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Showing posts with label Amor. Show all posts
Showing posts with label Amor. Show all posts

Monday, December 30, 2019

Amors: (2019 QR6) and (2019 PR2) - investigation about cometary origin

These two asteroids have similar orbital parameters.
A possibility that should be investigated is that these asteroids separated recently from a common body ... see previous posts for a draft analysis.

Another aspect is that they might have a cometary origin.

For what's worth, considering the uncertainty (orbit condition code 4) and considering that I do not take into account non gravitational effects, I made a backward simulation with 2019 PR2

2019 PR2
Orbital Elements at Epoch 2458600.5 (2019-Apr-27.0) TDB
Reference: JPL 47 (heliocentric ecliptic J2000)
 Element Value Uncertainty (1-sigma)   Units 
e .7976773108833863 1.3756e-05  
a 5.772423469462186 0.00040358 au
q 1.167892239061442 2.2478e-06 au
i 10.98950352005738 9.7173e-05 deg
node 349.038132037726 0.00014302 deg
peri 57.08261419342178 0.00010673 deg
M 347.1019573973371 0.0013592 deg
tp 2458781.991800392675
(2019-Oct-25.49180039)
9.5194e-05 TDB
period 5065.656096365621
13.87
0.53125
0.001454
d
yr
n .07106680618494488 7.453e-06 deg/d
Q 10.37695469986293 0.00072551 au
  Orbit Determination Parameters
   # obs. used (total)      215  
   data-arc span      139 days  
   first obs. used      2019-08-10  
   last obs. used      2019-12-27  
   planetary ephem.      DE431  
   SB-pert. ephem.      SB431-N16  
   condition code      4  
   norm. resid. RMS      .40041  
   source      ORB  
   producer      Otto Matic  
   solution date      2019-Dec-28 08:29:27  

Additional Information
 Earth MOID = .236158 au 
 Jupiter MOID = .430847 au 
 T_jup = 2.149 


Clones
I generated 100 clones trying to achieve the same orbital parameters as calculated by JPL Small Body Database

Clones  Target
mean sd   mean sd
q 1.16789207 2.25e-06   1.16789224 2.25e-06
e 0.79767637 1.375e-05   0.79767731 1.376e-05
i 10.98949691 9.732e-05   10.98950352 9.717e-05
peri 57.08261449 0.00010684   57.08261419 0.00010673
node 349.03812785 0.00014309   349.03813204 0.00014302
tp 2458781.99180559 9.518e-05   2458781.99180039 9.519e-05


Simulation
Mercury6 simulator was set up like this (param.in file):



)---------------------------------------------------------------------
) Important integration parameters:
)---------------------------------------------------------------------
 algorithm (MVS, BS, BS2, RADAU, HYBRID etc) = BS
 start time (days)= 2458849.5
 stop time (days) = -1d8
 output interval (days) = 100
 timestep (days) = 0.05
 accuracy parameter=1.d-12
...
ejection distance (AU)= 1d2

As shown above, the arbitrary threshold to declare  that a clone has a cometary origin is set to 100 AU
I take into account all planets plus asteroids Ceres, Pallas and Vesta.

Simulation results 
At the end of the simulation, we find:
  • 72 out of 100 clones were ejected from the solar system
  • 2 out of 100 clones "hit" the sun

Considering that the simulation is backward in time, the above results must be read as:
  • 72 out of 100 clones have a cometary origin (they entered the solar system from a distance greater that 100 AU)
  • 2 out of 100 clones seem to have originated from the sun ! (we have to discard these as impossible results)

The following plots have been done using R scripts and package ggplot2.

First of all, we can see that there is not a "single" point in time when the clones likely to have a cometary origin have entered the solar system even though the are slightly more concentrated around 29000 years ago


Distribution of min perihelium
The simulation time has been divided into 10 slots.
In every slot, for every asteroid, we calculate the minimum perihelium that it had during that period.
The various values  are shown in a boxplot.
A similar approach is used for all the other plots. 

