2018 TM7 - a member of Datura cluster?

According to https://astro.troja.mff.cuni.cz/davok/papers/clusters_Icarus2018.pdf , asteroid 2016 TW15 is a probable member of the Datura cluster.

Asteroids 2018 TM7 and 2016 TW15 have similar orbital parameters, so one can wonder whether they are related as well.

Using a similar approach as described in the previous post, I got the following preliminary results.

Horizons Web-Interface

[ Ephemeris | Orbit Diagram | Orbital Elements | Mission Design | Physical Parameters ]

[ show orbit diagram ]

Orbital Elements at Epoch 2458600.5 (2019-Apr-27.0) TDB Reference: JPL 2 (heliocentric ecliptic J2000)  Element Value Uncertainty (1-sigma)   Units  e .2073298995769193 3.8379e-06 a 2.235046338287878 2.301e-05 au q 1.771654405420891 1.2968e-05 au i 5.990117205423358 4.7269e-05 deg node 97.82547015326649 0.00054111 deg peri 259.4145809193611 0.0032119 deg M 68.99123090087689 0.0020078 deg tp 2458366.605711434710 (2018-Sep-05.10571143) 0.0058977 TDB period 1220.473135266737 3.34 0.018847 5.16e-05 d yr n .2949675741296193 4.5551e-06 deg/d Q 2.698438271154865 2.7781e-05 au

Orbit Determination Parameters    # obs. used (total)      29      data-arc span      79 days      first obs. used      2018-08-21      last obs. used      2018-11-08      planetary ephem.      DE431      SB-pert. ephem.      SB431-N16      condition code      4      norm. resid. RMS      .44663      source      ORB      producer      Otto Matic      solution date      2019-Feb-18 10:04:49   Additional Information  Earth MOID = .778475 au   Jupiter MOID = 2.75817 au   T_jup = 3.603

(2018 TM7)

Classification: Main-belt Asteroid          SPK-ID: 3835925

[ Ephemeris | Orbit Diagram | Orbital Elements | Mission Design | Physical Parameters ]

[ show orbit diagram ]

Orbital Elements at Epoch 2458600.5 (2019-Apr-27.0) TDB Reference: JPL 3 (heliocentric ecliptic J2000)  Element Value Uncertainty (1-sigma)   Units  e .2074483215033754 6.276e-05 a 2.235611802114912 0.00019509 au q 1.771837886233037 0.00014694 au i 5.991604667652219 0.00042723 deg node 97.1620742657492 0.0056502 deg peri 260.1246967378749 0.051079 deg M 285.0627975716027 0.045951 deg tp 2458854.648758455576 (2020-Jan-06.14875846) 0.18292 TDB period 1220.936331742965 3.34 0.15982 0.0004376 d yr n .2948556698989184 3.8596e-05 deg/d Q 2.699385717996787 0.00023556 au

Orbit Determination Parameters    # obs. used (total)      30      data-arc span      59 days      first obs. used      2016-08-12      last obs. used      2016-10-10      planetary ephem.      DE431      SB-pert. ephem.      SB431-N16      condition code      5      norm. resid. RMS      .2906      source      ORB      producer      Otto Matic      solution date      2017-Oct-09 14:42:03   Additional Information  Earth MOID = .778751 au   Jupiter MOID = 2.75758 au   T_jup = 3.603

(2016 TW15)

Classification: Main-belt Asteroid          SPK-ID: 3760646

Clone generation
100 clones were generated for both asteroids, trying to achieve the same orbital parameters and uncertainty as above:

summary_2018+TM7

	Clones			Target
	mean	sd		mean	sd
q	1.77165498	1.294e-05		1.77165441	1.297e-05
e	0.20732936	3.84e-06		0.2073299	3.84e-06
i	5.99011663	4.722e-05		5.99011721	4.727e-05
peri	259.41529374	0.00321844		259.41458092	0.0032119
node	97.82537494	0.00053868		97.82547015	0.00054111
tp	2458366.60704583	0.00589821		2458366.60571143	0.0058977

summary_2016+TW15

	Clones			Target
	mean	sd		mean	sd
q	1.77183536	0.00014688		1.77183789	0.00014694
e	0.20745945	6.28e-05		0.20744832	6.276e-05
i	5.99162255	0.00042743		5.99160467	0.00042723
peri	260.11780583	0.05113712		260.12469674	0.051079
node	97.16314414	0.00565394		97.16207427	0.0056502
tp	2458854.62514345	0.18310294		2458854.64875846	0.18292

