Again on comet D/1770 L1 (Lexell)

Year 1757.

Three comets:

• D/1770 L1 (Lexell)
• P/2014 R5 (Lemmon-PANSTARRS)
• P/1999 RO28 (LONEOS)

Let's compare their nominal distance using JPL Horizons and Mercury6 software by John E. Chambers.

According to Mercury6 software, on 1757-Jul-1, the Lexell comet was at 0.33 (AU) from comet P/2014 R5 (Lemmon-PANSTARRS) and it was  at 0.16 (AU) from  comet P/1999 RO28 (LONEOS).

JPL Horizons models the Lexell comet in a different way.
According to JPL Horizons, the Lexell comet was at 1.53 (AU) from comet P/2014 R5 (Lemmon-PANSTARRS) and it was at 1.61 (AU) from  comet P/1999 RO28 (LONEOS).

Both JPL Horizons and Mercury agree and get the same result when looking  at the nominal distance between P/2014 R5 (Lemmon-PANSTARRS) and P/1999 RO28 (LONEOS).


Comet P/2014 R5 (Lemmon-PANSTARRS)

*******************************************************************************
JDCT 
   X     Y     Z
   VX    VY    VZ
   LT    RG    RR
*******************************************************************************
$$SOE
2362988.500000000 = A.D. 1757-Jul-17 00:00:00.0000 (CT)
  -5.257637317706235E+00  2.477814508385187E-01  6.790907841994050E-02
   1.426562748323473E-03 -5.796128684565190E-03  2.940516606550701E-05
   3.040181361915521E-02  5.263910851719347E+00 -1.697317088053800E-03
$$EOE
*******************************************************************************

Comet P/1999 RO28 (LONEOS)

*******************************************************************************
JDCT 
   X     Y     Z
   VX    VY    VZ
   LT    RG    RR
*******************************************************************************
$$SOE
2362988.500000000 = A.D. 1757-Jul-17 00:00:00.0000 (CT)
  -5.430809043797567E+00  3.084110607570195E-01 -7.118879844782251E-02
   2.327107819955809E-04 -4.558198020424996E-03  2.130564382053195E-03
   3.141896416246138E-02  5.440025008914496E+00 -5.186150467730436E-04
$$EOE
*******************************************************************************

Nominal distance (according to JPL Horizons): 0.23 (AU)
I get the same result using Mercury6 orbit simulator.

Given the orbit uncertainty that I am unable to evaluate, the idea that these comets are related is still a speculation.

I do not know if MPC should be involved in a case like this.

However, It would be nice to investigate this matter in a deeper way.


Kind Regards,
Alessandro Odasso

P/2014 R5 (Lemmon-PANSTARRS) vs D/1770 L1 (Lexell)

According to Horizons Web Interface, the nominal distance between the comet P/2014 R5 (Lemmon-PANSTARRS) and the Comet D/1770 L1 (Lexell) was 0.49 (AU) on 1772-Jun-25.

Symbol meaning [1 au=149597870.700 km, 1 day=86400.0 s]:

    JDCT     Epoch Julian Date, Coordinate Time
      X      x-component of position vector (AU)                               
      Y      y-component of position vector (AU)                               
      Z      z-component of position vector (AU)                               
      VX     x-component of velocity vector (AU/day)                           
      VY     y-component of velocity vector (AU/day)                           
      VZ     z-component of velocity vector (AU/day)                           
      LT     One-way down-leg Newtonian light-time (day)                       
      RG     Range; distance from coordinate center (AU)                       
      RR     Range-rate; radial velocity wrt coord. center (AU/day)

Comet      P/2014 R5 (Lemmon-PANSTARRS)

JDCT 
   X     Y     Z
   VX    VY    VZ
   LT    RG    RR
*******************************************************************************
$$SOE
2368445.500000000 = A.D. 1772-Jun-25 00:00:00.0000 (CT)
  -5.350772153692991E+00  7.519737209984863E-01  6.507105626789669E-02
   5.429545955058305E-04 -5.709574426723797E-03  4.064357076622107E-05
   3.120942901941327E-02  5.403745123539087E+00 -1.331674861182269E-03
$$EOE
******************************************************************************* 

