Blog Archive

Saturday, November 11, 2017

Asteroid 2016 TS54 - Simulation: one hyperbolic clone

11.Nov.2017 - Thanks to Marshall Eubanks for replying to my post.

===========================================
Original post:

This is an Apollo asteroid and a NEO.
The orbit uncertainty is very high (condition code 7).

JPL data:

(2016 TS54)

Classification: Apollo [NEO]          SPK-ID: 3760683
Ephemeris | Orbit Diagram | Orbital Elements | Physical Parameters | Close-Approach Data ]

[ show orbit diagram ]

Orbital Elements at Epoch 2458000.5 (2017-Sep-04.0) TDB
Reference: JPL 3 (heliocentric ecliptic J2000)
 Element Value Uncertainty (1-sigma)   Units 
e .6765980973308807 0.00042289
a 2.468718466581417 0.0029955 au
q .7983882492468207 7.6008e-05 au
i 6.14907656306426 0.0027978 deg
node 16.99108750103253 0.00070824 deg
peri 300.2822592251591 0.0016973 deg
M 93.48517533503207 0.17205 deg
tp 2457632.586247835889
(2016-Sep-01.08624784)
0.0074744 JED
period 1416.790954334841
3.88
2.5787
0.00706
d
yr
n .2540953546453251 0.00046247 deg/d
Q 4.139048683916013 0.0050223 au
Orbit Determination Parameters
   # obs. used (total)      32  
   data-arc span      3 days  
   first obs. used      2016-10-11  
   last obs. used      2016-10-14  
   planetary ephem.      DE431  
   SB-pert. ephem.      SB431-N16  
   condition code      7  
   fit RMS      .49696  
   data source      ORB  
   producer      Otto Matic  
   solution date      2017-Apr-06 08:23:07  

Additional Information
 Earth MOID = 4.26889E-5 au 
 Jupiter MOID = 1.25134 au 
 T_jup = 3.116 


Just for fun, I simulated 100 clones of this Apollo asteroid in the past 10^8 days trying to see if there are signs of a possible cometary origin:
i.e. whether some clones might have arrived from the outskirt of the solar system - threshold: 100 AU.

Simulation approach


reference:
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.

           Integration parameters
           ----------------------

   Algorithm: Bulirsch-Stoer (conservative systems)

   Integration start epoch:         2458000.5000000 days
   Integration stop  epoch:      -100000000.0000000
   Output interval:                     100.000
   Output precision:                 medium

   Initial timestep:                0.050 days
   Accuracy parameter:              1.0000E-12
   Central mass:                    1.0000E+00 solar masses
   J_2:                              0.0000E+00
   J_4:                              0.0000E+00
   J_6:                              0.0000E+00
   Ejection distance:               1.0000E+02 AU
   Radius of central body:          5.0000E-03 AU



Simulation Results

The cometary origin of Asteroid 2016 TS54 is less clear than in other cases where I got a lot of clones with cometary-like orbits.
Anyway, in this case 9 out of 100 clones arrived in the solar system from a distance greater than 100 AU.

I would not be surprised if many more clones would get ejected if the simulation went more back in the past.

> summary(ejected$Year):

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
-276671 -243932 -219308 -221057 -202058 -141985


This plot shows the distribution time in a graphical way:


One thing that sometimes occurr during these simulations ... many clones that had to be discarded - because they seem to have originated from the sun due to a very high eccentricity:

From file.out of Mercury simulator:
  was hit by TS_94    at     -35503 11  8.1
  was hit by TS_47    at     -54568  9 14.4
  was hit by TS_98    at     -99015 10 20.5
  was hit by TS_72    at     -99560  2 21.8
  was hit by TS_96    at    -148788 10  6.0
  was hit by TS_91    at    -149964 11 28.2
  was hit by TS_7     at    -156722  2  4.0
  was hit by TS_77    at    -162338  5 30.9
  was hit by TS_73    at    -166169  2 21.5
  was hit by TS_9     at    -168018 11 11.8
  was hit by TS_18    at    -191284  7 16.3
  was hit by TS_48    at    -200641 11 13.5
  was hit by TS_8     at    -207786  9 27.0
  was hit by TS_51    at    -217189 12 14.4




A curious clone - hyperbolic orbit
What is curious is that one clone (only one!) seems to have entered the solar system following an hyperbolic trajectory.


