Sam hat Bahnelemente gegeben. Hier seine Mail von der Kometenmailing-Liste.
Hi all,
Alright, this ended up being so much more elaborate than I expected it to be- including me manually transcribing a few hundred old Minor Planet Circular observations, only to find they're already easily published in the existing observations data, analyzing offset data, and reconciling lost comet fragments.
First of all, a brief description of things for context to everyone:
141P/Machholz 2 was discovered in on August 13, 1994 by Don Machholz, and quickly followed up by a number of observatories. It was observed well over the next several weeks until August 30th, when four secondary objects were found, designated 141P-b through 141P-e (with the original being redesignated 141P-a. It's worth noting that for all intents and purposes 141P-a is the exact same object as 141P, despite being listed as separate objects by the MPC and JPL)
141P AKA 141P-a has been observed reliably in 1994, 1999-2000, 2015, and 2020, consistently around the same brightness/slope since the 1999 opposition.
141P-b was quite well observed in 1994, being seen until November 10, with 43 observations.
141P-c was decently well observed in 1994, being seen until October 11, with 22 observations. It seems to have hung around fragment d, although a decent bit to the south. I estimate it probably split off from D in 1989.
141P-d was very well observed in both 1994 and 1999, with 161 observations.
141P-e was poorly observed in 1994, being seen until September 10, with 7 observations.
On october 5th, two more fragments (141p-f and 141p-g) were discovered:
141P-f was decently observed in 1994, being seen until November 2, with 12 observations. I should note that it never moved more than a couple of arcseconds from 141P-d and likely split from 141P-d during the 1994 apparition.
141P-g was poorly observed in 1994, being seen until October 11, with 6 observations.
Then, lastly, on August 17th, 2015, the final fragment, 141P-h was discovered:
141P-h was very well observed in 2015, being seen until September 15, with 91 observations.
---
I did some calculating on these fragments- their distance from 141P during 1994, 1999, 2015, and 2020. Based on these, I think I can identify Michael's objects, as well as some others.
141P-h in 2015 is the same object as 141P-b as observed in 1994, as well as Michael's 141PB:
Perihelion 1994 Sep 18.865354 +/- 0.000441 TT = 20:46:06 (JD 2449614.365354)
A1: 2.63e-9 +/- 9.69e-10 A2: -7.72e-10 +/- 4.06e-12 AU/day^2
Epoch 1994 Nov 10.0 TT = JDT 2449666.5 Earth MOID: 0.1058 Ju: 0.6243
M 9.82552507 +/- 0.00013 Ve: 0.0676 Find_Orb
n 0.18846440 +/- 1.84e-6 Peri. 149.25697 +/- 0.0009
a 3.01288917 +/- 1.96e-5 Node 246.17610 +/- 0.0008
e 0.7502236 +/- 1.3e-6 Incl. 12.78694 +/- 0.00031
P 5.23 M(N) 20.3 K 10.0 U 3.9
q 0.75254836 +/- 2.12e-6 Q 5.27322999 +/- 3.79e-5
From 136 observations 1994 Aug. 30-2020 Dec. 7; mean residual 3".63