Simulation results
I analyzed the 10000 clones pairs searching for the time when every pair had the minimum distance (registering the relative velocity as well).
Of course every pair is different and we can get a feel of variations looking at the following plots:

Best Clone Couple
About 30% of the clone pairs reached a minimum distance below 1 Lunar Distance.
The best one made far better as you can see here:

Kind Regards,
Alessandro Odasso

486081 (2012 UX41) vs 504375 (2007 VV73) - Divorced pair?

Asteroids 486081 (2012 UX41)  504375 (2007 VV73) are two distinct objects that have a similar orbit.

I tried to investigate whether these two objects could be a divorced binary pair generating clones and simulating their past behaviour.

The answer is not conclusive but I think these two objects are interesting.

Connecting to the HORIZONS Web-Interface from JPL, you get:

486081 (2012 UX41)

[ Ephemeris | Orbit Diagram | Orbital Elements | Mission Design | Physical Parameters | Discovery Circumstances ]

[ show orbit diagram ]

Orbital Elements at Epoch 2458600.5 (2019-Apr-27.0) TDB Reference: JPL 14 (heliocentric ecliptic J2000)  Element Value Uncertainty (1-sigma)   Units  e .1032904301220536 6.5866e-08 a 2.245458730002628 4.6918e-08 au q 2.013524331959336 1.3717e-07 au i 6.007363025544946 1.256e-05 deg node 200.7854247185886 6.8302e-05 deg peri 266.0282980023908 9.2854e-05 deg M 272.0908404992332 6.2565e-05 deg tp 2458900.614977660203 (2020-Feb-21.11497766) 0.00021456 TDB period 1229.011772734908 3.36 3.8519e-05 1.055e-07 d yr n .2929182681455487 9.1806e-09 deg/d Q 2.47739312804592 5.1764e-08 au

Orbit Determination Parameters    # obs. used (total)      47      data-arc span      4156 days (11.38 yr)      first obs. used      2005-10-07      last obs. used      2017-02-22      planetary ephem.      DE431      SB-pert. ephem.      SB431-N16      condition code      0      norm. resid. RMS      .61043      source      ORB      producer      Otto Matic      solution date      2017-Apr-09 04:48:41   Additional Information  Earth MOID = 1.04097 au   Jupiter MOID = 2.63527 au   T_jup = 3.617

486081 (2012 UX41)

Classification: Main-belt Asteroid          SPK-ID: 2486081

504375 (2007 VV73)

[ Ephemeris | Orbit Diagram | Orbital Elements | Mission Design | Physical Parameters | Discovery Circumstances ]

[ show orbit diagram ]

Orbital Elements at Epoch 2458600.5 (2019-Apr-27.0) TDB Reference: JPL 12 (heliocentric ecliptic J2000)  Element Value Uncertainty (1-sigma)   Units  e .1029111754557024 5.6919e-08 a 2.245493461895011 2.2879e-08 au q 2.014407090253301 1.2474e-07 au i 6.013781035001495 9.9051e-06 deg node 200.7565685960872 5.9357e-05 deg peri 263.9747204655452 7.9426e-05 deg M 83.6944551442494 5.1702e-05 deg tp 2458314.767063259248 (2018-Jul-15.26706326) 0.00017487 TDB period 1229.040287667593 3.36 1.8784e-05 5.143e-08 d yr n .2929114721562046 4.4767e-09 deg/d Q 2.476579833536721 2.5234e-08 au

