Blog Archive

Saturday, January 23, 2016

KBO clustering

I refer to this MPML message and to the associated conversation, in particular to the interesting comments made by Aldo Vitagliano, author of Solex orbit simulator, about the difficulty to see a cluster of KBOs.

I do not know the answer but this prompted me to look at the KBO's orbit parameter distribution. What follows next is an exercise ... so I do not claim that it is correct!

I used the Web service made available by MPC to look for KBOs characterized by:
 250 AU < a < 1000 AU

I found this list:


Asteroidaeiwom
2006 UL321260.76420.909904137.36673-6.20276-17.0798
2012 VP113268.25090.700563524.0183-66.96890.88303
1996 PW271.48480.990582129.72461-178.15845144.61041
2011 OR17287.18750.9892086110.3377214.03442-88.40106
336756 319.04390.9704821140.81617132.96423136.19752
2013 RF98325.10390.888374629.57957-43.4549967.57105
2004 VN112339.08370.860411525.51725-32.7647966.06033
2010 GB174364.85130.867026421.53648-12.61199130.60394
2015 DB216418.72130.980003840.48768-119.15783.27749
2010 BK118484.38160.987395143.90195179.11098175.97502
2007 DA61518.39540.994876676.71542-10.32894145.98047
90377 539.6680.858831511.92852-48.91693144.50447
2007 TG422546.44730.93488518.57957-74.16184112.98074
87269 586.59610.964551820.07087-147.4484142.37805
2002 RN109746.67250.996380257.99165-147.53176170.49258
308933 780.17640.96901119.46659122.49628-162.61603
2013 AZ60990.12810.99201316.52296157.9403-10.77058

Then I used the R package to produce a hierarchical cluster as follows:
1) I scaled the above table so that every column has mean 0 and variance 1.
2) I calculated the distance between any two rows (manhattan distance).
3) I submitted the scaled table to the function hclust choosing clustering method complete.
4) I used a further R function ( see rect.hclust ) to display colored rectangles at different height: the purpose is to help visualize the various clusters at different levels.

Result

I do not know, whether these clusters have a statistical significance or not.

The left cluster maybe interesting: in fact, it consistently maintains its shape even when you cut the dendogram at a level where the second big cluster gets split into 5 subgroups.

The left cluster contains asteroid 2012 VP113 plus other 4 even more similar asteroids.
From now on I will refer to this cluster as "cluster 2" as opposed to "cluster1" made by all other KBOs without further distinctions.

A nice R function is cutree: you can tag the original table with a further column i.e. the cluster where it is supposed to belong. By doing this, you can use, for example, the function ggpairs of the GGally library to make a set of plots like these:
  • in the diagonal, you can see the density distribution, each cluster being given a different color. Cluster 2 is coloured in blue. 
  • above the diagonal: you can see the correlation between pairs of parameters, with cluster detail and total as well.
  • below the diagonal: you can see a scatter plot diagram of each pair of parameters, again the colour represents a cluster.

.... and, if you are interested in a specifc plot, you can make it alone with the ggplot function.

For example:
  • let's see a scatter plot of orbital parameters a and w where we add the name of the asteroids
  • finally, let's see the density distribution of orbital parameter w
a versus w
w density distribution


Kind Regards,
Alessandro Odasso




Wednesday, December 9, 2015

(111298) = 2001 XZ55 versus 2008 YL20

See an update about this case received on Dec 10th: look at this MPML msg.



===============================================
I am looking again at these two asteroids.

A couple of years ago, as clearly explained by Bill Gray (see MPML msg ), it was a bit too early to make meaningful simulations trying to go back in the past as far as about 25000 years ago.

Now the orbit uncertaintly of asteroid 2008 YL20 has improved from +/- 1.62e-6 degrees /day to +/-1.1568e-08 degrees/day.

I tried a new simulation to investigate the possibility that these two asteroids separated in the past and I got a new result consisting in a nominal distance of about 4000 km, relative velocity about 15 cm/s. This event occurred about 34000 years ago.