Day             a        e      i        w       om
...
...
-99309899.5 -61.47015 1.111092 2.6958 241.4296 241.5559
-99309799.5 -61.48959 1.111059 2.6970 241.4380 241.5471
-99309699.5 -61.41541 1.111200 2.6980 241.4380 241.5401
-99309599.5 -61.29102 1.111422 2.6994 241.4445 241.5318
-99309499.5 -61.07459 1.111812 2.7014 241.4495 241.5226
-99309399.5 -60.62682 1.112621 2.7044 241.4565 241.5127
-99309299.5 -59.72419 1.114282 2.7101 241.4700 241.5018
-99309199.5 -57.25347 1.119078 2.7246 241.5052 241.4958
-99309099.5 -36.49813 1.182189 2.7886 242.9846 241.5639



Then, there was an encounter with Saturn:



Days Planet       Dmin        a1       e1    i1
-99309089 SATURN 0.02332127 -402.1809 1.013726 0.314 


The encounter distance was 0.02 AU, the semi-major axis had a spike ...physically possible or not? (I do not know!) but the clone was then captured in an elliptical orbit:

After the encounter we see:


Day             a        e      i        w       om
-99308999.5  28.48699 0.812484 1.3768  71.9542  78.5563
-99308899.5  27.76675 0.807261 1.3830  71.9916  78.5274
-99308799.5  27.55270 0.805645 1.3842  71.9835  78.5263
-99308699.5  27.45602 0.804901 1.3846  71.9719  78.5273
-99308599.5  27.40985 0.804531 1.3848  71.9557  78.5286
-99308499.5  27.39724 0.804417 1.3849  71.9409  78.5301
-99308399.5  27.38719 0.804331 1.3850  71.9305  78.5308
-99308299.5  27.39765 0.804393 1.3850  71.9164  78.5324

 ....

I think this is just a simulation fluke due to the fact that clones "diverge" quite a lot and so some of them seem to have an hyperbolic trajectory.

However, this raises a question: people who are really expert in this field may be able to put some constraint about the probability of these "unstable" asteroids (or old comets?) being hidden interstellar objects captured a long time ago.

This possibility is related to the question "how rare is a close passage of an interstellar rock to our star?" discussed by Alan Harris in this MPML message.

This analysis would be interesting considering the very recent discovery of the first recognized interstellar object by Robert Weryk on October 19, 2017 with observations made by the Pan-STARRS telescope:

A/2017 U1 = 1I/'Oumuamua (MPEC 2017-V17)

A few nice links about this discovery (impossible to give all ... but I share with you the ones that most impressed me):
  • the "early warning" given by Bill Gray, probably the first public mention!
  • A deep analysis from Bill Gray that summarizes why the object is with no doubt interstellar (in response to many questions, including mine,  on whether there might be alternative explanations).
  •  images of the objects taken by Paolo Bacci and Martina Maestripieri
  • look at MPML to see very interesting threads about this object.

Kind Regards,
Alessandro Odasso

Thursday, October 26, 2017

asteroid 2016 WU9 vs comet 3D/Biela

Comet 3D/Biela was a Jupiter Family comet discovered in 1772 by Montaigne and, independentely, by Messier. 

It was identified as periodic in 1826 by Wilhelm Van Biela (period 6.6 years).

In the following decades, the comet disintegrated and in 1872, quoting Wikipedia , "...a brilliant meteor shower (3,000 per hour) was observed radiating from the part of the sky where the comet had been predicted to cross in September 1872. This was the date when Earth intersected the comet's trajectory. These meteors became known as the Andromedids or "Bielids" and it seems apparent that they were produced by the breakup of the comet. The meteors were seen again on subsequent occasions for the rest of the 19th century, but have now faded away, probably due to gravitational disruption of the main filaments".

