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