The uncertainty is 1.1568e-08 * 365 * 34000 = 0.14 degrees that at an average distance of 2.39 AU corresponds to an uncertainty of about 0.0057 AU (i.e. three time the moon-earth distance).

So ... on one side no proof that these asteroids separated but it seems to me that this pair is still interesting.

More details looking the JPL Small Body Data:

(111298) = 2001 XZ55
Orbital Elements at Epoch 2457200.5 (2015-Jun-27.0) TDB
Reference: JPL 11 (heliocentric ecliptic J2000)

 Element Value Uncertainty (1-sigma)   Units 
e .1837905901861221 6.7074e-08
a 2.391320808768463 2.2177e-08 AU
q 1.951818546000553 1.6999e-07 AU
i 3.192061836722895 7.0356e-06 deg
node 111.491991193275 0.00011791 deg
peri 297.8338388091076 0.0001197 deg
M 257.5887075379197 2.2491e-05 deg
tp 2457584.738198736595
(2016-Jul-15.23819874)
8.7199e-05 JED
period 1350.688466278188
3.70
1.879e-05
5.144e-08
d
yr
n .2665307426456207 3.7078e-09 deg/d
Q 2.830823071536374 2.6253e-08 AU


2008 YL20
Orbital Elements at Epoch 2457200.5 (2015-Jun-27.0) TDB
Reference: JPL 8 (heliocentric ecliptic J2000)

 Element Value Uncertainty (1-sigma)   Units 
e .1837937583380851 5.5869e-07
a 2.391150352530784 6.9177e-08 AU
q 1.951671842487714 1.3831e-06 AU
i 3.193600462494826 1.3927e-05 deg
node 111.4717983197325 0.00025271 deg
peri 298.0606134273407 0.00030036 deg
M 320.5524746963916 0.00012064 deg
tp 2457348.487835047940
(2015-Nov-21.98783505)
0.00045708 JED
period 1350.544050792078
3.70
5.8608e-05
1.605e-07
d
yr
n .2665592431352864 1.1568e-08 deg/d
Q 2.830628862573854 8.1891e-08 AU


Mercury Simulator Results

Simulation parameters:

 algorithm (MVS, BS, BS2, RADAU, HYBRID etc) = bs2
 start time (days)= 2457387.5
 stop time (days) = -17.3d6
 output interval (days) = 20
 timestep (days) = 0.1
 accuracy parameter=1.d-12

The result shown as a graph (done with R package):




Kind Regards,
Alessandro Odasso



      Mercury Simulator - Mercury6
      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.

Tuesday, November 24, 2015

11842 Kap'bos (1987 BR1) vs 436415 (2011 AW46)

11842 Kap'bos (1987 BR1) is an interesting asteroid indeed!

First of all, looking at proper elements (see this page), this asteroid has already been recognized to be associated to (228747) 2002 VH3

Furthermore, but this is not sure, it may be even more strictly associated to 436415 (2011 AW46)

JPL Small-Body Database Browser

11842 Kap'bos (1987 BR1)
Orbital Elements at Epoch 2457200.5 (2015-Jun-27.0) TDB
Reference: JPL 14 (heliocentric ecliptic J2000)

 Element Value Uncertainty (1-sigma)   Units 
e .09426143976452217 5.4457e-08  
a 2.250221196226988 1.1502e-08 AU
q 2.038112106481987 1.1993e-07 AU
i 3.688461615022471 5.8652e-06 deg
node 272.8444791596755 7.5115e-05 deg
peri 172.3596586176659 8.1653e-05 deg
M 181.7294574254017 3.145e-05 deg
tp 2457811.038885071140
(2017-Feb-26.53888507)
0.00010929 JED
period 1232.923821576616
3.38
9.4533e-06
2.588e-08
d
yr
n .2919888428626886 2.2388e-09 deg/d
Q 2.462330285971989 1.2586e-08 AU


