CBET 2852, issued on Oct 03 2011, announced the discovery of a new comet of 15m.7 in the course of the Catalina survey through the 0.68-m Schimdt + CCD, on images obtained by R. A. Kowalski on Sep. 30.48 UT, 2011. The coma is about 15" and the broad tail is 1' long in approximately P.A. 300°. Initially the comet bore the name "Kowalski" but soon Gareth V. Williams posted a clarification to cancel the decision so thus far the comet remains unnamed.
MPEC 2011-T12
comments that the orbit of this object is essentially indeterminate at the
present time. It is possible that this is a short-period comet. Among the
wide range of
possible short-period orbits are orbits that appear similar to P/2006 T1 (Levy).
Initial attempts to link the two apparitions have not been successful.
Further observations are encouraged.
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| The comet shows a curved tail judging from the stacked image. The trend can be seen even more manifest in the image filtered by Larson-Sekanina processing. However, it may well be imperfection of the image due to the quality of flatfield and dark images. Mouseover to browse the entire version without the two specially processed images. |
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| Pseudo-colors have been applied to the b/w stacked image so as to present the coma along with its tail to a somewhat better extent. |
The following MPC observations were compiled with coordinates measured in Astrometrica by UCAC-3 star catalog and photometry by CMC-14 star catalog in R band:
I try to compute a seemingly appropriate orbital solution for comet C/2011 F1 (LINEAR) by feeding our own astrometrical measurements and measurements from other stations and observatories, totally 141 observations (10 or 9 of them rejected in two following corresponding cases), to FindOrb.
Here come my two reasonable solutions:
[1] Auto-solved mode:
Orbital elements: C/2011 S2 Perihelion 2011 Oct 25.308117 TT = 7:23:41 (JD 2455859.808117) Epoch 2011 Oct 4.0 TT = JDT 2455838.5 Earth MOID: 0.1497 M 359.97345 (2000.0) P Q n 0.00124563 Peri. 190.95895 -0.48405469 -0.82719996 a 85.5478070 Node 288.54031 0.82387343 -0.32095783 e 0.9868199 Incl. 17.51663 0.29482810 -0.46122260 P 791.25 M(N) 15.1 K 10.0 q 1.12752518 Q 169.968088 From 85 observations 2011 Sept. 30-Oct. 3; RMS error 0.608 arcseconds
Residuals in arcseconds: 110930 703( 1.4- .76+) 111001 J95 .05+ .20- 111002 106 .41+ .39- 110930 703 .53- .36- 111001 J95 .14+ .05- 111002 106( 1.3- .37+) 110930 703( 2.3- .10-) 111001 B86 .03- .13+ 111002 461 .70- .29+ 110930 703 .22- .03+ 111001 B86 .00 .04+ 111002 461 .31+ .11- 111001 A17 .44- .15+ 111001 B86 .21+ .26- 111002 461 .14+ .28- 111001 595 .95- .68+ 111001 J95 .27+ .02+ 111002 461 .23- .30+ 111001 595 .47- .10- 111001 B86 .18- .15+ 111002 106( 1.1- .06+) 111001 A17 .01+ .18- 111001 H21 .57+ .33+ 111002 510 .75- .18+ 111001 A17 .12+ .19+ 111001 H21 .24- .01+ 111002 510 .31- .04- 111001 113 .42+ .03- 111001 H21 .35- .08+ 111002 510 .86- .15+ 111001 510 .40- .07+ 111001 H21 .05+ .42- 111002 510 .55- .34+ 111001 A71( 1.5- .30-) 111001 H21 .24- .49- 111002 704( 1.2- .87+) 111001 113 .67- .06+ 111001 H21 .30- .30- 111002 704 .48- 1.1+ 111001 A71 .68- 1.5+ 111001 H21 .31+ .06- 111002 H17 .00 .08- 111001 A71( 2.3- 1.9+) 111001 H21 .07+ .25- 111002 704( 2.6- 1.4+) 111001 113 .25+ .17- 111001 H17 .56- .83+ 111002 H17( 1.3- 2.1+) 111001 510 .00 .05- 111001 H17 .34- .93+ 111002 H36 .73- .12+ 111001 A71 .82- .24+ 111001 H06 .49- .17- 111002 H36 .39- .22- 111001 A71( 1.6- 1.3+) 111001 H17 .02- .22+ 111002 H17 .47- .26- 111001 204 .08- .42- 111001 H06 .74+ 1.1- 111002 H36 .75- .23+ 111001 113 .05+ .10- 111001 H06( 1.1+ .11-) 111002 H01 .52+ .12+ 111001 A71( 4.0- 3.7+) 111001 H06( 1.0+ .09-) 111002 704( 3.8- 1.7+) 111001 510 .16- .13+ 111001 H06 .37+ .12+ 111002 H17 .59- .40- 111001 204 .17- .44- 111001 H10 .75+ .03+ 111002 H01 .43+ .15- 111001 510 .12+ .11+ 111001 H01 .82+ .04- 111002 H17 .42+ .09- 111001 204 .37- .24- 111001 H10( 1.3+ .15-) 111002 H01 .17+ .07+ 111001 B86 .24- .08- 111001 H01 .78+ .09- 111002 H01 .26+ .29+ 111001 B86 .17- .03- 111001 H01 .90+ .04- 111003 C42 .59- .22- 111001 B86 .07- .22- 111001 H01 .73+ .06- 111003 C42 .73+ .76- 111001 510 .16- .30+ 111001 G96 .97+ .32- 111003 C42 .08+ .12- 111001 B86 .03+ .01- 111001 G96 .92+ .11+ 111003 C42 .33+ .38+ 111001 157 .51+ .19+ 111001 G96 .90+ .29- 111003 C42 .02- .42+ 111001 157 .94+ .28- 111001 G96 .68+ .08+ 111001 157 .38+ .38- 111002 106 .06- .38- # State vector (heliocentric ecliptic J2000): # -0.124481969422 1.168805617857 0.080048863295 AU # -20.329949020904 -6.355816011461 -6.721335836236 mAU/day # MOIDs: Me 0.8114 Ve 0.4161 Ea 0.1497 Ma 0.3040 # MOIDs: Ju 1.2084 Sa 1.6910 Ur 1.6343 Ne 2.2862 # Elements written: 4 Oct 2011 8:50:05 (JD 2455838.868113) # Full range of obs: 2011 Sept. 30-Oct. 3 (100 observations) # Find_Orb ver: Oct 11 2010 13:08:42 # Perturbers: 00000000 (unperturbed orbit) # Tisserand relative to Earth: 2.86633 # Tisserand relative to Jupiter: 1.31227 # Tisserand relative to Neptune: 0.87207
[2] With constraint e = 1:
Orbital elements: C/2011 S2 Perihelion 2011 Oct 25.213819 TT; Constraint: e=1 Epoch 2011 Oct 4.0 TT = JDT 2455838.5 Earth MOID: 0.1523 q 1.13023030 (2000.0) P Q M(N) 15.1 K 10.0 Peri. 190.84903 -0.48424052 -0.82713416 Node 288.65692 0.82359203 -0.32088605 e 1.0 Incl. 17.52111 0.29530879 -0.46139052 From 85 observations 2011 Sept. 30-Oct. 3; RMS error 0.607 arcsecondsResiduals in arcseconds: 110930 703( 1.4- .78+) 111001 J95 .05+ .20- 111002 106 .40+ .39- 110930 703 .51- .34- 111001 J95 .13+ .05- 111002 106( 1.3- .37+) 110930 703( 2.3- .08-) 111001 B86 .03- .13+ 111002 461 .71- .28+ 110930 703 .21- .04+ 111001 B86 .00 .05+ 111002 461 .29+ .11- 111001 A17 .44- .15+ 111001 B86 .21+ .26- 111002 461 .13+ .28- 111001 595 .95- .68+ 111001 J95 .27+ .02+ 111002 461 .25- .30+ 111001 595 .47- .10- 111001 B86 .19- .15+ 111002 106( 1.2- .05+) 111001 A17 .01+ .18- 111001 H21 .57+ .33+ 111002 510 .76- .17+ 111001 A17 .12+ .19+ 111001 H21 .25- .01+ 111002 510 .33- .04- 111001 113 .43+ .03- 111001 H21 .35- .08+ 111002 510 .88- .15+ 111001 510 .39- .07+ 111001 H21 .05+ .42- 111002 510 .57- .34+ 111001 A71( 1.5- .30-) 111001 H21 .24- .49- 111002 704( 1.2- .87+) 111001 113 .66- .06+ 111001 H21 .30- .30- 111002 704 .49- 1.1+ 111001 A71 .68- 1.5+ 111001 H21 .31+ .06- 111002 H17 .01- .08- 111001 A71( 2.3- 1.9+) 111001 H21 .07+ .25- 111002 704( 2.6- 1.4+) 111001 113 .25+ .17- 111001 H17 .56- .83+ 111002 H17( 1.4- 2.1+) 111001 510 .00 .05- 111001 H17 .35- .93+ 111002 H36 .75- .11+ 111001 A71 .82- .24+ 111001 H06 .49- .17- 111002 H36 .40- .22- 111001 A71( 1.6- 1.3+) 111001 H17 .03- .22+ 111002 H17 .48- .26- 111001 204 .08- .42- 111001 H06 .74+ 1.1- 111002 H36 .76- .23+ 111001 113 .05+ .10- 111001 H06( 1.1+ .10-) 111002 H01 .51+ .12+ 111001 A71( 4.0- 3.7+) 111001 H06( 1.0+ .09-) 111002 704( 3.8- 1.7+) 111001 510 .16- .13+ 111001 H06 .36+ .12+ 111002 H17 .60- .40- 111001 204 .17- .44- 111001 H10 .74+ .04+ 111002 H01 .42+ .15- 111001 510 .12+ .11+ 111001 H01 .81+ .04- 111002 H17 .41+ .09- 111001 204 .37- .24- 111001 H10( 1.3+ .15-) 111002 H01 .16+ .07+ 111001 B86 .24- .08- 111001 H01 .78+ .08- 111002 H01 .26+ .28+ 111001 B86 .17- .03- 111001 H01 .89+ .04- 111003 C42 .56- .23- 111001 B86 .08- .22- 111001 H01 .72+ .05- 111003 C42 .76+ .77- 111001 510 .17- .30+ 111001 G96 .96+ .32- 111003 C42 .12+ .13- 111001 B86 .03+ .01- 111001 G96 .91+ .12+ 111003 C42 .37+ .38+ 111001 157 .51+ .19+ 111001 G96 .90+ .29- 111003 C42 .01+ .42+ 111001 157 .94+ .28- 111001 G96 .67+ .08+ 111001 157 .38+ .37- 111002 106 .07- .38- # State vector (heliocentric ecliptic J2000): # -0.127183234640 1.171217736955 0.080243618590 AU # -20.360380014630 -6.421701632900 -6.738631533044 mAU/day # MOIDs: Me 0.8141 Ve 0.4187 Ea 0.1523 Ma 0.3025 # MOIDs: Ju 1.2294 Sa 1.7619 Ur 1.7290 Ne 2.6677 # Elements written: 4 Oct 2011 9:04:27 (JD 2455838.878090) # Full range of obs: 2011 Sept. 30-Oct. 3 (100 observations) # Find_Orb ver: Oct 11 2010 13:08:42 # Perturbers: 00000000 (unperturbed orbit) # Tisserand relative to Earth: 2.86746 # Tisserand relative to Jupiter: 1.25707 # Tisserand relative to Neptune: 0.52292
In celestial mechanics, there is a criterion called Tisserand's Criterion to determine whether or not an observed orbiting body is the same as a previously observed orbiting one, as a consequence of Tisserand's relation. For a small body with semimajor axis $a$, eccentricity $e$, and inclination $i$, with respect to a massive perturbing body with semimajor axis $a_P$, the parameter is definded by the following formula:
$T_P=\frac{a_P}{a} + 2\left [ \frac{a}{a_P} (1-e^2)\right ]^\frac{1}{2} \cos i $
According to MPC 75514, the elements of P/2006 T1 (Levy) at the same epoch as the above two solutions are as follows:
Epoch (TT/JD) T (TT/JD) Peri. Node Incl. e q a Epoch (TT) 2455838.50000 2455939.0245593 179.62257 279.74449 18.26280 0.6679327 1.0073994 3.03372 2011/10/04.00