ephemerides for the next few days:
#Geocentric
Date (UTC) HH RA Dec delta r elong mag '/hr PA " sig PA
---- -- -- -- ------------- ----------- ------ ------ ----- --- ------ ------ ---- ---
2020 12 09 00 20 39 01.650 -09 40 35.76 .80190 .81382 53.0 19.0 2.83 88.0 54.7 92
2020 12 09 06 20 40 10.628 -09 39 59.48 .79916 .81334 53.0 19.0 2.84 88.0 55.2 92
2020 12 09 12 20 41 19.886 -09 39 23.19 .79641 .81288 53.0 19.0 2.85 88.0 55.6 92
2020 12 09 18 20 42 29.426 -09 38 46.91 .79367 .81244 53.0 18.9 2.86 88.0 56.1 93
2020 12 10 00 20 43 39.250 -09 38 10.63 .79093 .81203 53.1 18.9 2.88 88.0 56.6 93
2020 12 10 06 20 44 49.360 -09 37 34.35 .78819 .81163 53.1 18.9 2.89 88.0 57.0 93
2020 12 10 12 20 45 59.759 -09 36 58.09 .78545 .81125 53.1 18.9 2.90 88.0 57.5 94
2020 12 10 18 20 47 10.448 -09 36 21.83 .78272 .81090 53.1 18.9 2.91 88.0 58.0 94
2020 12 11 00 20 48 21.429 -09 35 45.59 .77998 .81056 53.2 18.9 2.92 88.0 58.5 94
2020 12 11 06 20 49 32.706 -09 35 09.36 .77725 .81025 53.2 18.9 2.94 88.0 59.0 95
2020 12 11 12 20 50 44.279 -09 34 33.14 .77453 .80995 53.2 18.9 2.95 88.0 59.6 95
2020 12 11 18 20 51 56.152 -09 33 56.94 .77180 .80968 53.2 18.9 2.96 88.1 60.1 95
2020 12 12 00 20 53 08.326 -09 33 20.75 .76908 .80942 53.3 18.9 2.97 88.1 60.6 96
2020 12 12 06 20 54 20.803 -09 32 44.59 .76636 .80919 53.3 18.9 2.99 88.1 61.2 96
2020 12 12 12 20 55 33.587 -09 32 08.44 .76364 .80898 53.3 18.8 3.00 88.1 61.8 96
2020 12 12 18 20 56 46.678 -09 31 32.31 .76093 .80879 53.4 18.8 3.01 88.1 62.3 97
2020 12 13 00 20 58 00.080 -09 30 56.19 .75822 .80862 53.4 18.8 3.02 88.1 62.9 97
2020 12 13 06 20 59 13.794 -09 30 20.10 .75551 .80847 53.4 18.8 3.04 88.1 63.5 97
2020 12 13 12 21 00 27.823 -09 29 44.02 .75281 .80834 53.5 18.8 3.05 88.1 64.2 98
2020 12 13 18 21 01 42.170 -09 29 07.97 .75011 .80823 53.5 18.8 3.06 88.1 64.8 98
Similarly, Michael's 141PA is 141P-d, which was not observed in 2015 expect because it's much further from the main comet than b. Still, here is the linked orbit:
Perihelion 1999 Dec 9.953475 +/- 0.00116 TT = 22:53:00 (JD 2451522.453475)
A1: 2.89e-9 +/- 8.91e-10 A2: -6.9e-10 +/- 2.53e-12 AU/day^2
Epoch 1999 Nov 26.0 TT = JDT 2451508.5 Earth MOID: 0.1078 Ju: 0.6266
M 357.36517741 +/- 0.00017 Ve: 0.0645 Find_Orb
n 0.18882913 +/- 3.84e-6 Peri. 149.29849 +/- 0.00055
a 3.00900823 +/- 4.08e-5 Node 246.13606 +/- 0.00056
e 0.7510970 +/- 3.29e-6 Incl. 12.81145 +/- 0.00012
P 5.22 M(N) 19.6 K 10.0 U 4.4
q 0.74895107 +/- 7.04e-7 Q 5.26906539 +/- 8.13e-5
From 171 observations 1994 Aug. 30-2020 Dec. 7; mean residual 2".09
and ephemerides for the next dfew days as well:
#Geocentric
Date (UTC) HH RA Dec delta r elong mag '/hr PA " sig PA
---- -- -- -- ------------- ----------- ------ ------ ----- --- ------ ------ ---- ---
2020 12 09 00 20 37 39.436 -09 40 05.14 .82493 .81573 52.7 18.3 2.80 87.5 23.4 91
2020 12 09 06 20 38 47.794 -09 39 21.35 .82219 .81518 52.7 18.3 2.82 87.5 23.5 92
