Blog Archive

Monday, April 20, 2015

Asteroid Physical Parameters

Let's use Horizons Web Interface to search for asteroids with the following contraints:
  • H mag defined
  • diameter defined
  • albedo defined
  • B-V mag defined
  • U-B mag defined
It would be nice to look for I-R mag values but these data are not available. 
Let's also extract the asteroid designations and their spectral type (SMASSII) when available.


We get a list of 813 asteroids.

I try to use a data mining package called Weka to visualize and analyze the data.
To start simple: let's look at a well known relation, the one linking H and diameter.

Diameter versus H mag

We can see this graph ( H mag is on the X-axis, Diameter on the Y-axis):

Two distinct but similar curves exist beyond a certain H  threshold (very roughy H = 12 - 12.5 ).

Diameter and H are related via albedo, so we can try to use Weka to cluster the asteroids using for example H and albedo.


Cluster results
Let's run the K-Means clustering algorithm with K=2 using H and albedo.
The following two clusters are identified (Weka returns the two cluster centroids and numerosity):

Let's look at the same plot as before using the blue color for the smaller cluster and the red color for the larger one to see if the clusters can be visually associated to the two distinct branches:



The relation between the two branches of the plot and the clusters defined based on H and albedo is not "perfect" (some of the red instances are displayed in proximity of the blue ones) but, at least roughly, it seems to be well confirmed.

Let's now cluster based on B-V and U-B.
We get this result (do not mind about the fact that this time the smaller cluster is called cluster 1 ... we will continue to display the smaller cluster with a blue color):

This is interesting because we have got almost the same result as before suggesting that the two clusters based on B-V and U-B are almost overlapped with those defined based on H and albedo.

Let's try to use another software package called QTIPlot to estimate a polynomial fit for the two Diameter vs H curves.




Clusters versus spectral type

First of all, we display the two clusters on the B-V and U-B plane:

We want to analyze the two clusters in more detail trying to see if we can see a relation with the spectral type.

Before doing this, let's look at the overall spectral type distribution:


Cluster1

First we look at the spectral type distribution of the 322 asteroids that belong to this cluster.


What is interesting in this cluster is this: almost all S-type asteroids (94 out of 96) belong to this cluster and they constitute a little more than half of their cluster population. 

Let's use Weka ZeroR algorithm to put a lower boundary on the performance of any classification model.
The ZeroR model always predicts the largest numerosity class: 94 S asteroid, 182 asteroids with a known spectral type (94 / 182 = 51.6%).
In fact, this is the Weka output:

Let's see if it is possible to use H, diameter, albedo B-V, U-B to discriminate the S-type asteroids from the other asteroids types.

We try with the logistic model (cross validation N=10). The result is this:

I would say that the logistic model has failed to make any significant prediction.
Other classification models give apparently a better result but I think that this is just due to an overfitting effect because there is a too big difference between the n=10 cross-classification performance versus the whole training set performance.

Cluster 0

Again, first we look at the spectral type distribution of the 491 asteroids that belong to this cluster.
What is interesting in this cluster is this: it contains most of the carbonaceous and metallic asteroids and it is quite etherogeneous.
Let's use Weka ZeroR algorithm to put a lower boundary on the performance of any classification model.
The ZeroR model always predicts the largest numerosity class: 60 Ch asteroids, 228 asteroids with a known spectral type (60 / 228 = 26.3%).
In fact, this is the Weka output:

Let's see if it is possible to use H, diameter, albedo B-V, U-B to discriminate among the various asteroid types.
We try with the logistic model (cross validation N=10). The result is this:

This time it seems that the logistic model has a moderate success (44% performance compared to a minimum 26% performance), so the asteroid physical parameters seem to have some predicting power in this cluster.
However, the fact that the accuracy  jumps to 57% when you run the model on the whole set of asteroids belonging to this cluster seems to be an overfitting effect.
Better not to believe this model!

Before giving up, we can see that the situation improves a little bit if we reduce the number of variables just focusing on the B-V and U-B parameters.
In fact, this is what happens with the logistic model that just uses B-V and U-B (cross validation N=10):

... and this is what happens when running the model on the whole cluster:


Not sure of this: the relative small increase in the amount of correctly classified instances may indicate that the overfitting effect is not so big and so we may hope that the model has at least in part been able to correctly generalize.

In that case, as you see in the section "Detailed Accuracy by Class", we may have some  success with the prediction of asteroids belonging to these spectral types:
  • B (average precision 0.647)
  • CH (average precision 0.535)
  • X (average precision 0.38)
  • C (average precision 0.368)
Just for curiosity ... here is the list of predictions.

Note that:
  • column spec_B: this is the already known spectral type as downloaded by Horizons database. When no spectral type is available in the Horizon database, you can see a question mark.
  • column classification: this is the prediction of the model. Of course, if the previous column is known and the predicted type is different ... this is an error. If the previous column is a question mark ... this is the prediction.
  • all other columns contain the probability distribution: the spectral class with the greatest probability is the predicted class.
In spite of the fact that the average precision is not high, there are a few cases where it is very high.

The fact that Weka returns the probability distribution is very nice because you can plot other graphs, for example: probability distribution of a given spectral type versus B-V.

Look for example at these plots:

type B distribution versus (B-V)


type C distribution versus (B-V)


... but before going to these details, it would be better to be more confident about the validity of the model!

Kind Regards,
Alessandro Odasso

Thursday, March 19, 2015

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

Friday, March 13, 2015

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

Thursday, December 4, 2014

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 

 

Saturday, November 22, 2014

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:







Monday, October 20, 2014

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):



Monday, April 7, 2014

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
 ElementValueUncertainty (1-sigma)  Units 
e.2073624269619966.897e-08
a2.235094166093447.619e-09AU
q1.7716196153237051.539e-07AU
i5.9885816202296165.1796e-06deg
node97.850123248398166.7015e-05deg
peri258.86746322964586.7965e-05deg
M69.44566178840651.2739e-05deg
tp2456565.057541251396
(2013-Sep-29.55754125)
4.2797e-05JED
period1220.512310873357
3.34
6.2407e-06
1.709e-08
d
yr
n.2949581063564991.5082e-09deg/d
Q2.6985687168631749.1989e-09AU

2013 ST71

 ElementValueUncertainty (1-sigma)  Units 
e.20729262417119732.4439e-07
a2.2353326392135043.0253e-08AU
q1.7719646705354085.4988e-07AU
i5.986886374438261.0741e-05deg
node97.997511815003830.00026181deg
peri258.89438164414010.00026916deg
M78.48520361323184.0622e-05deg
tp2456534.368087665562
(2013-Aug-29.86808767)
0.00013895JED
period1220.707649718649
3.34
2.4781e-05
6.785e-08
d
yr
n.29491090686862945.9869e-09deg/d
Q2.6987006078915983.6524e-08AU

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