Distribution of max aphelium
Some clones entered the solar system on a hyperbolic trajectory, it does not make sense to calculate an aphelium (infinite) so they are not shown here:

... ooops!, an outlier ... if we omit it we have a better idea ... actually, we have to omit them about a dozen times before seeing something:

Distribution of max Orbital Period
...again after omitting several outliers:

Distribution of max Orbital Energy
In this graph, those clones with orbital energy >0 are on a hyperbolic orbit:

Distribution of Vinfinity
For those asteroids having an hyperbolic trajectory, it make sense to plot their Vinfinity:


Distribution of max eccentricity




References

Mercury6 simulator:
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.

package R:
  R Core Team (2019). R: A language and environment for statistical
  computing. R Foundation for Statistical Computing, Vienna, Austria.
  URL https://www.R-project.org/.

package ggplot2:
  H. Wickham. ggplot2: Elegant Graphics for Data Analysis.
  Springer-Verlag New York, 2016.




Cheers,
Alessandro Odasso

Sunday, October 6, 2019

Amors: (2019 QR6) and (2019 PR2)

On October 06th, 2019 I post a message on MPML list wondering about the nature of these two objects.

In fact that I was unable to link their orbits with Find_Orb

The message  was almost immediately answered by Bill Gray that already noticed the orbit similarity as you see in his answer.

For what is's worth, I tried a simulation going back just a few centuries.

I used the Mercury6 simulator (Bulirsch-Stoer algorithm, output every 100 days) to integrate the orbit of 100 clones for every Amor.
package by 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.

Ephemeris | Orbit Diagram | Orbital Elements | Mission Design | Physical Parameters | Close-Approach Data ]

[ 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 .7978288096308341 0.00032564
a 5.77647017220784 0.0096039 au
q 1.16783585084724 6.0685e-05 au
i 10.97219839923067 0.0022769 deg
node 349.0031380596452 0.0032242 deg
peri 57.11459122817678 0.0037867 deg
M 347.1017843073122 0.032425 deg
tp 2458782.185121653621
(2019-Oct-25.68512165)
0.0037127 TDB
period 5070.983875109436
13.88
12.646
0.03462
d
yr
n .07099214055225742 0.00017705 deg/d
Q 10.38510449356844 0.017266 au
Orbit Determination Parameters
   # obs. used (total)      55  
   data-arc span      37 days  
   first obs. used      2019-08-30  
   last obs. used      2019-10-06  
   planetary ephem.      DE431  
   SB-pert. ephem.      SB431-N16  
   condition code      6  
   norm. resid. RMS      .23771  
   source      ORB  
   producer      Otto Matic  
   solution date      2019-Oct-06 05:59:04  

Additional Information
 Earth MOID = .236027 au 
 Jupiter MOID = .430677 au 
 T_jup = 2.148 
(2019 QR6)
Classification: Amor [NEO]          SPK-ID: 3843716


Ephemeris | Orbit Diagram | Orbital Elements | Mission Design | Physical Parameters | Close-Approach Data ]

[ show orbit diagram ]

Orbital Elements at Epoch 2458600.5 (2019-Apr-27.0) TDB
Reference: JPL 13 (heliocentric ecliptic J2000)
 Element Value Uncertainty (1-sigma)   Units 
e .7976395056810581 7.5679e-05
a 5.771314015088342 0.0022317 au
q 1.167885956963114 1.4922e-05 au
i 10.98927716153723 0.0004847 deg
node 349.0377844945419 0.00064504 deg
peri 57.08297761694006 0.0010614 deg
M 347.0982101299367 0.0075621 deg
tp 2458781.992192675281
(2019-Oct-25.49219268)
0.0011319 TDB
period 5064.195745018806
13.87
2.9374
0.008042
d
yr
n .0710872995685642 4.1233e-05 deg/d
Q 10.37474207321357 0.0040118 au
Orbit Determination Parameters
   # obs. used (total)      79  
   data-arc span      56 days  
   first obs. used      2019-08-10  
   last obs. used      2019-10-05  
   planetary ephem.      DE431  
   SB-pert. ephem.      SB431-N16  
   condition code      5  
   norm. resid. RMS      .47936  
   source      ORB  
   producer      Otto Matic  
   solution date      2019-Oct-06 05:59:04  

Additional Information
 Earth MOID = .236151 au 
 Jupiter MOID = .430922 au 
 T_jup = 2.149 
(2019 PR2)
Classification: Amor [NEO]          SPK-ID: 3843547

I generated the clones trying to achieve the same orbital values as above.
This is what I got:

2019 QR6 

Clones Target
mean sd mean sd
q 1.16782936 6.072e-05 1.16783585 6.068e-05
e 0.7977961 0.00032594 0.79782881 0.00032564
i 10.97196669 0.00227869 10.9721984 0.0022769
peri 57.11505214 0.00378487 57.11459123 0.0037867
node 349.00281358 0.00322763 349.00313806 0.0032242
tp 2458782.18556559 0.00370968 2458782.18512165 0.0037127


2019 PR2

Clones Target
mean sd mean sd
q 1.16788572 1.491e-05 1.16788596 1.492e-05
e 0.79763725 7.562e-05 0.79763951 7.568e-05
i 10.98925764 0.00048534 10.98927716 0.0004847
peri 57.08297444 0.00106018 57.08297762 0.0010614
node 349.03776263 0.00064461 349.03778449 0.00064504
tp 2458781.99219263 0.00113238 2458781.99219268 0.0011319

I analyzed the 100*100 pairs, looking for pairs being very near with low relative velocity.

The best couple that I found behaved like this:



Apparently, somewhere around  year 1950 these two asteroids were at 2500 km with a relative velocity abot 10 m/s.

Does this make any sense?

Kind Regards
Alessandro Odasso


Monday, November 20, 2017

Amor 2002 RN38

This NEO is listed in the page of Asteroids with Comet-Like Orbits maintained by Y. Fernandez.

It was also discussed as an object with a likely cometary origin in some papers, among which I found:

At the time I made this analysis, this Amor was last observed on November 11th, 2017 and the orbit uncertainty is 0 being based on 119 observations acquired in the last 15 years.

JPL Small-Body Database Browser:

Orbital Elements at Epoch 2458000.5 (2017-Sep-04.0) TDB
Reference: JPL 31 (heliocentric ecliptic J2000)

 Element Value Uncertainty (1-sigma)   Units 
e .6730769823381273 2.1793e-07
a 3.820825408551513 1.2346e-07 au
q 1.249115772522818 7.9678e-07 au
i 4.160437503290696 1.756e-05 deg
node 296.1904517164833 0.00024613 deg
peri 118.6156866423836 0.00026072 deg
M 357.1006606538095 3.1062e-05 deg
tp 2458022.470035828635
(2017-Sep-25.97003583)
0.00023642 JED
period 2727.936248200967
7.47
0.00013222
3.62e-07
d
yr
n .1319678933983206 6.3964e-09 deg/d
Q 6.392535044580208 2.0656e-07 au

Orbit Determination Parameters
   # obs. used (total)      119  
   data-arc span      5568 days (15.24 yr)  
   first obs. used      2002-08-18  
   last obs. used      2017-11-15  
   planetary ephem.      DE431  
   SB-pert. ephem.      SB431-N16  
   condition code      0  
   fit RMS      .55328  
   data source      ORB  
   producer      Otto Matic  
   solution date      2017-Nov-16 07:18:58  

Additional Information
 Earth MOID = .270556 au 
 Jupiter MOID = .260678 au 
 T_jup = 2.626 


I simulated 100 clones of this asteroid in the past 10^8 days trying to confirm its possible cometary origin: the goal is to determine whether some clones might have arrived from the outskirt of the solar system - arbitrary 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
  • 79 out of 100 clones have a cometary like orbit.
    • of which: 13 came on a hyperbolic orbit (Vinfinity = 42.1219*sqrt(-0.5/a) --> the minimum absolute value for semi-major axis a was -17.46 AU -->the maximum value for Vinfinity was 7.14 km/s 
  • 1 out of 100 was discarded because "hit" the sun (due to extremely high eccentricity).

The time when they entered the solar system was distributed as follows:

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
-272319 -151956  -85380 -100222  -38660    -370


In a graphical form:



The most recent arrival in the solar system could have happened a relatively short time ago compared to other asteroids with a cometary like orbit: year 370 B.C.

A look at the nominal asteroid
The nominal asteroid is one of the 79 clones with a cometary like orbit. It apparently arrived in the solar system about in year 87000 B.C 

In the following plots (made with R package ggplot2), the vertical dashed lines show a close encounter with Jupiter.






Close Approaches analysis
For every given planet, every clone had a certain number of close approaches so we can calculate the mean number of close approaches and the mean number of Dmin (distance of the close approach). Even better, we can print a boxplot showing the distribution of the number of close approaches and their distances.










Kind Regards,
Alessandro Odasso