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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.

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