304873 (2007 RD148) vs 95750 (2003 ED28)

These two main belt asteroids have similar obit parameters.

Their orbits are well known, in fact they are numbered objects and their orbit condition code is 0

Using the JPL Small-Body Database Browser, we can see:

304873 (2007 RD148)

Classification: Main-belt Asteroid          SPK-ID: 2304873

[ Ephemeris | Orbit Diagram | Orbital Elements | Physical Parameters | Discovery Circumstances | Close-Approach Data ]

[ show orbit diagram ]

Orbital Elements at Epoch 2458000.5 (2017-Sep-04.0) TDB Reference: JPL 8 (heliocentric ecliptic J2000)  Element Value Uncertainty (1-sigma)   Units  e .112706956254304 8.1867e-08 a 2.356322451918862 3.2148e-08 au q 2.090748520409409 2.1203e-07 au i 7.649992278043358 1.0168e-05 deg node 27.84270465718106 5.3513e-05 deg peri 271.5923935241259 6.9656e-05 deg M 320.2483032081591 4.5862e-05 deg tp 2458146.382661936927 (2018-Jan-27.88266194) 0.00016876 JED period 1321.145071424301 3.62 2.7037e-05 7.402e-08 d yr n .2724908927767416 5.5765e-09 deg/d Q 2.621896383428315 3.5771e-08 au

Orbit Determination Parameters    # obs. used (total)      122      data-arc span      5996 days (16.42 yr)      first obs. used      2000-11-30      last obs. used      2017-05-01      planetary ephem.      DE431      SB-pert. ephem.      SB431-N16      condition code      0      fit RMS      .62685      data source      ORB      producer      Otto Matic      solution date      2017-May-15 18:17:37   Additional Information  Earth MOID = 1.09229 au   Jupiter MOID = 2.56959 au   T_jup = 3.534

95750 (2003 ED28)

Classification: Main-belt Asteroid          SPK-ID: 2095750

[ 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 15 (heliocentric ecliptic J2000)  Element Value Uncertainty (1-sigma)   Units  e .1131879964824657 5.3076e-08 a 2.356588129411903 1.9765e-08 au q 2.089850640509408 1.2124e-07 au i 7.650207304601344 7.0217e-06 deg node 27.83162309848563 3.2879e-05 deg peri 271.7844693300495 4.7721e-05 deg M 252.9376849706002 3.6597e-05 deg tp 2458393.468812675760 (2018-Oct-01.96881268) 0.00013583 JED period 1321.368518179582 3.62 1.6624e-05 4.551e-08 d yr n .2724448138782385 3.4276e-09 deg/d Q 2.623325618314398 2.2002e-08 au

Orbit Determination Parameters    # obs. used (total)      464      data-arc span      7627 days (20.88 yr)      first obs. used      1996-04-17      last obs. used      2017-03-05      planetary ephem.      DE431      SB-pert. ephem.      SB431-N16      condition code      0      fit RMS      .57403      data source      ORB      producer      Otto Matic      solution date      2017-Apr-11 13:52:05   Additional Information  Earth MOID = 1.09141 au   Jupiter MOID = 2.56949 au   T_jup = 3.533

I tried to simulate their behavior in the past to investigate whether they might be related.

Simulation set-up

Mercury6 Integrator

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

In order to perform the simulation I generated 30 clones for each asteroids (same average orbital parameters as the nominal ones and standard deviation almost about the one calculated by JPL).

Thus, I evaluated 900 couples to check whether there was a moment in the past when two clones were very near with a very low relative velocity.

In particular, I used two arbitrary thresholds to detect interesting couples:

• distance less than 1 Lunar Distance - about 0.0020 AU
• relative velocity less than 1 m/s

The clone generation and the couples evaluation have been done using scripts written in R.

Simulation Results
The results are interesting because 770 out of 900 couples satisfy the thresholds mentioned above.

Distance between clones (km):

   Min. 1st Qu.  Median    Mean  3rd Qu.   Max.     sd
    961    4540    6849   13342   21245  126502    11832


Relative velocity (m/s) when at minimum distance:

   Min. 1st Qu.  Median    Mean   3rd Qu.  Max.     sd
   0.33    0.57    0.77    0.74    0.92    1.00     0.18


Time of minimum distance (Years):
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.     sd
-276373 -115975 -114199 -130260 -113592 -109542    42281

In a graphical form:

The couple that went very near
Note that the time step is 100 days (this is consistent with a physical separation):

Conclusion
This does not prove that the asteroids originated from a common body but I think that this is certainly a possibility.

Kind Regards,
Alessandro Odasso