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Thursday, March 19, 2015

Again on comet D/1770 L1 (Lexell)

Year 1757.

Three comets:

  • D/1770 L1 (Lexell)
  • P/2014 R5 (Lemmon-PANSTARRS)
  • P/1999 RO28 (LONEOS)
Let's compare their nominal distance using JPL Horizons and Mercury6 software by John E. Chambers.

According to Mercury6 software, on 1757-Jul-1, the Lexell comet was at 0.33 (AU) from comet P/2014 R5 (Lemmon-PANSTARRS) and it was  at 0.16 (AU) from  comet P/1999 RO28 (LONEOS).

JPL Horizons models the Lexell comet in a different way.
According to JPL Horizons, the Lexell comet was at 1.53 (AU) from comet P/2014 R5 (Lemmon-PANSTARRS) and it was at 1.61 (AU) from  comet P/1999 RO28 (LONEOS).

Both JPL Horizons and Mercury agree and get the same result when looking  at the nominal distance between P/2014 R5 (Lemmon-PANSTARRS) and P/1999 RO28 (LONEOS).

Comet P/2014 R5 (Lemmon-PANSTARRS)
   X     Y     Z
   VX    VY    VZ
   LT    RG    RR
2362988.500000000 = A.D. 1757-Jul-17 00:00:00.0000 (CT)
  -5.257637317706235E+00  2.477814508385187E-01  6.790907841994050E-02
   1.426562748323473E-03 -5.796128684565190E-03  2.940516606550701E-05
   3.040181361915521E-02  5.263910851719347E+00 -1.697317088053800E-03

Comet P/1999 RO28 (LONEOS)
   X     Y     Z
   VX    VY    VZ
   LT    RG    RR
2362988.500000000 = A.D. 1757-Jul-17 00:00:00.0000 (CT)
  -5.430809043797567E+00  3.084110607570195E-01 -7.118879844782251E-02
   2.327107819955809E-04 -4.558198020424996E-03  2.130564382053195E-03
   3.141896416246138E-02  5.440025008914496E+00 -5.186150467730436E-04

Nominal distance (according to JPL Horizons): 0.23 (AU)
I get the same result using Mercury6 orbit simulator.

Given the orbit uncertainty that I am unable to evaluate, the idea that these comets are related is still a speculation.

I do not know if MPC should be involved in a case like this.

However, It would be nice to investigate this matter in a deeper way.

Kind Regards,
Alessandro Odasso

1 comment:

  1. Interesting comment received from Bill Gray:

    Hi Alessandro,

    Just a few comments in reply...

    Here's what I get for P/1999 RO28 for that date in 1757 :

    Orbital elements: P/1999 RO28
    Perihelion 1754 May 26.576772 +/- 1014 TT = 13:50:33 (JD 2361841.076772)
    Epoch 1757 Jul 17.0 TT = JDT 2362988.5 Earth MOID: 0.5950 Ju: 0.0640
    M 170.931837 +/- 140 Find_Orb
    n 0.148970173 +/- 0.016 Peri. 174.660964 +/- 2.4
    a 3.524275352 +/- 0.255 Node 178.284714 +/- 170
    e 0.54644962 +/- 0.0914 Incl. 25.274719 +/- 5.6
    P 6.62 M(N) 20.5 K 10.0 U 10.5
    q 1.598436419 +/- 0.382 Q 5.450114285 +/- 0.0599
    107 of 109 observations 1999 Sept. 7-Nov. 13; mean residual 0".70
    # State vector (heliocentric ecliptic J2000):
    # -5.355787260104 0.889402950047 -0.344056947875 AU
    # -1.195678515894 -4.367823707766 2.078277947583 mAU/day

    You'll notice that the state vector isn't particularly close to the
    JPL one. That's not terribly surprising; the mean anomaly has a sigma
    of 140 degrees, i.e., "it could be just about anywhere". The low
    MOID with Jupiter would mean that it might have had a close encounter
    somewhere in between, and the effect would multiply (possibly chaotically)
    over the decades/centuries. JPL probably excluded more/fewer observations
    and weighted them differently.

    P/2014 R5 seems to be much more tightly constrained, so
    (unsurprisingly) we get something that agrees with JPL much more closely :

    Orbital elements: P/2014 R5
    Perihelion 1760 Apr 1.754697 +/- 0.624 TT = 18:06:45 (JD 2363978.254697)
    Epoch 1757 Jul 17.0 TT = JDT 2362988.5 Ju: 0.0545 Find_Orb
    M 231.022554 +/- 0.12
    n 0.130312536 +/- 4.33e-5 Peri. 212.712292 +/- 0.022
    a 3.853114516 +/- 0.000853 Node 122.105019 +/- 0.015
    e 0.45175966 +/- 7.15e-5 Incl. 0.900181 +/- 0.0006
    P 7.56 M(N) 14.3 K 10.0 U 6.1
    q 2.112432781 +/- 0.000737 Q 5.593796252 +/- 0.000974
    106 of 109 observations 2014 Sept. 7-Nov. 18; mean residual 0".55
    # State vector (heliocentric ecliptic J2000):
    # -5.257601360037 0.247397796243 0.067910675529 AU
    # 1.427285180724 -5.796163583128 0.029405574386 mAU/day

    Both JPL and I are neglecting non-gravitational effects here, which
    is probably not a great idea. I've thought about attempting to include
    them, perhaps by telling Find_Orb that they have been "observed" to have
    certain values with certain sigmas, with those values and sigmas simply
    rough guesses as to what range a typical comet chunk might have.

    However, I really don't think that's going to get a link with
    Lexell, because the velocity is all wrong. Unless you're thinking
    that P/2014 R5 broke off from Lexell in some very explosive manner,
    the two really should have velocities that at least resemble each
    other, and they don't.

    I can't do a similar analysis of elements for Lexell... I've
    no idea where the astrometry is (short of digging out original sources
    that may not even be scanned in, then doing a little data entry).
    It _would_ be interesting to see a natural object in Find_Orb that
    actually had a seriously hyperbolic heliocentric orbit...

    -- Bill


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