Blog Archive

Monday, July 10, 2017

(2012 TQ236) vs 341874 (2008 GB53)

(2012 TQ236) vs 341874 (2008 GB53)

This is another interesting couple (same simulation approach described in the previous post).

(2012 TQ236)

Classification: Main-belt Asteroid          SPK-ID: 3612103
Ephemeris | Orbit Diagram | Orbital Elements | Physical Parameters ]

[ show orbit diagram ]

Orbital Elements at Epoch 2458000.5 (2017-Sep-04.0) TDB
Reference: JPL 6 (heliocentric ecliptic J2000)
 Element Value Uncertainty (1-sigma)   Units 
e .1666400181863286 5.5861e-06
a 2.181322170293682 2.3565e-06 au
q 1.817826604165701 1.4148e-05 au
i 3.706000259833047 2.3889e-05 deg
node 130.8866173415038 0.00037736 deg
peri 225.066713022466 0.0031505 deg
M 207.0510430328395 0.0025163 deg
tp 2458500.444927002519
(2019-Jan-16.94492700)
0.0088584 JED
period 1176.73358020709
3.22
0.0019068
5.221e-06
d
yr
n .3059316110760132 4.9574e-07 deg/d
Q 2.544817736421663 2.7491e-06 au
Orbit Determination Parameters
   # obs. used (total)      25  
   data-arc span      1078 days (2.95 yr)  
   first obs. used      2012-09-23  
   last obs. used      2015-09-06  
   planetary ephem.      DE431  
   SB-pert. ephem.      SB431-N16  
   condition code      3  
   fit RMS      .65133  
   data source      ORB  
   producer      Otto Matic  
   solution date      2017-Apr-07 17:13:15  

Additional Information
 Earth MOID = .814749 au 
 Jupiter MOID = 2.88145 au 
 T_jup = 3.660 

341874 (2008 GB53)

Classification: Main-belt Asteroid          SPK-ID: 2341874
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 4 (heliocentric ecliptic J2000)
 Element Value Uncertainty (1-sigma)   Units 
e .1669528069531998 1.1233e-07
a 2.180875946944555 3.0388e-08 au
q 1.816772585985444 2.5263e-07 au
i 3.706556681959036 1.2083e-05 deg
node 130.8943547687225 0.0001365 deg
peri 225.0440620302201 0.00014182 deg
M 182.8634290772902 3.7363e-05 deg
tp 2458579.329428649479
(2019-Apr-05.82942865)
0.00013018 JED
period 1176.372519962207
3.22
2.4587e-05
6.732e-08
d
yr
n .306025509684267 6.3962e-09 deg/d
Q 2.544979307903666 3.5462e-08 au
Orbit Determination Parameters
   # obs. used (total)      78  
   data-arc span      5842 days (15.99 yr)  
   first obs. used      2001-02-02  
   last obs. used      2017-01-31  
   planetary ephem.      DE431  
   SB-pert. ephem.      SB431-N16  
   condition code      0  
   fit RMS      .48759  
   data source      ORB  
   producer      Otto Matic  
   solution date      2017-Apr-10 08:47:34  

Additional Information
 Earth MOID = .813692 au 
 Jupiter MOID = 2.88132 au 
 T_jup = 3.660 

Simulation results ((note, Time 0 is JD 0 --> 4713 B.C.)

Kind Regards,
Alessandro Odasso

Monday, June 26, 2017

481085 (2005 SA135) vs 21028 (1989 TO)

I wonder if these two mars crossing asteroids might have generated from a common body.

The asteroid 21028 (1989 TO) is itself a recognized binary asteroid (Pravec et others). The rotation period is 3.6644 hours.

This is the result of my simulation (note, Time 0 is JD 0 --> 4713 B.C.) :



Approach
  • download orbital prameters from JPL Small-Body Database
  • perform simulation using Mercury6 software by John Chambers
  • establish a threshold rule (distance and relative velocity) for  stating that a couple of asteroids might have a common origin
  • analyze results and plot using R programming environment

Orbital parameters


481085 (2005 SA135)

Classification: Mars-crossing Asteroid          SPK-ID: 2481085
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 10 (heliocentric ecliptic J2000)
 Element Value Uncertainty (1-sigma)   Units 
e .2984405268289324 8.8599e-08
a 2.334110493987974 2.4417e-08 au
q 1.637517328485263 1.9453e-07 au
i 21.80096788876684 1.6384e-05 deg
node 340.5993513550984 1.7134e-05 deg
peri 98.81719065459441 6.9324e-05 deg
M 91.04532224832778 4.774e-05 deg
tp 2457671.090833414662
(2016-Oct-09.59083341)
0.00017073 JED
period 1302.508432528503
3.57
2.0438e-05
5.596e-08
d
yr
n .2763897653247032 4.3369e-09 deg/d
Q 3.030703659490684 3.1704e-08 au
Orbit Determination Parameters
   # obs. used (total)      243  
   data-arc span      4215 days (11.54 yr)  
   first obs. used      2005-09-11  
   last obs. used      2017-03-27  
   planetary ephem.      DE431  
   SB-pert. ephem.      SB431-N16  
   condition code      0  
   fit RMS      .52233  
   data source      ORB  
   producer      Otto Matic  
   solution date      2017-Apr-09 05:41:20  