Comet      D/1770 L1 (Lexell)

JDCT 
   X     Y     Z
   VX    VY    VZ
   LT    RG    RR
*******************************************************************************
$$SOE
2368445.500000000 = A.D. 1772-Jun-25 00:00:00.0000 (CT)
  -5.065183309814054E+00  1.154049192420066E+00  7.604951982430537E-02
  -3.367607369438152E-03 -2.956615617800361E-03  1.213072905725020E-04
   3.000696938171253E-02  5.195545691263794E+00  2.628153989642551E-03
$$EOE
******************************************************************************* 

Nominal distance: 0.49 (AU), Uncertainty: uknown

The same nominal result is obtained using the Mercury Integrator by John E. Chambers.

Before that date, the JPL Horizons and the Mercury results are no longer similar.

I suspect this is due to the different way used to model the close approaches with Jupiter but I am not sure.
In fact, as already known, comet Lexell went very near to Jupiter:

• 1779-07-27 - close approach at about 0.0015 (AU)
• 1767-03-28 - close approach at about 0.022 (AU)

Strange: the 1779 close approach was very low and yet JPL Horizons and Mercury go back to 1772 consistently.

However, the 1767 close approach is managed differently: before that date the results of JPL Horizons and Mercury are very different for comet Lexell (but still consistent for the other comet). Thus, the calculated distance between the two comets is very different.
To give an idea:

• according to Mercury software, in 1757-05-21 (ten years before the first close approach between Lexell and Jupiter)  the nominal distance between the two comets was as low as 0.14 (AU)

• according to JPL Horizons, on the same date, the distance was quite different: 1.68 (AU)

Conclusion

It would be nice to be able to male a statistical analysis (Montecarlo simulation?) to see if is possible to evaluate the uncertainty of the 1772 result and (if it holds up) the uncertainty of the 1757 result.

This analysis could confirm or reject what in this moment is only a speculation: these two comets might be related.

Kind Regards,
Alessandro Odasso

Asteroid 2005 QQ87

JPL/HORIZONS                     (2005 QQ87)               2014-Dec-03 15:43:43
Rec #:530344 (+COV)   Soln.date: 2014-Sep-12_12:17:06     # obs: 52 (2005-2014)
 
FK5/J2000.0 helio. ecliptic osc. elements (au, days, deg., period=Julian yrs): 
 
  EPOCH=  2454437.5 ! 2007-Dec-03.00 (CT)          Residual RMS= .27303        
   EC= .3031120594670821   QR= .6968320203827482   TP= 2454614.6607866557      
   OM= 155.0827683457962   W=  54.47813449079076   IN= 33.94229881367796       
   A= .9999197573283777    MA= 185.3679511050879   ADIST= 1.303007494274007    
   PER= .9999              N= .985726285           ANGMOM= .016392167          
   DAN= .77208             DDN= 1.10215            L= 204.3708543              
   B= 27.0291607           MOID= .0794868          TP= 2008-May-28.1607866557  
 
Asteroid physical parameters (km, seconds, rotational period in hours):        
   GM= n.a.                RAD= n.a.               ROTPER= n.a.                
   H= 22.7                 G= .150                 B-V= n.a.                   
                           ALBEDO= n.a.            STYP= n.a.                  
 
ASTEROID comments: 
1: soln ref.= JPL#11, OCC=1
2: source=ORB 

These are two graphs showing the movement of the asteroid in a frame of reference co-rotating

with earth

Sun is at (0,0) and Earth is at (1,0).

In this moment, the asteoroid seems a quasi-satellite of earth

 

However, the libration seems quite fast, so the "quasi-satellite" status is absolutely 

temporary:

Cheers,

Alessandro Odasso 

2010 TK7 and (3753) Cruithne - Libration comparison

Asteroid 2010 TK7

Asteroid 2010 TK7 is the first Earth "trojan" asteroid to be discovered.

