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)
[ 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
Additional Information
|
21028 (1989 TO)
[ 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
Additional Information
|
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