Compared to what we have about 2011 S2, we will find no much difficulty in identifying some similarities in the orbital elements between 2011 S2 and P/2006 T1 (Levy). In that I do not possess many observations of P/2006 T1, I turn to respectively analyze their Tisserand's parameters with respect to all the planets from the innermost Mercury to the outermost Neptune in the solar system. To achieve the target, I myself wrote a routine in IDL to carry out the calculations for me. All of the three orbital solutions for comet 2011 S2 of mine and from MPEC 2011-T12 were taken into the calculation. Here come the results as follows:
Comet $T_{Mercury}$ $T_{Venus}$ $T_{Earth}$ $T_{Mars}$ $T_{Jupiter}$ $T_{Saturn}$ $T_{Uranus}$ $T_{Neptune}$ Source 2011 S2 4.6187111 3.3787994 2.8736290 2.3280082 1.2596546 0.9283308 0.6553122 0.5237470 MPEC 2011-T12 4.6087911 3.3715426 2.8674569 2.3230082 1.2569491 0.9263370 0.6539048 0.5226222 FindOrb 4.5927198 3.3649310 2.8663322 2.3304379 1.3121666 1.0342053 0.8757625 0.8721799 FindOrb 2006 T1 4.0845766 3.1331422 2.7915469 2.4967171 2.7946545 3.9538304 6.8999819 10.371726 MPC 75514
We can learn from the table that the Tisserand's parameters with respect to the four terrestial planets are close to each other, yet from Jupiter, the Tisserand's parameters of the two bodies start to digress further and further, based upon the assumption that if the orbital solutions are reliable or relatively close to the fact to be proven by further observations. I boldly venture to guess that perhaps the two bodies have some possibilities to be linked to each other, however, this statement need to be meticulously treated without support from more evidence. If it happens to be correct, it means that the comet has been driven out of the Jupiter-family since a close encounter with some terrestial planet.
As said, further observations of comet 2011 S2 are intensely encouraged so as to smooth the noise.
Copyright © Man-To Hui 2011/10/04
As more observations have been obtained, MPEC 2011-T39 publicized an updated orbital solution for 2011 S2. I used JPL to generate its orbital elements at Epoch 2455880.5 (2011 Nov 15.0 CT) as follows:
*******************************************************************************
Target body name: C/2011 S2
# obs: 150 (7 days) data arc: 2011-Sep-30 to 2011-Oct-07
Residual RMS= .63681
*******************************************************************************
EC= 9.066346719791114E-01 QR= 1.109950500254332E+00 IN= 1.755092011502044E+01
OM= 2.878264558173418E+02 W = 1.923106502381481E+02 Tp= 2455860.951143381651
N = 2.404512826156002E-02 MA= 4.700547647537690E-01 TA= 2.220893578515344E+01
A = 1.188825149316681E+01 AD= 2.266655248607930E+01 PR= 1.497184777240375E+04
*******************************************************************************
Coordinate system description:
Ecliptic and Mean Equinox of Reference Epoch
Reference epoch: J2000.0
xy-plane: plane of the Earth's orbit at the reference epoch
x-axis : out along ascending node of instantaneous plane of the Earth's
orbit and the Earth's mean equator at the reference epoch
z-axis : perpendicular to the xy-plane in the directional (+ or -) sense
of Earth's north pole at the reference epoch.
