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Sunday, December 10, 2017

174P/Echeclus

60558 Echeclus (2000 EC98) also known as 174P/Echeclus is a centaur that occasionally shows a cometary activity.

Outbursts happened in 2005, 2011 and in the first days of December 2017 (see MPML message from Brian Skiff) and confirmation from Richard Miles and Jean-Fran├žois Soulier.

The 2017 outburst is the strongest ever witnessed.

I simulated 100 clones of this centaur in the past 10^8 days trying to confirm its possible cometary origin: note that I am not taking into account the non gravitational forces associated to its outburst, not clear to me if they have a considerable effect.

The first step was to generate clones having orbital parameters distributed around the nominal ones with 1-sigma uncertainty as follows:

JPL Small-Body Database Browser

60558 Echeclus (2000 EC98)

Classification: Centaur          SPK-ID: 2060558
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 85 (heliocentric ecliptic J2000)
 Element Value Uncertainty (1-sigma)   Units 
e .4556668817376728 1.2005e-07
a 10.68172886788859 2.2774e-06 au
q 5.814418783090517 4.1275e-07 au
i 4.344445692331014 6.4394e-06 deg
node 173.3332131350017 5.505e-05 deg
peri 162.8042218299513 5.7268e-05 deg
M 24.47205469604485 6.4974e-06 deg
tp 2457133.680473384613
(2015-Apr-21.18047338)
0.00022632 JED
period 12751.48464064088
34.91
0.004078
1.116e-05
d
yr
n .02823200671493785 9.0289e-09 deg/d
Q 15.54903895268667 3.3152e-06 au
Orbit Determination Parameters
   # obs. used (total)      2888  
   data-arc span      13948 days (38.19 yr)  
   first obs. used      1979-09-23  
   last obs. used      2017-11-30  
   planetary ephem.      DE431  
   SB-pert. ephem.      SB431-N16  
   condition code      0  
   fit RMS      .44363  
   data source      ORB  
   producer      Otto Matic  
   solution date      2017-Dec-07 16:00:47  

Additional Information
 Earth MOID = 4.80483 au 
 Jupiter MOID = .838614 au 
 T_jup = 3.031 



Simulation approach


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 (general)

   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



Simulation Results
  • 77 out of 100 clones have a cometary orbit (i.e. they came from a distance greater than 100 AU).
    • of which: 3 came on a hyperbolic orbit. The one that had the highest speed had a Vinfinity about 3.7 km/s (Vinfinity = 42.1219*sqrt(-0.5/a) --> the semi-major axis being about -63.6 AU

The time (Year) when they entered the solar system was distributed as follows:

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
-272080 -109330  -62183  -82802  -36357   -4980


In a graphical form:

A look at the nominal asteroid
The nominal asteroid itself has a cometary origin.
It entered into the solar system at about year -105000 B.C.
In the plot below, the dashed vertical lines correspond to a close approach with Jupiter.
Note that Jupiter was not immediately important. 
In its early history, 174P/Echeclus was much more influenced by Saturn as shown here:

Coming back to plots showing the role of Jupiter, we can see these other ones:





A look at the clones - "footprint" diagrams
At any given time in the past, a clone had a certain perihelium q and a certain aphelium Q (I disregard the clones when on an hyperbolic trajectory because Q would be infinite).
Let's imagine that we plot all possible q-Q points in a diagram: the highest density area is the one where the clones happened to be for most of the time.

This is shown here ( I have used the R function stat_density2d - color scale implemented by viridis library):




Analysis of close approaches
These plots show the distribution of close appproaches (number and Dmin distance) between the clones and the major planets.









Kind Regards,
Alessandro Odasso

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