(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

2009 WQ62 and 63440 (2001 MD30) and 331933 (2004 TV14) - A cluster?

According to http://www.johnstonsarchive.net/astro/asteroidpairs.html asteroid 63440 (2001 MD30) and 331933 (2004 TV14)are considered to be an asteroid pair.

It seems to me that asteroid 2009 WQ62 (U code 2) has similar orbit parameters.

I made a simulation comparing clones of these three asteroids.

In the best case, it seems that the clones could be as near as about 20000 km (0.05 LD) and considering the periodicity maybe in the past they could be even more near.

I wonder whether these three asteroids can be considered to belong to a cluster of physically related asteroids ... or is it just a "statistical fluke"?

Quite unexpectedely, the two pairs 63440 (2001 MD30) and 331933 (2004 TV14) reached the minimum distance very recently ... but not particularly interesting as a close approach!

Actually what shown above is "the best case".

The simulation involved 100 clones for every asteroid, looking back atthe last 10^7 JD, output every 100 days.

I tried to achieve a "clone distribution" coherent with  the real ones  (with uncertainty read from JPL Horizons Web interface):

 

clones of 2004 TV14

[ 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 .08843948312784312 8.4849e-08 a 1.937933640687897 1.2579e-08 au q 1.7665437911694 1.5808e-07 au i 19.98889163261023 8.0042e-06 deg node 229.4563583326874 1.4922e-05 deg peri 205.5107460888095 3.7259e-05 deg M 107.6788596209243 3.7957e-05 deg tp 2458305.762954214937 (2018-Jul-06.26295422) 0.00010276 TDB period 985.3868889042742 2.70 9.5939e-06 2.627e-08 d yr n .36533873552987 3.557e-09 deg/d Q 2.109323490206394 1.3691e-08 au

Orbit Determination Parameters    # obs. used (total)      166      data-arc span      6513 days (17.83 yr)      first obs. used      2001-07-01      last obs. used      2019-05-01      planetary ephem.      DE431      SB-pert. ephem.      SB431-N16      condition code      0      norm. resid. RMS      .60289      source      ORB      producer      Otto Matic      solution date      2019-Jul-13 19:23:38   Additional Information  Earth MOID = .787571 au   Jupiter MOID = 3.18038 au   T_jup = 3.828

331933 (2004 TV14)

Classification: Inner Main-belt Asteroid          SPK-ID: 2331933

	Clones			Target
	mean	sd		mean	sd
q	1.76654379	1.6e-07		1.76654379	1.6e-07
e	0.08843948	8e-08		0.08843948	8e-08
i	19.9888926	7.9e-06		19.98889163	8e-06
peri	205.51074903	3.748e-05		205.51074609	3.726e-05
node	229.45635664	1.488e-05		229.45635833	1.492e-05
tp	2458305.76295692	0.00010125		2458305.76295422	0.00010276

clones of 2001 MD30

[ 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 22 (heliocentric ecliptic J2000)  Element Value Uncertainty (1-sigma)   Units  e .08842579345910323 5.0822e-08 a 1.937954727685901 7.1105e-09 au q 1.766589543202455 9.6691e-08 au i 19.9888850307184 5.8423e-06 deg node 229.4570161987519 1.1316e-05 deg peri 205.5022586712172 2.7892e-05 deg M 110.8795473674578 2.7236e-05 deg tp 2458296.997123521674 (2018-Jun-27.49712352) 7.3995e-05 TDB period 985.4029722010249 2.70 5.4233e-06 1.485e-08 d yr n .3653327726380746 2.0106e-09 deg/d Q 2.109319912169347 7.7392e-09 au

Orbit Determination Parameters    # obs. used (total)      913      data-arc span      15178 days (41.56 yr)      first obs. used      1977-10-20      last obs. used      2019-05-11      planetary ephem.      DE431      SB-pert. ephem.      SB431-N16      condition code      0      norm. resid. RMS      .51323      source      ORB      producer      Otto Matic      solution date      2019-May-30 05:23:47   Additional Information  Earth MOID = .787609 au   Jupiter MOID = 3.18036 au   T_jup = 3.828

63440 (2001 MD30)

Classification: Inner Main-belt Asteroid          SPK-ID: 2063440

	Clones			Target
	mean	sd		mean	sd
q	1.76658954	1e-07		1.76658954	1e-07
e	0.08842579	5e-08		0.08842579	5e-08
i	19.98888503	5.85e-06		19.98888503	5.84e-06
peri	205.50225416	2.817e-05		205.50225867	2.789e-05
node	229.45701705	1.135e-05		229.4570162	1.132e-05
tp	2458296.99711268	7.407e-05		2458296.99712352	7.4e-05

clones of 2009 WQ62

[ 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 .08804383689315186 1.158e-05 a 1.93801279355177 2.6273e-07 au q 1.767382711259456 2.2659e-05 au i 19.97084321515778 0.00012904 deg node 229.9007989831988 5.6862e-05 deg peri 204.9048096269857 0.010821 deg M 167.0534712631619 0.008655 deg tp 2458143.215595676715 (2018-Jan-24.71559568) 0.023758 TDB period 985.4472601592967 2.70 0.00020039 5.486e-07 d yr n .3653163538572387 7.4287e-08 deg/d Q 2.108642875844083 2.8586e-07 au

Orbit Determination Parameters    # obs. used (total)      23      data-arc span      2927 days (8.01 yr)      first obs. used      2009-11-16      last obs. used      2017-11-21      planetary ephem.      DE431      SB-pert. ephem.      SB431-N16      condition code      2      norm. resid. RMS      .55576      source      ORB      producer      Otto Matic      solution date      2019-Sep-28 03:02:47   Additional Information  Earth MOID = .788005 au   Jupiter MOID = 3.18123 au   T_jup = 3.828

(2009 WQ62)

Classification: Inner Main-belt Asteroid          SPK-ID: 3846838

	Clones			Target
	mean	sd		mean	sd
q	1.76737733	2.263e-05		1.76738271	2.266e-05
e	0.08804657	1.157e-05		0.08804384	1.158e-05
i	19.97082241	0.00012943		19.97084322	0.00012904
peri	204.90656857	0.01081596		204.90480963	0.010821
node	229.90081685	5.704e-05		229.90079898	5.686e-05
tp	2458143.21931216	0.0237189		2458143.21559568	0.023758

Clones Comparison

I compared clones of every couple (100*100 comparisons) trying to trace the minimum distance that they reached (taking note of the time and relative velocities):

 Kind Regards,
Alessandro Odasso