Additional Information
 Earth MOID = .79863 au 
 Jupiter MOID = 2.52193 au 
 T_jup = 3.416 

21028 (1989 TO)

Classification: Mars-crossing Asteroid          SPK-ID: 2021028
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 17 (heliocentric ecliptic J2000)
 Element Value Uncertainty (1-sigma)   Units 
e .2998944450657227 5.4262e-08
a 2.332990251676451 1.1059e-08 au
q 1.633339434806201 1.2906e-07 au
i 21.78593156617378 8.7621e-06 deg
node 340.5615644130669 1.7944e-05 deg
peri 98.59272923713611 2.2979e-05 deg
M 263.6251062251222 1.3504e-05 deg
tp 2458348.940978486229
(2018-Aug-18.44097849)
4.9949e-05 JED
period 1301.570848400155
3.56
9.2546e-06
2.534e-08
d
yr
n .2765888621756544 1.9666e-09 deg/d
Q 3.032641068546701 1.4375e-08 au
Orbit Determination Parameters
   # obs. used (total)      751  
   data-arc span      9775 days (26.76 yr)  
   first obs. used      1989-10-04  
   last obs. used      2016-07-09  
   planetary ephem.      DE431  
   SB-pert. ephem.      SB431-N16  
   condition code      0  
   fit RMS      .43258  
   data source      ORB  
   producer      Otto Matic  
   solution date      2017-Apr-05 23:49:35  

Additional Information
 Earth MOID = .795177 au 
 Jupiter MOID = 2.52435 au 
 T_jup = 3.417 

Simulation setup

Let's try to investigate the last 1d8 days (about 274000 years), output interval every 100 days.

N-body algorithm:  Conservative Bulirsch-Stoer

This simulation will generate a file with almost 1e6 lines per asteroid.

)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) = bs2
 start time (days)= 2457800.5
 stop time (days) = -1d8
 output interval (days) = 100
 timestep (days) = 0.1
 accuracy parameter=1.d-12


Threshold rule
The following two conditions must be true at the same timestep:
  • distance less that 0.0020 AU (about 1 lunar distance)
  • relative velocity less than 1 meter/s

R custom program
I developed a small custom program to quickly analyze the results.

This program loads the output of the Mercury6 simulator (for every asteroid: a file with Time plus X,Y,Z and VX, VY, VZ).
For every couple of asteroids a dataframe is built: every row is associated to a specific timestep plus positions and velocities of the couple being investigated.
For every row, the distance and relative velocity is calculated and the threshold rules are checked. 
A couple of asteroids is interesting if the threshold rule is satisfied in at least one timestep. 
Once a couple is identified, a graph is built to show both distance and relative velocity.



Kind Regards,
Alessandro Odasso

Sunday, February 12, 2017

2016 WF9 - a simulation based on Feb 11th orbital params

This is a simulation of asteroid 2016 WF9 based on orbital parameters published on HORIZONS Web-Interface on Feb 11th, 2017.
 
At this time, the orbital condition code is 4

Orbital Elements at Epoch 2457800.5 (2017-Feb-16.0) TDB
Reference: JPL 13 (heliocentric ecliptic J2000)

 Element Value Uncertainty (1-sigma)   Units 
e .6580360863711519 9.9808e-06
a 2.870895540801432 8.6058e-05 au
q .9817426747520661 8.7514e-07 au
i 14.99562014245548 9.8595e-05 deg
node 125.4263986134548 0.00019086 deg
peri 342.4337260195148 8.1316e-05 deg
M 3.004319337477674 0.00013463 deg
tp 2457785.672494105614
(2017-Feb-01.17249411)
9.1832e-05 JED
period 1776.742590373345
4.86
0.07989
0.0002187
d
yr
n .2026179830159605 9.1105e-06 deg/d
Q 4.760048406850797 0.00014269 au

This asteroid was simulated with the Mercury6 orbit simulator together with 100 virtual clones generated with the package R.

These 100 clones were generated so that their orbital parameters are normally distributed around the nominal value of asteroid 2016 WF9 and their standard deviation is almost equal to the uncertainty shown above.

