I refer to this MPML message (and related thread) where we discussed about possible cometary objects captured in trojan like orbits.
Sam Deen has found precovery data for 2015 EL77 - the condition code is now 4.6
I used Find_Orb online by Bill Gray to get the updated nominal orbit
"Pseudo-MPEC" for 2015 EL77
Created 2021 Jan 17 20:37:56 UT using Find_Orb
Astrometry: K15E77L ZC2014 12 10.60290 11 55 11.83 +02 57 42.3 21.5 i F51 K15E77L ZC2014 12 10.63036 11 55 12.83 +02 57 34.7 F51 K15E77L* C2015 03 10.31054 11 55 34.03 +02 03 16.7 21.3 Vo~4A7m691 K15E77L C2015 03 10.32942 11 55 33.38 +02 03 18.8 21.0 Vo~4A7m691 K15E77L C2015 03 10.34830 11 55 32.70 +02 03 22.1 20.6 Vo~4A7m691 K15E77L C2015 03 17.28001 11 51 28.30 +02 21 36.9 20.7 Vq~4A7mG96 K15E77L C2015 03 17.28458 11 51 28.18 +02 21 37.3 20.3 Vq~4A7mG96 K15E77L C2015 03 17.28915 11 51 28.10 +02 21 37.9 x20.5 Vq~4A7mG96 K15E77L C2015 03 17.29372 11 51 27.86 +02 21 39.0 21.1 Vq~4A7mG96 K15E77L C2015 04 10.22495 11 37 57.58 +03 17 25.2 21.8 Vq~4A7mG96 K15E77L C2015 04 10.23007 11 37 57.43 +03 17 26.2 21.3 Vq~4A7mG96 K15E77L C2015 04 10.23518 11 37 57.27 +03 17 25.8 21.1 Vq~4A7mG96 K15E77L C2015 04 10.24029 11 37 57.11 +03 17 26.3 22.1 Vq~4A7mG96 K15E77L C2015 04 11.14392 11 37 31.30 +03 18 58.7 21.2 Vo~4A7m691 K15E77L C2015 04 11.17458 11 37 30.46 +03 19 02.1 21.3 Vo~4A7m691 K15E77L C2015 04 11.20520 11 37 29.57 +03 19 05.2 21.2 Vo~4A7m691 K15E77L C2015 04 15.15549 11 35 43.17 +03 25 04.8 20.9 Vo~4A7m691 K15E77L C2015 04 15.18213 11 35 42.47 +03 25 07.1 21.0 Vo~4A7m691 K15E77L C2015 04 15.20944 11 35 41.76 +03 25 09.4 21.0 Vo~4A7n691 K15E77L C2015 04 17.13591 11 34 54.12 +03 27 37.7 21.2 Vo~4A7n691 K15E77L C2015 04 17.16280 11 34 53.44 +03 27 39.9 21.3 Vo~4A7n691 K15E77L C2015 04 17.18969 11 34 52.71 +03 27 42.1 20.7 Vo~4A7n691 K15E77L C2015 04 20.14344 11 33 45.40 +03 30 51.9 20.7 Vo~4A7n691 K15E77L C2015 04 20.16935 11 33 44.92 +03 30 54.0 20.9 Vo~4A7n691 K15E77L C2015 04 20.19526 11 33 44.26 +03 30 55.6 20.9 Vo~4A7n691 K15E77L C2018 09 05.18753522 57 52.75 -09 53 18.0 22.5 g W84 K15E77L C2018 09 05.30735022 57 48.93 -09 53 36.3 22.0 r W84 K15E77L C2018 10 05.99057922 43 38.70 -10 55 51.7 22.1 z W84 K15E77L C2018 10 05.99231522 43 38.67 -10 55 52.0 22.1 z W84 Station data: (691) Steward Observatory, Kitt Peak - Spacewatch (N31.962189 W111.600340) US/Arizona. Observer J. V. Scotti. 0.9-m f/3 reflector + CCD. (F51) Pan-STARRS 1, Haleakala (N20.707235 W156.255910) US/Hawaii. Observers N. Primak, A. Schultz, S. Watters, J. Thiel, T. Goggia. Measurer PS1 Science Consortium. 1.8-m Ritchey-Chrétien + CCD. (G96) Mt. Lemmon Survey (N32.442754 W110.788720) US/Arizona. Observers B. M. Africano, E. J. Christensen, G. A. Farneth, D. C. Fuls, A. R. Gibbs, A. D. Grauer, H. Gröller, R. E. Hill, J. A. Johnson, R. A. Kowalski, S. M. Larson, G. J. Leonard, R. G. Matheny, R. H. McNaught, R. L. Seaman, F. C. Shelly. 