Looking at JPL Small-Body Database Browser, it seems that the current Apollo asteroid 2016 WU9 orbit bears some resemblance with the orbit of comet 3D/Biela (orbital element estimated at epoch 1832-Dec-03.0).

3D/Biela

Classification: Jupiter-family Comet [NEO]          SPK-ID: 1000504
Ephemeris | Orbit Diagram | Orbital Elements | Physical Parameters | Discovery Circumstances ]

[ show orbit diagram ]

:
Orbital Elements at Epoch 2390520.5 (1832-Dec-03.0) TDB
Reference: IAUCAT03 (heliocentric ecliptic J2000)
 Element Value Uncertainty (1-sigma)   Units 
e 0.751299 n/a
a 3.53465808340135 n/a au
q 0.879073 n/a au
i 13.2164 n/a deg
node 250.669 n/a deg
peri 221.6588 n/a deg
M .9469569963959761 n/a deg
tp 2390514.115200000000
(1832-Nov-26.61520000)
n/a JED
period 2427.278122182916
6.65
n/a
n/a
d
yr
n .1483142770949718 n/a deg/d
Q 6.190243166802708 n/a au

Additional Model Parameters
 Parameter Value Uncertainty (1-sigma) 
A1 [SET] 0.39E-8 n/a
A2 [SET] -0.0254E-8 n/a
Orbit Determination Parameters
   # obs. used (total)      26  
   planetary ephem.      DE405  
   data source      ORB  
   producer      Marsden  

Additional Information
 Earth MOID = .000518224 au 
 T_jup = 2.531 


(2016 WU9)

Classification: Apollo [NEO]          SPK-ID: 3764861
Ephemeris | Orbit Diagram | Orbital Elements | Physical Parameters | Close-Approach Data ]

[ show orbit diagram ]

Orbital Elements at Epoch 2457719.5 (2016-Nov-27.0) TDB
Reference: JPL 3 (heliocentric ecliptic J2000)
 Element Value Uncertainty (1-sigma)   Units 
e .7580579821266318 0.0032624
a 3.542266282670314 0.046712 au
q .8570230522740508 0.00025535 au
i 11.74490053832628 0.036722 deg
node 243.8119317636647 0.0028055 deg
peri 238.6437633713563 0.0047637 deg
M 354.0963591324415 0.12305 deg
tp 2457759.433526534912
(2017-Jan-05.93352654)
0.042468 JED
period 2435.119255232367
6.67
48.168
0.1319
d
yr
n .1478367021354146 0.0029243 deg/d
Q 6.227509513066578 0.082122 au
Orbit Determination Parameters
   # obs. used (total)      14  
   data-arc span      5 days  
   first obs. used      2016-11-26  
   last obs. used      2016-12-01  
   planetary ephem.      DE431  
   SB-pert. ephem.      SB431-N16  
   condition code      8  
   fit RMS      .57283  
   data source      ORB  
   producer      Otto Matic  
   solution date      2017-Apr-06 08:21:48  

Additional Information
 Earth MOID = .0396698 au 
 Jupiter MOID = .640753 au 
 T_jup = 2.523 

One can wonder whether asteroid 2016 WU9 is a remnant of comet 3D/Biela.

In order to answer, it would be important to be able to model the effect of non gravitational forces.
I am unable to do that but I show you the result of a simulation done with Mercury6 taking into account only gravitational forces.

Simulation set-up

reference:
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.

           Integration parameters
           ----------------------

   Algorithm: Bulirsch-Stoer (conservative systems)

   Integration start epoch:         2458000.5000000 days
   Integration stop  epoch:      -100000000.0000000
   Output interval:                     100.000
   Output precision:                 medium

   Initial timestep:                0.050 days
   Accuracy parameter:              1.0000E-12
   Central mass:                    1.0000E+00 solar masses
   J_2:                              0.0000E+00
   J_4:                              0.0000E+00
   J_6:                              0.0000E+00
   Ejection distance:               1.0000E+02 AU
   Radius of central body:          5.0000E-03 AU


In order to perform the simulation I generated 100 clones of asteroid 2016 WU9 (same average orbital parameters as the nominal ones and standard deviation almost about the one calculated by JPL).