436415 (2011 AW46) 
Orbital Elements at Epoch 2457200.5 (2015-Jun-27.0) TDB
Reference: JPL 8 (heliocentric ecliptic J2000)

 Element Value Uncertainty (1-sigma)   Units 
e .09435201650783409 1.8231e-07  
a 2.25006679453928 5.9552e-08 AU
q 2.03776845519718 4.095e-07 AU
i 3.688904837606787 1.5844e-05 deg
node 272.8087674388969 0.00022201 deg
peri 172.3636156199904 0.0002396 deg
M 151.7058568204286 9.5288e-05 deg
tp 2456680.993016870443
(2014-Jan-23.49301687)
0.00031517 JED
period 1232.7969258828
3.38
4.8942e-05
1.34e-07
d
yr
n .2920188981994789 1.1593e-08 deg/d
Q 2.462365133881379 6.5171e-08 AU


This is the result of a simulation made with Mercury6 software (graphs made with package R):



Looking at nominal parameters, it seems that these two asteroids had a very close encounter (nearly 9000 km) with a relative velocity of about 30 cm/s about 11500 years ago.

I do not know whether this is true and, if yes, whether this is just a coincidence or these two asteroids separated in that moment from a common body.

Kind Regards,
Alessandro Odasso

Tuesday, November 17, 2015

421781 (2014 QG22) vs 53576 (2000 CS47)

These two asteroids are a potentially interesting couple.
I do not know if this couple is already known and if it is really a couple with a common origin.

Let's look at the JPL data, showing very similar orbital parameters:
421781 (2014 QG22)
Orbital Elements at Epoch 2457200.5 (2015-Jun-27.0) TDB
Reference: JPL 5 (heliocentric ecliptic J2000)

 Element Value Uncertainty (1-sigma)   Units 
e .1415490034245739 7.6497e-08
a 2.219666740174171 5.0262e-08 AU
q 1.905475125167845 1.6225e-07 AU
i 5.547751979163497 1.1933e-05 deg
node 270.894647775993 0.00023172 deg
peri 334.1685226014454 0.00025596 deg
M 170.5342535281013 0.00011344 deg
tp 2456628.311384753553
(2013-Dec-01.81138475)
0.00037629 JED
period 1207.897517520007
3.31
4.1027e-05
1.123e-07
d
yr
n .2980385295758646 1.0123e-08 deg/d
Q 2.533858355180498 5.7376e-08 AU
 Orbit Determination Parameters
   # obs. used (total)      49  
   data-arc span      3697 days (10.12 yr)  
   first obs. used      2004-08-14  
   last obs. used      2014-09-28  
   planetary ephem.      DE431  
   SB-pert. ephem.      SB431-BIG16  
   condition code      0  
   fit RMS      .55494  
   data source      ORB  
   producer      Otto Matic  
   solution date      2015-Jan-08 13:35:22  

Additional Information
 Earth MOID = .893565 AU 
 T_jup = 3.631 

53576 (2000 CS47)
Orbital Elements at Epoch 2457200.5 (2015-Jun-27.0) TDB
Reference: JPL 11 (heliocentric ecliptic J2000)

 Element Value Uncertainty (1-sigma)   Units 
e .1413172303277337 5.195e-08
a 2.219866104654218 1.5604e-08 AU
q 1.906160775046069 1.1284e-07 AU
i 5.548153406788004 6.1614e-06 deg
node 270.899183954788 6.9605e-05 deg
peri 334.2072656882382 7.5251e-05 deg
M 151.5995810376835 2.9164e-05 deg
tp 2456691.773809093385
(2014-Feb-03.27380909)
9.8063e-05 JED
period 1208.060256319952
3.31
1.2737e-05
3.487e-08
d
yr
n .2979983805581422 3.142e-09 deg/d
Q 2.533571434262367 1.7809e-08 AU