A beatiful orbit visualization is available here:
http://youtu.be/VGmdSbtkFS0

As shown in the second part of the clip, there is an interesting long-term libration  around Lagrange points L4  possibly extending to L3.

I have tried myself to plot the relative position of sun, earth and asteroid 2010 TK7 in the last 7000 years in order to have a better visualization of the whole libration movement.

In a frame of reference co-rotating with earth, sun is at coordinates (0,0) and earth is fixed, let's say at coordinates (1,0).

This is the graph showing (X,Y) of the asteroid as time passes:

So we can see the so called "tadpole" orbits around L4 (red).
If the graph is correct, in the past, there had been "tadpole" orbits around L5 (blue) as well.
Furthermore, there has been a period when the asteroid librated along the so called "horse-shoe" orbit.

Of course, if you forget about the "time dimension" (imagine to look at the "spring-like" shape from the center), you get a simple X,Y diagram, where the overall path is that of a "horse-shoe":

Asteroid (3753) Cruithne

Just for comparison, let's do the same looking at the libration movement of asteroid (3753) Cruithne.

Here is what I get:

If correct, the result seems to say that the orbit of Cruithne is much more stable than that of 2010 TK7 (no tadpole and no horse-shoe orbit is displayed in most parts of the period in analysis) even if there had been a couple of times when the libration movement did changed direction somewhere on the L5 side.

Again, if we forget the time dimension we just get a simpler graph that does not show any "horse-shoe" or "tadpole" just because everything overlaps:

Mars-crossing Asteroids - Absolute Magnitude Model

The H mag median for the Mars-crossing asteroids is about 18.

I tried to use a data mining software (Weka) to find a classification model that builds a decision tree based on orbital parameters (a,e,i) to estimate whether a mars-crossing asteroid has H<=18.

After many trials, I found a model that is far from being perfect but that might have some interest.

The model seems to be able to correctly identify the H mag level of the mars-crossing asteroids in 67% of the cases (a performance much better than the 50% probability of success that it could have just by chance).

The data mining program has processed 12477 asteroids using the J48 algorithm (66% of the asteroids used for training, the remainder for testing it). When it finished, the following report was displayed:

In the above report, we see the overall performance of the model (67% of correctly identified instances) plus a detailed accuracy summary for each class showing the rate of True Positives, False Positives  and Precision.

At the bottom, we can see the so called "Confusion Matrix" or contingency table showing the two classes of asteroids magnitude:

• class a: bright asteroid (H <= 18.0)
• class b: dim asteroid (H > 18.0)

In order to understand it better, let's explain it looking for example at class b, i.e., the class of dim asteroids:

• TP Rate: we see that the dim asteroids were correctly predicted with a rate of 72.8% (1554 / (1554+580))

• FP Rate: we see that 796 bright asteroid were mistakenly classified as dim asteroids, thus the proportion of bright asteroids not correctly classified is 37.8% (796/(1312+796))

• Precision: any asteroid classified as dim  was truly dim in about 66% of the cases (1554 / (1554+796)).

In the following section, you can see the model itself (as a tecnique called bagging was used, the output contains 10 decision trees that taken together produced the overall result):

2013 ST71 - A member of the Datura cluster ?

These 7 asteroids are already recognized as belonging to the Datura cluster:

• (1270) Datura
• (60151) 1999UZ6 
• (89309) 2001VN36 
• (90265) 2003CL5 
• (203370) 2001 WY35
• (215619) 2003 SQ168
• 2003 UD112

Is asteroid 2013 ST71  a member of the Datura cluster ?

At first glance, I would say yes: the orbit of 2013 ST71 is very similar to the orbit of (1270) Datura, but it is not clear to me if this happens by chance or not .