Orbit Determination Parameters    # obs. used (total)      72      data-arc span      4241 days (11.61 yr)      first obs. used      2007-09-14      last obs. used      2019-04-25      planetary ephem.      DE431      SB-pert. ephem.      SB431-N16      condition code      0      norm. resid. RMS      .68836      source      ORB      producer      Otto Matic      solution date      2019-Jul-14 13:44:52   Additional Information  Earth MOID = 1.04182 au   Jupiter MOID = 2.6423 au   T_jup = 3.617

504375 (2007 VV73)

Classification: Main-belt Asteroid          SPK-ID: 2504375

Clone Generation
I generated 100 clones for both asteroids, trying to achieve the same distribution read from JPL data:

summary_2012+UX41

	Clones			Target
	mean	sd		mean	sd
q	2.01352434	1.4e-07		2.01352433	1.4e-07
e	0.10329043	7e-08		0.10329043	7e-08
i	6.00736228	1.262e-05		6.00736303	1.256e-05
peri	266.02829744	9.299e-05		266.028298	9.285e-05
node	200.78542722	6.809e-05		200.78542472	6.83e-05
tp	2458900.61498223	0.0002149		2458900.61497766	0.00021456

summary_2007+VV73

	Clones			Target
	mean	sd		mean	sd
q	2.0144071	1.3e-07		2.01440709	1.2e-07
e	0.10291117	6e-08		0.10291118	6e-08
i	6.01378178	9.84e-06		6.01378104	9.91e-06
peri	263.97471761	7.905e-05		263.97472047	7.943e-05
node	200.75657263	5.961e-05		200.7565686	5.936e-05
tp	2458314.76706963	0.00017361		2458314.76706326	0.00017487

Simulation
I used the Mercury6 simulator by John E. Chambers:
J.E.Chambers (1999) ``A Hybrid
      Symplectic Integrator that Permits Close Encounters between
      Massive Bodies''. Monthly Notices of the Royal Astronomical
      Society, vol 304, pp793-799.

algorithm: Bulirsch-Stoer
start time: 2458604.5 JD
output interval : 100 days
stop time: -5d7 days
accuracy parameter=1.d-12

Simulation Results

I used an R script to compare the resulting 10000 clone couples looking for the minimum distance ever reached.

In particular, I used the library ggplot2 by Hadley Wickham to display the graphs that you see here.

As expected, every pair is different and you can collect the resulting minimum distances (plus correspondent relative velocities) and the time of minimum distanceto get an idea about the distribution:

Minimum distance

Relative velocities (at the time of min distance) 

Time of Minimum distance

Best couple
The couple of clones that according to the simulation ever reached the minimum distance show this behaviour:

Don't be fooled by the scale, the "zeros" are not really "zeros":

About 122000 years ago, this couple was separated by a distance about 20000 km and the relative velocity was about 50 m/s

Even though the numbers are small, they are not enough to claim that this is a divorced pair (on the other hand, given the uncertainty, I am not sure if you can rule out this idea specially if you could look much more in the past).

Kind Regards,
Alessandro Odasso

2017 FO161 - update May 17 2019

Thanks to Sam Deen that has recovered other observations and kindly shared them with me, the orbit condition code has improved and I repeated the simulation (see previous post).