I also simulated the behavior of nominal comet 3D/Biela for which I do not find the uncertainty estimates.

Thus, I evaluated 100 couples with an R script to check whether there was a moment in the past when two clones were very near to comet 3D/Biela with a very low relative velocity.

Simulation Results
First, you see a graph showing the relative distance between 2016 WU9 clones and come 3D/Biela (some outliers not shown).
Second, the correspondent graph for relative velocities.



At first glance nothing impressive but around January 1806, one clone and nominal comet D/Biela were separated by a distance of about 10 LD (i.e.  0.025 AU) with a relative velocity 0.0030 AU/Day.
For comparison: I read that in 1852  two fragments comet A and comet B were observed and their distance was estimated to be about 2.5 million km (i.e 6 LD).
In conclusion:
  • for a few clones, the order of magnitude of the distance may be compatible with 2016 WU9 being a fragment of the comet.
Not clear to me if this is just a coincidence or there could be more.

2016 WU9 - a possible cometary origin
While the relation between asteroid 2016 WU9 and comet 3D/Biela remains highly speculative, I think it is interesting to note a second result of the simulation of asteroid 2016 WU9: this Apollo asteroid seems to move on an unstable orbit, it might have a cometary origin itself (whether or not it is related to comet 3D/Biela).

Of course, the uncertainty is very high, but, at least, this result is consistent with the fact that asteroid 2006 WU9 appears in the  Asteroids with Comet-Like Orbits: Elements and Positions by Fernandez.
This is what I got (graph done with package ggplot2):

  • 68 out of 100 clones arrived in the solar system from a distance greater than 100 AU
  • 4 out of 100 clones "hit" the sun (considering that the integration was backword, this means that they seem to have originated from the sun - not clear if this is a simulation glitch or a "normal" result that happens when the eccentricity gets almost 1)

Arrival Time distribution

Year of clone arrival time :

     Min.   1st Qu.    Median      Mean   3rd Qu.      Max.
-271250.0 -158468.8  -79389.5 -103213.8  -40550.2     -32.0  


In a graphical form:


Every clone has its own story, no reason to choose a specific one.
Just to have a feeling of a possible macroscopic behaviour (the dotte lines correspond to a close encounter with Jupiter):






Kind Regards,
Alessandro Odasso

Sunday, October 15, 2017

470785 (2008 UX299) vs 233771 (2008 TO124)

These two main belt asteroids have similar obit parameters.
Their orbit condition codes are 1 and 0 respectively

Using the JPL Small-Body Database Browser, we can see:

470785 (2008 UX299)

Classification: Main-belt Asteroid          SPK-ID: 2470785
Ephemeris | Orbit Diagram | Orbital Elements | Physical Parameters | Discovery Circumstances ]

[ show orbit diagram ]
Orbital Elements at Epoch 2458000.5 (2017-Sep-04.0) TDB
Reference: JPL 8 (heliocentric ecliptic J2000)
 Element Value Uncertainty (1-sigma)   Units 
e .1009684932114735 2.8551e-07  
a 2.689930801283626 1.8626e-07 au
q 2.418332541434887 9.1801e-07 au
i 3.214698487892873 1.5513e-05 deg
node 305.753597645791 0.00017107 deg
peri 87.42148259454721 0.00027647 deg
M 13.75396504670777 0.00023418 deg
tp 2457938.934770288169
(2017-Jul-04.43477029)
0.0010426 JED
period 1611.42496879941
4.41
0.00016737
4.582e-07
d
yr
n .2234047547793786 2.3204e-08 deg/d
Q 2.961529061132366 2.0506e-07 au
  Orbit Determination Parameters
   # obs. used (total)      45  
   data-arc span      4277 days (11.71 yr)  
   first obs. used      2004-12-15  
   last obs. used      2016-08-31  
   planetary ephem.      DE431  
   SB-pert. ephem.      SB431-N16  
   condition code      1  
   fit RMS      .58441  
   data source      ORB  
   producer      Otto Matic  
   solution date      2017-Apr-09 07:28:47  

