astro: 2004 VB131 and 2004 VV131

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
t_p	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
t_p	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
t_p	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