     K17FG1O  C2015 03 29.02563110 54 49.70 +04 40 35.8                      W84
     K17FG1O  C2016 01 16.33138910 59 03.26 +04 31 59.3                      W84
     K17FG1O  C2016 01 16.33228610 59 03.25 +04 31 59.1                      W84
     K17FG1O  C2016 02 28.23331010 57 26.75 +04 43 59.5                      W84
     K17FG1O  C2017 01 10.23785311 00 35.66 +04 43 37.7                      W84
     K17FG1O  C2017 03 29.11459510 57 36.07 +05 06 24.5                      W84
     K17FG1O  C2017 03 30.10004610 57 33.77 +05 06 43.1                      W84
     K17FG1O  C2018 03 19.16210110 59 25.35 +05 16 04.6          24.1 V      W84
     K17FG1O  C2018 03 19.16325210 59 25.35 +05 16 04.5          23.4 V      W84
     K17FG1O*.C2017 03 23.13730 10 57 50.425+05 04 32.22         24.1 rc~2b81807
     K17FG1O !C2017 03 23.13730 10 57 50.39 +05 04 32.1          23.3 V ~2y3AW84
     K17FG1O .C2017 03 23.19683 10 57 50.260+05 04 33.54               c~2b81807
     K17FG1O !C2017 03 23.19683 10 57 50.24 +05 04 33.2                 ~2y3AW84
     K17FG1O .C2017 03 24.14054 10 57 47.960+05 04 51.33               c~2b81807
     K17FG1O !C2017 03 24.14054 10 57 47.94 +05 04 51.2                 ~2y3AW84
     K17FG1O  C2017 05 20.17658 10 56 17.838+05 18 18.36               c~2b81G37
     K17FG1O  C2017 05 20.19927 10 56 17.811+05 18 18.56               c~2b81G37
     K17FG1O  C2017 05 20.24493 10 56 17.795+05 18 19.03               c~2b81G37
     K17FG1O  C2017 05 20.27484 10 56 17.764+05 18 18.94               c~2b81G37
     K17FG1O  C2018 03 07.24780 10 59 56.061+05 12 09.72               c~2b81G37
     K17FG1O  C2018 03 07.30383 10 59 55.912+05 12 10.70               c~2b81G37
     K17FG1O  C2018 03 12.23446 10 59 43.088+05 13 49.05         24.0 rU~2b81304
     K17FG1O  C2018 03 12.29836 10 59 42.914+05 13 50.49               U~2b81304

Using Find_Orb by Bill Gray I get:

Find_Orb determines that the diameter is 433.9 km (assuming 10% albedo).

Simulation
I generated 100 clones trying to achieve the same mean and standard deviation calculated by Find_Orb.
This is the result:

	Clones			Target
	mean	sd		mean	sd
q	34.40346635	0.05606912		34.4045995	0.0562
e	0.42549611	0.00229206		0.4251786	0.00228
i	54.10666505	0.00430385		54.10673	0.0043
peri	151.07997749	0.59806858		151.09399	0.6
node	164.98929741	0.00015952		164.98932	0.00016
tp	2515192.39923773	448.01832028		2515227.815598	446

Then, I used Mercury6 simulator (*) by J.E Chambers using an arbitray threshold of 100 AU as ejection distance from the solar system:

Ejection Distance (AU): 100
Simulation period (days): -1d8
Simulation steps (days) : 100
Integration Algorithm:  Bulirsch-Stoer

(*)J.E.Chambers (1999) ``A Hybrid
      Symplectic Integrator that Permits Close Encounters between
      Massive Bodies''. Monthly Notices of the Royal Astronomical
      Society, vol 304, pp793-799.

The simulation is backward so the ejection distance actually is the "entry distance" in the solar system.

In this case - contrary to the previous simulation -  none of the clones  ever reached a distance greater than 100 AU from the sun.

In the following plots, one can see that the behaviour of all clones taken together.

Let's take the example of the Q-aphelium plot (similar concept for other orbital parameters):

the time has been divided into 10 slots and in every slot and for every clone, I calculated the (max) Q distance. Taking into account all the clones, the resulting value distribution is plotted with a boxplot.

Q plot

q plot

Period plot

Orbit Energy plot

e plot

i plot

w plot

om plot

all plots have been made using the R language - ggplot2 library (**)

(**)
R Core Team (2019). R: A language and environment for statistical
  computing. R Foundation for Statistical Computing, Vienna, Austria.
  URL https://www.R-project.org/.

  H. Wickham. ggplot2: Elegant Graphics for Data Analysis.
  Springer-Verlag New York, 2016.

Kind Regards,
Alessandro Odasso