Orbit Determination Parameters
   # obs. used (total)      610  
   data-arc span      7436 days (20.36 yr)  
   first obs. used      1994-07-08  
   last obs. used      2014-11-16  
   planetary ephem.      DE431  
   SB-pert. ephem.      SB431-BIG16  
   condition code      0  
   fit RMS      .49974  
   data source      ORB  
   producer      Otto Matic  
   solution date      2015-Mar-09 16:42:10  

Additional Information
 Earth MOID = .894238 AU 
 T_jup = 3.631 

 I tried to run the Mercury simulator (BS2 integrator, timestep 1 day) with the nominal parameters, with this result (graph done with the R package)



Kind Regards,
Alessandro Odasso

Sunday, November 15, 2015

2002 UP11 vs 2015 VF105

See update about this case:
https://groups.yahoo.com/neo/groups/mpml/conversations/messages/31516

=================================
2002 UP11 and 2015 VF105 have similar orbit parameters.
The uncertainty for 2015 VF105 is unknown and I do not find its observations.


Using the Mercury software, it seems that they had a relative close approach on May 8th, 2001 when their nominal relative distance and velocity were:
  • distance 0.00147 AU
  • velocity: ca 5 m/s
Maybe in the future, when further observations will be available, it will be possible to study them looking for a common origin

JPL Small-Body Database Browser:


(2002 UP11)
Classification: Mars-crossing Asteroid          SPK-ID: 3224224
Ephemeris | Orbit Diagram | Orbital Elements | Physical Parameters ]

[ show orbit diagram ]

Orbital Elements at Epoch 2457200.5 (2015-Jun-27.0) TDB
Reference: JPL 2 (heliocentric ecliptic J2000)
 Element Value Uncertainty (1-sigma)   Units 
e .382955379120253 0.00010057
a 2.187589320416579 0.00042822 AU
q 1.349840222857032 4.6502e-05 AU
i 22.87063099452443 0.0044292 deg
node 43.70403288617293 0.0014051 deg
peri 62.82185003664876 0.00090087 deg
M 293.5443079306065 0.40392 deg
tp 2457418.660842947343
(2016-Jan-31.16084295)
1.39 JED
period 1181.808525581734
3.24
0.34701
0.0009501
d
yr
n .3046178735449497 8.9443e-05 deg/d
Q 3.025338417976127 0.0005922 AU
Orbit Determination Parameters
   # obs. used (total)      17  
   data-arc span      49 days  
   first obs. used      2002-10-04  
   last obs. used      2002-11-22  
   planetary ephem.      DE431  
   SB-pert. ephem.      SB431-BIG16  
   condition code      6  
   fit RMS      .53879  
   data source      ORB  
   producer      Otto Matic  
   solution date      2014-Jun-13 03:11:31  

Additional Information
 Earth MOID = .485591 AU 
 T_jup = 3.482 


(2015 VF105)
Classification: Mars-crossing Asteroid          SPK-ID: 3734494
Ephemeris | Orbit Diagram | Orbital Elements | Physical Parameters ]

[ show orbit diagram ]

Orbital Elements at Epoch 2457300.5 (2015-Oct-05.0) TDB
Reference: E2015-VE1 (heliocentric ecliptic J2000)
 Element Value Uncertainty (1-sigma)   Units 
e 0.3831181 n/a
a 2.1883016 n/a AU
q 1.3499236 n/a AU
i 22.88002 n/a deg
node 43.69986 n/a deg
peri 62.82823 n/a deg
M 323.14568 n/a deg
tp 2457421.5445051
(2016-Feb-03.04450510)
n/a JED
period 1182.3857240
3.24
n/a
n/a
d
yr
n 0.30446917 n/a deg/d
Q 3.0266796 n/a AU
Orbit Determination Parameters
   # obs. used (total)      21  
   data-arc span      62 days  
   first obs. used      2015-09-11  
   last obs. used      2015-11-12  
   # oppositions      1  
   two-body model      T  
   fit RMS      0.13  
   data source      MPC:mp1  
   producer      MPCW  

Additional Information
 T_jup = 3.482 

Graph





Kind Regards,
Alessandro Odasso