(246095) = 2007 DQ102 versus 2016 CQ357

Following this message from Adrian Coffinet, I tried a backward simulation based on the current nominal orbital parameters.

The result seems to confirm that these two Hungarians might have a common origin:

(4765) Wasserburg cluster ?

On 03-12-2020 I asked to MPML group (see message) whether the following asteroids can be considered a cluster considering their orbit similarity:

(4765) Wasserburg

350716 (2001 XO105)

2017 DU131

2020 HF21

2016 GL253

2012 KH56

Petr Pravec kindly answered that (4765) Wasserburg and 350716 (2001 XO105) consitute an asteroid pair and that also 2016 GL253 is very close to the pair. Those three asteroids are likely to be a cluster but a final confirmation awaits for backward orbit integrations after a better orbit is derived for 2016 GL253.

So, out of curiosity, I tried a backward integration considering the nominal orbits derived from the Horizons Web Interface disregarding any non gravitational effects and, of course, with no certainty about the correctness of what follows! 

Integration parameters

The backward integration has been performed with Mercury6 software by J.E. Chambers.

)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

Results

I considered all the possible 15 asteroid combinations 

Possible combinations

N	asteroid1	asteroid2
1	2017 DU131	2016 GL253
2	2017 DU131	2020 HF21
3	2017 DU131	2012 KH56
4	2017 DU131	(4765) Wasserburg
5	2017 DU131	350716 (2001 XO105)
6	2016 GL253	2020 HF21
7	2016 GL253	2012 KH56
8	2016 GL253	(4765) Wasserburg
9	2016 GL253	350716 (2001 XO105)
10	2020 HF21	2012 KH56
11	2020 HF21	(4765) Wasserburg
12	2020 HF21	350716 (2001 XO105)
13	2012 KH56	(4765) Wasserburg
14	2012 KH56	350716 (2001 XO105)
15	(4765) Wasserburg	350716 (2001 XO105)

Same table as above sorted by velocity (AU/Day), distance (AU) at the time of the minimum distance:

	asteroid1	asteroid2	distance	velocity
	2020 HF21	350716 (2001 XO105)	2.84e-05	1.86e-07
	2017 DU131	350716 (2001 XO105)	4.1e-05	3.89e-07
	2017 DU131	2020 HF21	0.000109	4.65e-07
	2020 HF21	2012 KH56	0.000123	7.24e-07
	2017 DU131	2012 KH56	1.63e-05	1.17e-06
	2017 DU131	2016 GL253	7.76e-05	1.49e-06
	2016 GL253	(4765) Wasserburg	8.75e-05	1.52e-06
	2016 GL253	2012 KH56	0.000123	1.79e-06
	2012 KH56	(4765) Wasserburg	0.000166	2.1e-06
	2016 GL253	2020 HF21	9.89e-05	2.45e-06
	2017 DU131	(4765) Wasserburg	0.00017	3.43e-06
	2020 HF21	(4765) Wasserburg	0.000109	3.92e-06
	2012 KH56	350716 (2001 XO105)	6.79e-05	4.52e-06
	(4765) Wasserburg	350716 (2001 XO105)	7.89e-05	4.52e-06
	2016 GL253	350716 (2001 XO105)	0.926	0.00556

Here you can see the plots showing their relative distance in AU (and velocity in AU/day)

KInd Regards,

Alessandro Odasso

2004 VB131 and 2004 VV131 - Interesting TNOs

2004 VB131 and 2004 VV131

As described in this paper by C. de la Fuente Marcos and R. de la Fuente Marcos, TNO 2004 VB131 and 2003 UT291 are probably dynamically correlated.

I wonder whether TNO 2004 VV131 can be regarded as a third member of a cluster or it just happens to share similar orbital parameters with 2004 VB131 by chance.

The following simulation has been done using Mercury Integrator (package version 6) by John E. Chambers.
reference:
``A Hybrid
      Symplectic Integrator that Permits Close Encounters between
      Massive Bodies''. Monthly Notices of the Royal Astronomical
      Society, vol 304, pp793-799.







The graphs have been done using scripts written in language R, library ggplot2.

Nominal orbits from JPL

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

[ show orbit diagram ]

Orbital Elements at Epoch 2458600.5 (2019-Apr-27.0) TDB Reference: JPL 6 (heliocentric ecliptic J2000)  Element Value Uncertainty (1-sigma)   Units  e .06700099861890772 0.00084146   a 42.59056500132775 0.05372 au q 39.73695461449529 0.08529 au i 1.609969815239925 0.0010253 deg node 51.13004651765624 0.0029309 deg peri 205.5909322273696 0.62841 deg M 166.9050842729729 0.70297 deg tp 2411531.432483070632 (1890-Jun-12.93248307) 140.66 TDB period 101523.9552462122 277.96 192.08 0.5259 d yr n .003545961139190658 6.7089e-06 deg/d Q 45.4441753881602 0.057319 au