Symbol meaning [1 AU=149597870.691 km, 1 day=86400.0 s]:
JDCT Epoch Julian Date, Coordinate Time
EC Eccentricity, e
QR Periapsis distance, q (AU)
IN Inclination w.r.t xy-plane, i (degrees)
OM Longitude of Ascending Node, OMEGA, (degrees)
W Argument of Perifocus, w (degrees)
Tp Time of periapsis (Julian day number)
N Mean motion, n (degrees/day)
MA Mean anomaly, M (degrees)
TA True anomaly, nu (degrees)
A Semi-major axis, a (AU)
AD Apoapsis distance (AU)
PR Orbital period (day)
Also, I acquired orbital elements of comet P/2006 T1 at the same Epoch in JPL:
*******************************************************************************
Target body name: P/2006 T1 (Levy)
# obs: 314 (60 days) data arc: 2006-Oct-02 to 2006-Dec-01
Residual RMS= .72686
*******************************************************************************
EC= 6.679022959202969E-01 QR= 1.007416008064483E+00 IN= 1.826274662902490E+01
OM= 2.797401704965575E+02 W = 1.796208748878264E+02 Tp= 2455938.715627640951
N = 1.865475768733755E-01 MA= 3.491400157274438E+02 TA= 2.980565533697751E+02
A = 3.033492841681026E+00 AD= 5.059569675297568E+00 PR= 1.929802606036316E+03
*******************************************************************************
Coordinate system description:
Ecliptic and Mean Equinox of Reference Epoch
Reference epoch: J2000.0
xy-plane: plane of the Earth's orbit at the reference epoch
x-axis : out along ascending node of instantaneous plane of the Earth's
orbit and the Earth's mean equator at the reference epoch
z-axis : perpendicular to the xy-plane in the directional (+ or -) sense
of Earth's north pole at the reference epoch.
Symbol meaning [1 AU=149597870.691 km, 1 day=86400.0 s]:
JDCT Epoch Julian Date, Coordinate Time
EC Eccentricity, e
QR Periapsis distance, q (AU)
IN Inclination w.r.t xy-plane, i (degrees)
OM Longitude of Ascending Node, OMEGA, (degrees)
W Argument of Perifocus, w (degrees)
Tp Time of periapsis (Julian day number)
N Mean motion, n (degrees/day)
MA Mean anomaly, M (degrees)
TA True anomaly, nu (degrees)
A Semi-major axis, a (AU)
AD Apoapsis distance (AU)
PR Orbital period (day)
I wrote an improved routine to perform the calculations of the Tisserand's parameters with respect to different planets. The results are as follows:
Comet $T_{Mercury}$ $T_{Venus}$ $T_{Earth}$ $T_{Mars}$ $T_{Jupiter}$ $T_{Saturn}$ $T_{Uranus}$ $T_{Neptune}$ Source 2011 S2 4.4911973 3.3225379 2.8581554 2.3754728 1.6538106 1.7004738 2.2473768 3.0352627 JPL 2006 T1 4.0845779 3.1331517 2.7915698 2.4967429 2.7944679 3.9409660 6.8877047 10.361610 JPL
As seen, there is still no strong evidence indicating that 2011 S2 and 2006 T1 is the same body in two different apparitions. The only thing we now can do is to await more observations of 2011 S2 with a greater arc.
Copyright © Man-To Hui 2011/10/12
Feel free to e-mail me with any doubts or questions.