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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

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