Let's look at Horizons Web -

(1270) Datura

Element	Value	Uncertainty (1-sigma)	Units
e	.207362426961996	6.897e-08
a	2.23509416609344	7.619e-09	AU
q	1.771619615323705	1.539e-07	AU
i	5.988581620229616	5.1796e-06	deg
node	97.85012324839816	6.7015e-05	deg
peri	258.8674632296458	6.7965e-05	deg
M	69.4456617884065	1.2739e-05	deg
tp	2456565.057541251396 (2013-Sep-29.55754125)	4.2797e-05	JED
period	1220.512310873357 3.34	6.2407e-06 1.709e-08	d yr
n	.294958106356499	1.5082e-09	deg/d
Q	2.698568716863174	9.1989e-09	AU

2013 ST71

Element Value Uncertainty (1-sigma)   Units  e .2072926241711973 2.4439e-07 a 2.235332639213504 3.0253e-08 AU q 1.771964670535408 5.4988e-07 AU i 5.98688637443826 1.0741e-05 deg node 97.99751181500383 0.00026181 deg peri 258.8943816441401 0.00026916 deg M 78.4852036132318 4.0622e-05 deg tp 2456534.368087665562 (2013-Aug-29.86808767) 0.00013895 JED period 1220.707649718649 3.34 2.4781e-05 6.785e-08 d yr n .2949109068686294 5.9869e-09 deg/d Q 2.698700607891598 3.6524e-08 AU

A few month ago, we also mentioned that another asteroid (338309) 2002 VR17 might be a member of the same cluster - if these findings are confirmed, the Datura cluster would have at least 9 recognized members.

At the end of this embedded PDF (a list of potential asteroid pairs to be confirmed / rejected), there is an entry for 2013 ST71:



Click on asteroid names to get more details from the AstDyS service.
Click on Asteroid1_Asteroid2 distance to see a graph showing how the distance between the two asteroids varied in the past according to a simulation performed with Mercury simulator.

Kind Regards,
Alessandro Odasso

Potential Asteroid Pairs

This is a list of potential asteroid pairs (asteroid1 - asteroid2).

Asteroid1 and Asteroid2 have been very close in the past: whether this happened by chance or not needs to be confirmed. In fact, what you see here is just the result of a simulation made with Mercury software.

I am aware that any simulation result must be taken with caution. Besides any trivial error that I might have done, one must be aware that the simulation itself had these characteristics:

• no attempt to take into account Ceres, Pallas and Vesta
• no attempt to take into account non gravitational forces
• use of hybrid simplectic algorithm that is fast but maybe a little less precise than other algorithms

Once said this, if you look at the above list, you can get more details.
Open the embedded PDF in full screen mode, you will be able to click and follow the hyperlinks.

The hyperlink in column "Asteroid1_Asteroid2_Distance" will open a page  showing how the distance between the two asteroids varied in the past.

The hyperlink associated to the asteroid names will open a page of the AstDys system where you will find useful details that may help to put things in context.

For example, I already listed what I think is a useful information provided by AstDys , i.e.whether it is possible or not to identify a parent body for the family of the two asteroids of the pair and which are the nearest family members.

In some cases, the AstDys service is unable to identify a parent body for the asteroid pair:  it is not clear to me if this happens because the pair is really isolated or because it has not yet been associated to a family.
The fact that no parent body is identified does not  necessarily mean that the asteroid pair is not interesting and I guess that the opposite is also true: finding a parent body does not prove that the two asteroids are a divorced pair.

Let's look at the most important parent bodies listed above counting them.
This is the result :

Parent Body	Total
-	28
(158) Koronis	26
(135) Hertha	5
(4) Vesta	5
(1338) Duponta	3
(2076) Levin	2
(15) Eunomia	1
(1547) Nele	1
(16286) 4057P-L	1
(170) Maria	1
(20) Massalia	1
(606) Brangane	1
(668) Dora	1
(93) Minerva	1

In conclusion, about 1/3 of the cases belong to the (158) Koronis family, another 1/3 of the cases can not be related to known families, the last 1/3 is spread in other families.

Inside the Koronis family, the asteroid that more often appear to be related to the asteroid pairs are:

(11728) Einer

(2226) Cunitza (158) Koronis Kind Regards, Alessandro Odasso