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.

2016 WF9 - a simulation based on Jan 5th orbital params

On Jan 5th, I downloaded the orbital parameters of asteroid 2016 WF9 and their uncertainty from the Horizons Web interface:

param     value        1-sigma

a             2.8729806 0.00200340
e             0.6582656 0.00022291
i            14.9994893 0.00329270
w        342.4286190 0.00216310
om      125.4222393 0.00428050
M        353.6898676 0.00394660

In spite of the fact that the uncertainty is still very high, I tried to make a simulation generating 100 virtual asteroids to see how many of them in the past would seem to come from a distance greater than 100 AU (cometary origin).

First, I used the R programming environment to generate the virtual asteroids.

An obvious check is that the mean value of their orbital parameters must be almost equal to the nominal values of asteroid 2016 WF9 and their standard deviation should be also almost equal to the uncertainty shown above.

In fact, looking at the virtual asteroids, I got:

a     mean     2.8729   sd 0.002
e     mean     0.6583   sd 2e-04
i      mean   14.9988   sd 0.0035
w    mean 342.4285   sd 0.0023
om  mean 125.4218   sd 0.0046
M    mean 353.6903   sd 0.004

As a second step I used the Mercury6 simulator by John E. Chambers, to simulate the past 1e8 days, output interval 100 days (hybrid algorithm).

The program simulated the behaviour of 101 asteroids (100 virtual asteroid + the "real" asteroid):

The result was that about 60 virtual asteroids would seem to have a cometary orgin (i.e. there was a time in the past when their distance from the sun was grater than 100 AU).

The earliest date is about 37500 years ago, the oldest date is constrained by the simulation period (about 275000 years ago) and the median value is 155000 years ago.

(for curiosity: the nominal orbital values of 2016 WF9 itself tells us that this can be a comet arrived 76000 years ago).

This is the graph showing the arrival time of the 60 virtual comets:

In the next weeks, when the orbit of asteroid  2016 WF9 will be better defined, I would like to repeat the simulation to see if and how much the simulation results will be different.

Kind Regards,
Alessandro Odasso


Citations

      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.