1.5-m reflector + 4K CCD + 10K CCD. (W84) Cerro Tololo-DECam (S30.169661 W70.806525) Chile. 4.0-m f/2.87 reflector + CCD. Orbital elements: 2015 EL77 Perihelion 2016 Jan 25.44272 +/- 0.0186 TT = 10:37:31 (JD 2457412.94272) Epoch 2018 Oct 5.0 TT = JDT 2458396.5 Ju: 0.2017 Auto-Find M 84.64479728 +/- 0.006 (J2000 ecliptic) n 0.08605985 +/- 5.14e-6 Peri. 219.89562 +/- 0.0027 a 5.08084143 +/- 0.000202 Node 6.39360 +/- 0.00039 e 0.2969684 +/- 2.9e-5 Incl. 5.89755 +/- 0.00018 P 11.45 H 15.4 G 0.15 U 4.6 q 3.57199199 +/- 2.1e-5 Q 6.58969086 +/- 0.000409 28 of 29 observations 2014 Dec. 10-2018 Oct. 5; mean residual 0".34
Residuals in arcseconds: 141210 F51 .02+ .44+ 150410 G96 .28+ .67+ 150417 691 .19+ .12+ 141210 F51 .20+ .21- 150410 G96 .17+ .26- 150417 691 .67- .38+ 150310 691 .31- .24+ 150410 G96 .07+ .29- 150420 691 1.1- .67- 150310 691 .02- .58- 150411 691 .63- .14- 150420 691 .46+ .05- 150310 691 .18- .21- 150411 691 .22+ .18+ 150420 691 .66- .07+ 150317 G96 .32- .25+ 150411 691 .34+ .21+ 180905 W84 .13- .20- 150317 G96 .42+ .08- 150415 691 .04+ .09- 180905 W84 .19- .04+ 150317 G96( 1.7+ .20-) 150415 691 .14+ .02+ 181005 W84 .04+ .29+ 150317 G96 .68+ .17+ 150415 691 .36+ .08+ 181005 W84 .16+ .12+ 150410 G96 .22+ .20+ 150417 691 .32+ .12- ...
2015 EL77 - Clone generation I generated 100 clones trying to achieve the same orbital parameters and uncertainties as calculated by Find Orb:| Clones | Target | ||||
|---|---|---|---|---|---|
| mean | sd | mean | sd | ||
| q | 3.57199229514 | 2.087558e-05 | 3.57199199 | 2.1e-05 | |
| e | 0.29696990335 | 2.88812e-05 | 0.2969684 | 2.9e-05 | |
| i | 5.8975243641 | 0.00018175059 | 5.89755 | 0.00018 | |
| peri | 219.89550304999 | 0.00266661496 | 219.89562 | 0.0027 | |
| node | 6.39364451828 | 0.00039272039 | 6.3936 | 0.00039 | |
| tp | 2457412.94469156 | 0.01838184197 | 2457412.94272 | 0.0186 | |
Backward simulation
Mercury6 integrator package version 6 by J. E. Chambers
Main parameters:
)O+_06 Integration parameters (WARNING: Do not delete this line!!)
) Lines beginning with `)' are ignored.
)---------------------------------------------------------------------
) Important integration parameters:
)---------------------------------------------------------------------
algorithm (MVS, BS, BS2, RADAU, HYBRID etc) = BS
start time (days)= 2459167.50000
stop time (days) = -1d8
output interval (days) = 100
timestep (days) = 0.05
accuracy parameter=1.d-12
ejection distance (AU)= 100
A clone is considered to be a comet if it enters the solar system from a distance greater than arbitrary threshold = 100 AU
Simulation results
65 out of 100 clones have a cometary origin (i.e.arrived into solar system in the simulation window - back up tp 10^8 days in the past)
Clones are abbreviated as EL_<xx> with 01 <= xx <= 100
Beginning the main integration.