Orbit Determination Parameters    # obs. used (total)      15      data-arc span      3638 days (9.96 yr)      first obs. used      2003-10-22      last obs. used      2013-10-07      planetary ephem.      DE431      SB-pert. ephem.      SB431-N16      condition code      5      norm. resid. RMS      .13516      source      ORB      producer      Otto Matic      solution date      2017-Sep-03 18:51:51   Additional Information  Earth MOID = 38.7218 au   Jupiter MOID = 34.4139 au   T_jup = 5.829

(2003 UT291)

Classification: TransNeptunian Object          SPK-ID: 3170250

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

[ show orbit diagram ]

Orbital Elements at Epoch 2458600.5 (2019-Apr-27.0) TDB Reference: JPL 7 (heliocentric ecliptic J2000)  Element Value Uncertainty (1-sigma)   Units  e .07651698572696135 0.0001976   a 43.99692586931386 0.023306 au q 40.63041372054139 0.027328 au i 1.747331850985222 0.00056088 deg node 50.3788794397727 0.0033254 deg peri 206.9134956534745 0.43421 deg M 153.3613703123759 0.49693 deg tp 2413191.137426218222 (1894-Dec-28.63742622) 114.82 TDB period 106593.7953818755 291.84 84.699 0.2319 d yr n .003377307269248543 2.6836e-06 deg/d Q 47.36343801808632 0.02509 au

Orbit Determination Parameters    # obs. used (total)      22      data-arc span      3662 days (10.03 yr)      first obs. used      2004-11-09      last obs. used      2014-11-19      planetary ephem.      DE431      SB-pert. ephem.      SB431-N16      condition code      5      norm. resid. RMS      .41094      source      ORB      producer      Otto Matic      solution date      2017-Apr-08 20:54:11   Additional Information  Earth MOID = 39.6152 au   Jupiter MOID = 35.3111 au   T_jup = 5.914

(2004 VB131)

Classification: TransNeptunian Object          SPK-ID: 3564172

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

[ show orbit diagram ]

Orbital Elements at Epoch 2458600.5 (2019-Apr-27.0) TDB Reference: JPL 1 (heliocentric ecliptic J2000)  Element Value Uncertainty (1-sigma)   Units  e .07647397777967113 0.00011666   a 44.01275464882558 0.0049995 au q 40.64692422778918 0.0088412 au i 1.746638527260639 0.00023322 deg node 50.3833826820534 0.00077942 deg peri 207.2072988521391 0.097721 deg M 153.0207686419978 0.11517 deg tp 2413267.534322143576 (1895-Mar-15.03432214) 32.533 TDB period 106651.3244500145 292.00 18.172 0.04975 d yr n .003375485507155847 5.7515e-07 deg/d Q 47.37858506986198 0.0053819 au

Orbit Determination Parameters    # obs. used (total)      43      data-arc span      4461 days (12.21 yr)      first obs. used      2004-11-09      last obs. used      2017-01-26      planetary ephem.      DE431      SB-pert. ephem.      SB431-N16      condition code      4      norm. resid. RMS      .19842      source      ORB      producer      Otto Matic      solution date      2018-Nov-11 16:42:15   Additional Information  Earth MOID = 39.6317 au   Jupiter MOID = 35.3288 au   T_jup = 5.915

(2004 VV131)

Classification: TransNeptunian Object          SPK-ID: 3836183

Clone generations

I generated 100 clones trying to achieve the same orbital distribution as shown above (average and uncertainty) under the ideal assumption that we can deal with normal distributions.

2004 VB131

	Clones			Target
	mean	sd		mean	sd
q	40.6321499	0.02750148		40.63041372	0.027328
e	0.07649604	0.00019764		0.07651699	0.0001976
i	1.74731535	0.00056535		1.74733185	0.00056088
peri	206.91266172	0.43573354		206.91349565	0.43421
node	50.37912644	0.00333604		50.37887944	0.0033254
tp	2413189.25460454	115.05970535		2413191.13742622	114.82

2004 VV131

	Clones			Target
	mean	sd		mean	sd
q	40.64866623	0.0090227		40.64692423	0.0088412
e	0.07646112	0.00011592		0.07647398	0.00011666
i	1.74668055	0.00023669		1.74663853	0.00023322
peri	207.22233167	0.09641847		207.20729885	0.097721
node	50.38334862	0.00078214		50.38338268	0.00077942
tp	2413270.69430322	31.7570317		2413267.53432214	32.533

Simulation set-up

N-Body algorithm: Bulirsch-Stoer

integration in the last 500 years

output every 100 days

Simulation results

The resulting 100*100 pairs of clones were analyzed looking for the time when they reached the minimum distance (taking note of relative velocity as well).

The best clone couple behaved as shown below

The whole distribution of mininum distances, relative velocities and time was as shown below:

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