelion longitude and the libration resonance. If you are tracking
      Message 2 of 10 , Jul 28, 2011
        Aldo,

        This is consistent with what I suggested yesterday regarding the precession
        of the perihelion longitude and the libration resonance. If you are
        tracking the argument of perihelion, is it the case that around 12000 years
        from now it is close to 90 degrees or 270 degrees, resulting in very close
        Earth encounters every 400 years or so when the libration longitude goes to
        near-zero? Of course the situation is far too chaotic to make a firm
        prediction of what happens, but at least it indicates about when the
        ejection from trojan space is likely to occur. Likewise, integrating back
        in time you should find a similar alignment of argument of parihelion near
        90 or 270 degrees when close passes occurred. That is likely about the
        time when the object became captured in trojan space from an ordinary
        Earth-crossing NEA.

        cheers,

        Alan

        At 06:10 AM 7/28/2011, Aldo wrote:
        >Just an update:
        >
        >I keep the integration going, and I'm finding that the stability of this
        >Trojan does not last for long.
        >Around 12000 years from present, some clones step over the L3 point,
        >switching to a "horseshoe" path, and some are even captured on the
        >opposite side, becoming L5 trojans ...
        >
        >Aldo Vitagliano
        >
        >
        >
        >
        >------------------------------------
        >
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        *******************************************************************
        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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      • Aldo
        ... Mmm ... around 12000 years from now, the argument of perihelion of all the clones is in the range 130-140 degrees. On the other hand, approaches to Earth
        Message 3 of 10 , Jul 29, 2011
          --- In mpml@yahoogroups.com, Alan Harris <awharris@...> wrote:
          >
          > If you are tracking the argument of perihelion, is it the case
          > that around 12000 years from now it is close to 90 degrees or 270
          > degrees, resulting in very close Earth encounters every 400 years
          > or so when the libration longitude goes to near-zero?
          >

          Mmm ... around 12000 years from now, the argument of perihelion of all the clones is in the range 130-140 degrees. On the other hand, approaches to Earth in the future 20000 years won't be closer than about 23 million km, compared to 29.7 million km of the next approach on December 5, 2011.

          >
          > Of course the situation is far too chaotic to make a firm prediction
          > of what happens ...
          >

          This is quite true. Especially the situation of maximum libration longitude, when the body goes close or even past the L3 point appears to be where chaos is working, and a very tiny perturbation can push the body on one side or the other of the "trojan space" (much like a rigid pendulum turned upside-down in its unstable equilibrium position). Not all the clones are ejected from the L4 trojan region at the same time, some are ejected after 20000 or 30000 years and some are still there after 100000 years, some become L5 trojans (probably switching more than once between the two Lagrange points), some become "horseshoe" companions and some "free circulating" bodies. A few also become temporary "pseudo-satellites" ...

          Regards
          Aldo
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