Virtual Asteroids: summary


mean sd
a 2.8709 8.68E−05
e 0.65804 9.51E−06
i 14.9956 9.48E−05
w 342.434 8.18E−05
om 125.426 0.00019
M 3.00432 0.00014

Simulation parameters
  • period simulated: past 1e8 days 
  • time step 0.1 days
  • ejection distance = 100 au
  • N-body algorithm: Conservative Bulirsch-Stoer

Simulation results
  • 1 out of 101 virtual asteroid was discarded because it would have collided with Jupiter
  • 44 out of 101 virtual asteroids came from the outskirt of the solar system (i.e., there was a time in the past when their distance was more than 100 au - ejection distance from the simulator point of view), so it makes sense to think they were comets.

This is the density distribution of arrival time in the solar system:


 Actually, according to the simulation, the first cometary event was 30084 years ago and the last one occurred 273009 years ago.

Probability of being a comet
I tried to use a R survival package called survminer to display the probability of a virtual asteroid being a comet, a probability that increases as you go more and more in the past.

I built a table with three columns:
  • virtual asteroid id
  • year: time of arrival into solar system, or end-time of the simulation (right censored data)
  • event: in case of arrival from the outskirt of the solar system, this flag is TRUE, otherwise it is FALSE coherently with column year.
The Surv function available in R can be used to convert the table in order to have a formal "survival" object and the survfit function can then be used to display a summary table showing how the various asteroids were progressively lost in favor of a comet - the lost of an asteroid is equivalent to the "death" event in a survival analysis).

These are the first lines of the survfit result:

Year(in the past) n.risk n.event survival std.err lower 95% CI upper 95% CI
30084 101 1 0.990 0.010 0.971 1.000
67281 100 1 0.980 0.014 0.953 1.000
70233 99 1 0.970 0.017 0.938 1.000
73898 98 1 0.960 0.019 0.923 0.999
74074 97 1 0.950 0.022 0.909 0.994
75356 96 1 0.941 0.024 0.896 0.988
80292 95 1 0.931 0.025 0.882 0.982
90790 94 1 0.921 0.027 0.870 0.975

How to read:
we started with 101 virtual asteroids, then at Year 30084 in the past we see one of them coming from the outskirt of the solar system, so we do not count it as an asteroid ...then, at Year 67281 in the past, this event occurs again ... and so on till we arrive at the last virtual asteroid being counted as a comet at Year 273009 in the past (last row not shown).

Based on this, we can draw a plot showing the probability of a virtual asteroid being a comet as a function of time:




Kind Regards,
Alessandro Odasso

Citations:
Survminer
Alboukadel Kassambara and Marcin Kosinski (2016). survminer: Drawing Survival Curves using 'ggplot2'
      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.

Monday, January 9, 2017

2016 WF9 - a simulation based on Jan 5th orbital params

On Jan 5th, I downloaded the orbital parameters of asteroid 2016 WF9 and their uncertainty from the Horizons Web interface:

param     value        1-sigma

a             2.8729806 0.00200340
e             0.6582656 0.00022291
i            14.9994893 0.00329270
w        342.4286190 0.00216310
om      125.4222393 0.00428050
M        353.6898676 0.00394660

In spite of the fact that the uncertainty is still very high, I tried to make a simulation generating 100 virtual asteroids to see how many of them in the past would seem to come from a distance greater than 100 AU (cometary origin).

First, I used the R programming environment to generate the virtual asteroids.
An obvious check is that the mean value of their orbital parameters must be almost equal to the nominal values of asteroid 2016 WF9 and their standard deviation should be also almost equal to the uncertainty shown above.

In fact, looking at the virtual asteroids, I got:

a     mean     2.8729   sd 0.002
e     mean     0.6583   sd 2e-04
i      mean   14.9988   sd 0.0035
w    mean 342.4285   sd 0.0023
om  mean 125.4218   sd 0.0046
M    mean 353.6903   sd 0.004


As a second step I used the Mercury6 simulator by John E. Chambers, to simulate the past 1e8 days, output interval 100 days (hybrid algorithm).
The program simulated the behaviour of 101 asteroids (100 virtual asteroid + the "real" asteroid):

The result was that about 60 virtual asteroids would seem to have a cometary orgin (i.e. there was a time in the past when their distance from the sun was grater than 100 AU).

The earliest date is about 37500 years ago, the oldest date is constrained by the simulation period (about 275000 years ago) and the median value is 155000 years ago.

(for curiosity: the nominal orbital values of 2016 WF9 itself tells us that this can be a comet arrived 76000 years ago).

This is the graph showing the arrival time of the 60 virtual comets:



In the next weeks, when the orbit of asteroid  2016 WF9 will be better defined, I would like to repeat the simulation to see if and how much the simulation results will be different.

Kind Regards,
Alessandro Odasso


Citations

      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.