2020 12 09 12 20 39 56.422 -09 38 37.48 .81945 .81464 52.7 18.3 2.83 87.5 23.7 92
2020 12 09 18 20 41 05.323 -09 37 53.53 .81671 .81413 52.7 18.3 2.84 87.5 23.9 92
2020 12 10 00 20 42 14.497 -09 37 09.52 .81397 .81364 52.8 18.3 2.85 87.5 24.1 93
2020 12 10 06 20 43 23.947 -09 36 25.43 .81123 .81316 52.8 18.3 2.86 87.5 24.3 93
2020 12 10 12 20 44 33.675 -09 35 41.27 .80850 .81271 52.8 18.3 2.87 87.6 24.5 93
2020 12 10 18 20 45 43.682 -09 34 57.05 .80576 .81228 52.8 18.3 2.88 87.6 24.7 94
2020 12 11 00 20 46 53.971 -09 34 12.76 .80303 .81187 52.8 18.3 2.90 87.6 24.9 94
2020 12 11 06 20 48 04.544 -09 33 28.41 .80030 .81147 52.9 18.3 2.91 87.6 25.1 94
2020 12 11 12 20 49 15.402 -09 32 44.00 .79757 .81110 52.9 18.2 2.92 87.6 25.3 95
2020 12 11 18 20 50 26.548 -09 31 59.53 .79484 .81075 52.9 18.2 2.93 87.6 25.5 95
2020 12 12 00 20 51 37.983 -09 31 15.01 .79212 .81042 52.9 18.2 2.94 87.6 25.7 95
2020 12 12 06 20 52 49.710 -09 30 30.42 .78940 .81011 53.0 18.2 2.96 87.6 25.9 95
2020 12 12 12 20 54 01.730 -09 29 45.78 .78668 .80982 53.0 18.2 2.97 87.6 26.1 96
2020 12 12 18 20 55 14.046 -09 29 01.08 .78396 .80955 53.0 18.2 2.98 87.6 26.4 96
2020 12 13 00 20 56 26.659 -09 28 16.33 .78125 .80930 53.1 18.2 2.99 87.6 26.6 96
2020 12 13 06 20 57 39.572 -09 27 31.52 .77854 .80908 53.1 18.2 3.01 87.6 26.8 97
2020 12 13 12 20 58 52.787 -09 26 46.66 .77583 .80887 53.1 18.2 3.02 87.6 27.1 97
2020 12 13 18 21 00 06.306 -09 26 01.75 .77313 .80868 53.2 18.2 3.03 87.6 27.3 97
So, in summary:
141P (1994, 1999, 2005, 2015) = 141P
141P-b (1994) = 141P-h (2015) = Michael's 141PB
141P-d (1994, 1999) = Michael's 141PA
(annotated version of Michael's image labelling the fragments for maximum clarity:
https://i.imgur.com/ZkYXlXn.png )
And lastly, as for what Dr. Clay saw, if it was indeed a real thing, I would guess it's fragment c. The location I think he's potinting to matches up decently, and the 1994 observations show it being around 1-1.5 mags dimmer than d, which matches up pretty well with it being barely detectable in this image.
Ultimately we'll have to see if my identifications are correct, as linking comet bits with nongravs on the order of 3E-9 / -7E10 au^2/day over 25 years turns out to be quite the tricky challenge. More detailed observation of these fragments over the next ~week or so should allow one to confidently tell if they're as I think. Additionally, even with all this work, this leaves e, f, and g unaccounted for. The fact that b/h, c, and d seem to remain intact gives good indication that efg should still be around as well, albeit quite dim. e should be a fair bit further southeast than even b/h, f should be hanging quite close to d, and g should be hanging around the west of the main comet.
(BTW if anyone wants to be sent the orbits and observations of all of the fragments found to date, I would be happy to send privately but would rather not clog this already-long post with all of that data)
~Sam