EL_64 ejected at -46141 7 7.66483
EL_22 ejected at -54004 7 13.04497
EL_95 ejected at -58787 2 10.36615
EL_97 ejected at -61738 3 29.42279
EL_3 ejected at -62842 10 12.43896
EL_89 ejected at -62843 6 10.48001
EL_25 ejected at -66320 1 28.69544
EL_11 ejected at -67224 4 18.80180
EL_66 ejected at -69523 6 6.72318
EL_91 ejected at -76290 5 28.23664
EL_12 ejected at -77604 12 16.11145
EL_33 ejected at -79343 12 15.19062
EL_6 ejected at -80788 10 16.99425
EL_48 ejected at -83533 4 17.92191
EL_71 ejected at -87015 1 25.24236
EL_87 ejected at -88939 8 17.07250
EL_41 ejected at -91238 5 19.99891
EL_1 ejected at -93576 5 26.00883
EL_52 ejected at -97525 3 28.56210
EL_76 ejected at -98392 6 27.63136
EL_82 ejected at -100242 9 30.44242
EL_34 ejected at -109661 5 2.91190
EL_63 ejected at -111694 8 8.28741
EL_39 ejected at -112995 7 23.17464
EL_21 ejected at -113013 10 14.02220
EL_59 ejected at -113502 9 19.60363
EL_86 ejected at -114409 9 6.10029
EL_68 ejected at -115449 9 2.07513
EL_55 ejected at -122395 2 18.18319
EL_62 ejected at -123044 6 23.36232
EL_96 ejected at -123200 11 19.24066
EL_29 ejected at -132608 9 22.62730
EL_45 ejected at -132867 3 25.99649
EL_7 ejected at -132914 8 5.74390
EL_38 ejected at -138752 1 11.96940
EL_85 ejected at -139152 9 7.87151
EL_14 ejected at -143728 11 26.00313
EL_75 ejected at -144479 8 15.54337
EL_44 ejected at -148125 11 10.01233
EL_74 ejected at -148379 2 11.01097
EL_70 ejected at -150626 11 15.21742
EL_46 ejected at -150909 11 14.27464
EL_92 ejected at -158751 2 6.56521
EL_4 ejected at -171194 3 3.69811
EL_88 ejected at -191422 11 24.83374
EL_18 ejected at -191433 10 30.34998
EL_32 ejected at -194882 9 1.96188
EL_16 ejected at -199430 6 16.42980
EL_31 ejected at -203156 2 25.26967
EL_77 ejected at -205024 9 24.15732
EL_43 ejected at -211742 2 14.19068
EL_61 ejected at -212216 3 12.36277
EL_50 ejected at -219919 2 29.90785
EL_93 ejected at -224512 9 8.91093
EL_49 ejected at -224744 7 2.99308
EL_23 ejected at -225546 1 28.97203
EL_28 ejected at -231532 2 28.98184
EL_78 ejected at -231695 11 22.50623
EL_15 ejected at -233462 2 6.20325
EL_36 ejected at -239025 4 8.76140
EL_67 ejected at -241109 9 5.85502
EL_60 ejected at -246440 5 24.49606
EL_65 ejected at -260950 5 10.65600
EL_10 ejected at -266269 3 8.22146
EL_99 ejected at -273480 3 21.02202
The arrival time distribution into the solar system is shown graphically below:
Curiosity: 7 clones arrived on a hyperbolic trajectory with the following V-infinity (Km/s):
ast V
1: EL_76.aei 5.2104487
2: EL_93.aei 4.9340891
3: EL_21.aei 3.0706005
4: EL_4.aei 2.8995143
5: EL_68.aei 2.8558247
6: EL_52.aei 2.2027882
7: EL_36.aei 0.6715961
If we take all 100 clones togetherand divide the simulation time into slots, we can see the distribution of the orbital parameters.
Orbital Param distribution
In every time slot, we calculate the minimum perihelium for every clone and then we show the distribution of these distances for all clones (from 25th to 75th quartile).
Perihelium q
Eccentricity e
Inclination i
Argument of Perihelium
Ascending Node
Peri + Node
Cheers,
Alessandro Odasso
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