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