Additional Information
 Earth MOID = 1.42674 au 
 Jupiter MOID = 2.43518 au 
 T_jup = 3.363 

233771 (2008 TO124)

Classification: Main-belt Asteroid          SPK-ID: 2233771
Ephemeris | Orbit Diagram | Orbital Elements | Physical Parameters | Discovery Circumstances | Close-Approach Data ]

[ show orbit diagram ]
Orbital Elements at Epoch 2458000.5 (2017-Sep-04.0) TDB
Reference: JPL 8 (heliocentric ecliptic J2000)
 Element Value Uncertainty (1-sigma)   Units 
e .1009140923237167 8.811e-08  
a 2.690005559689887 3.9217e-08 au
q 2.41854609028803 2.3857e-07 au
i 3.214945766069064 1.0959e-05 deg
node 305.7617498385058 0.00017798 deg
peri 87.60982730687554 0.0001892 deg
M 353.2000614611609 6.4573e-05 deg
tp 2458030.939020972455
(2017-Oct-04.43902097)
0.00028938 JED
period 1611.492146214952
4.41
3.5241e-05
9.648e-08
d
yr
n .2233954418242512 4.8853e-09 deg/d
Q 2.961465029091743 4.3175e-08 au
  Orbit Determination Parameters
   # obs. used (total)      112  
   data-arc span      7084 days (19.39 yr)  
   first obs. used      1995-11-18  
   last obs. used      2015-04-11  
   planetary ephem.      DE431  
   SB-pert. ephem.      SB431-N16  
   condition code      0  
   fit RMS      .60277  
   data source      ORB  
   producer      Otto Matic  
   solution date      2017-Apr-10 21:12:24  

Additional Information
 Earth MOID = 1.42701 au 
 Jupiter MOID = 2.43425 au 
 T_jup = 3.363 


I tried to simulate their behavior in the past to investigate whether they might be related.

Simulation set-up
Mercury6 Integrator

reference:
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.

           Integration parameters
           ----------------------

   Algorithm: Bulirsch-Stoer (conservative systems)

   Integration start epoch:         2458000.5000000 days
   Integration stop  epoch:      -100000000.0000000
   Output interval:                     100.000
   Output precision:                 medium

   Initial timestep:                0.050 days
   Accuracy parameter:              1.0000E-12
   Central mass:                    1.0000E+00 solar masses
   J_2:                              0.0000E+00
   J_4:                              0.0000E+00
   J_6:                              0.0000E+00
   Ejection distance:               1.0000E+02 AU
   Radius of central body:          5.0000E-03 AU


In order to perform the simulation I generated 30 clones for each asteroids (same average orbital parameters as the nominal ones and standard deviation almost about the one calculated by JPL).

Thus, I evaluated 900 couples to check whether there was a moment in the past when two clones were very near with a very low relative velocity.
In particular, I used two arbitrary thresholds to detect interesting couples:
  • distance less than 1 Lunar Distance - about 0.0020 AU
  • relative velocity less than 1 m/s

The clone generation and the couples evaluation have been done using scripts written in R.

Simulation Results
The results are interesting because 819 out of 900 couples satisfy the thresholds mentioned above.

Distance between clones (km):
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.   sd
    105    1200    2190    3270    3230  119000  9030

Relative velocity (m/s) when at minimum distance:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.   sd
  0.034   0.092   0.120   0.140   0.150   0.940  0.09

Time of minimum distance (Years):
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.   sd
-272820  -75850  -62761  -74560  -56070  -18177  41444


In a graphical form:

same as above but with a little more  "zoom" ...:



The couple that went very near
Note that the time step is 100 days (this is consistent with a physical separation):



Conclusion
While this does not prove that the asteroids originated from a common body,  it seems that this is certainly a possibility.

Kind Regards,
Alessandro Odasso