J/A+A/556/A8 100 asteroids rotational parameters (Lhotka+, 2013)
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Obliquity, precession rate, and nutation coefficients for a set of 100
asteroids.
Lhotka C., Souchay J., Shahsavari A.
=2013A&A...556A...8L
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ADC_Keywords: Minor planets
Keywords: minor planets, asteroids: general - catalogs - methods: data analysis
Abstract:
We compute for a set of 100 asteroids their rotational parameters: the
moments of inertia along the principal axes of the object, the
obliquity of the axis of rotation with respect to the orbital plane,
the precession rates, and the nutation coefficients.
We select 100 asteroids for which the parameters for the study are
well-known from observations or space missions. For each asteroid, we
determine the moments of inertia, assuming an ellipsoidal shape. We
calculate their obliquity from their orbit (instead of the ecliptic)
and the orientation of the spin-pole. Finally, we calculate the
precession rates and the largest nutation components. The number of
asteroids concerned leads to some statistical studies of the output.
We provide a table of rotational parameters for our set of asteroids.
The table includes the obliquity, their axes ratio, their dynamical
ellipticity H_d_, and the scaling factor K. We compute the precession
rate {psi} and the leading nutation coefficients {Delta}{psi} and
{Delta}{epsilon}. We observe similar characteristics, as observed by
previous authors that is, a significantly larger number of asteroids
rotates in the prograde mode (~60%) than in the retrograde one with
a bimodal distribution. In particular, there is a deficiency of
objects with a polar axis close to the orbit. The precession rates
have a mean absolute value of 18"/y, and the leading nutation
coefficients have an average absolute amplitude of 5.7" for
{Delta}{psi} and 5.2" for {Delta}{epsilon}. At last, we identify and
characterize some cases with large precession rates, as seen in 25143
Itokawa, with has a precession rate of about - 475"/y.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
table1.dat 202 100 *Target list (Version: 2013-07-19)
table1.ori 95 404 Original table of
target list (Version: 2013-07-19)
table2.dat 82 100 Rotational parameters
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Notes on table1.dat : [1]-[4] refers to the content of the databases
taken from PDS (Planetary Data System Asteroid/Dust Archive), DAMIT
(Database of Asteroid Models from Inversion Techniques), MPC (IAU
Minor Planet Center) and WCD (Wolfram Curated Data), respectively.
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Description of file: table1.ori
We provide our target list in which one data point entry consists of
four lines in table1.ori. Each line starts with the IAU designation
number of the asteroid:
1:id., name,
2:id., m[1],[4], R[4] [km], a/b[1], b/c[1], no., c[2] [km], a/b[2], b/c[2],
3:id., T_rot_[2],[4] [h], {lambda}[2], {beta}[2], {epsilon}[2],[3], no.,
{lambda}[1], {beta}[1],{epsilon}[1],[3],
4:id., T_rev_[4] [y], T0[3], a[3] [AU], e[3], i[3], {omega}[3], {Omega}[3],
M[3], n[3] [{deg}/d].
In line1 id. stands for the designation number, and name is the
official IAU name of the object, as published in [3].
In line2: m, taken from [1] or [4], is the mass of the object given in
the mass unit of Ceres; the equatorial radius R is given in [km]; the
first two ratios, a/b and b/c, are the ratios of the semi axes
published in [1]; no. defines the number of shape models that exist
for one asteroid in [2] from which a,b,c and the respective ratios are
calculated (see below).
In line3, Trot is the rotation period (in hours) of the asteroid as
published in [2]. The first three parameters
({lambda},{beta},{epsilon}) denote the ecliptic longitude {lambda} and
latitude {beta} as they are published in [2]; the resulting obliquity
{epsilon} has been calculated on the basis of the orbital parameters
(line 4). The integer no. gives the number of spin-vector solutions,
which are published for one object in [1] (the number of triplets of
the form ({lambda},{beta},{epsilon}) that could be calculated using
the different ({lambda},{beta}) that are published in [1] on the
basis of the orbital parameters given in line4).
The first entry in line4 is the orbital period in [y] published in
[4], T0 defines the epoch for which the elements are given; a is the
semi-major axis in [AU]; e is the eccentricity, i is the inclination,
{omega} is the argument of perihelium; {Omega} is the longitude of the
ascending node; M is the mean anomaly at T0, and n is the mean motion
in [{deg}] and [{deg}/d].
We note that all values are taken as they are published in [1]-[4]
with the exception of the second set of shape parameters a/b,b/c, and
c in line2, which were calculated from shape models published in [2]
and the obliquities of the asteroids {epsilon} in line3. The
obliquities are obtained by combining the spin-vector solutions, which
are published in [1] or [2] with the orbital parameters (published for
the object in [3] and [4]) according to a method fully described in
Sect. 5.
See also:
B/astorb : Orbits of Minor Planets (Bowell+ 2013)
I/245 : Orbital Elements of Minor Planets 1998 (Batrakov+ 1997)
http://sbn.psi.edu/pds/ : PDS page [1]
http://astro.troja.mff.cuni.cz/projects/asteroids3D/web.php : DAMIT page [2]
http://www.minorplanetcenter.net/ : MPC page [3]
http://www.wolframalpha.com/ : WCD page [4]
Byte-by-byte Description of file: table1.dat
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Bytes Format Units Label Explanations
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1- 5 I5 --- Seq [1/25143] IAU asteroid designation number
7- 16 A10 --- Name Asteroid Name
18- 20 F3.1 --- M/C [0.1/1]?=- Mass (in m[Ceres]) from [1] (1)
22- 27 F6.2 km Rad [0.16/476.2] Radius from [4]
29- 33 F5.3 --- a/b [1/3.1]?=- Ratio of semi-axes a/b from [1]
35- 39 F5.3 --- b/c [1/1.8]?=- Ratio of semi-axes b/c from [1]
41 I1 --- no [0/2] Number of further solutions for
c, a/b, b/c from [2]
43- 47 F5.1 km c [15.2/260.6]?=- Semi-axis c from [2]
49- 52 F4.2 --- a/b2 [1/1.32]?=- Ratio of semi-axes a/b from [2]
54- 57 F4.2 --- b/c2 [1/2]?=- Ratio of semi-axes b/c from [2]
59- 63 F5.1 --- c2 [19.1/240.3]?=- Second semi-axis c from [2]
65- 68 F4.2 --- a/b3 [1/1.3]?=- Second ratio of semi-axes a/b from [2]
70- 73 F4.2 --- b/c3 [1/2]?=- Second ratio of semi-axes b/c from [2]
75- 82 F8.5 h Trot [2.87/35.5] Rotation period of the
asteroid from [2]
84- 86 I3 deg lambda [9,340]?=- Ecliptic longitude {lambda} from [1]
88- 90 I3 deg beta [-88,58]?=- Ecliptic latitude {beta} from [1]
92- 94 I3 deg eps [26,170]?=- Obliquity {epsilon} from [1]
96 I1 --- no2 [1/2]?=- Number of further solutions for
lambda, beta, eps from [2] (2)
98-100 I3 deg lam2 [4,360]?=- Ecliptic longitude from [2]
102-104 I3 deg beta2 [-88,74]?=- Ecliptic latitude from [2]
106-108 I3 deg eps2 [9,168]?=- Obliquity {epsilon} from [2]
110-112 I3 deg lam3 [89,365]?=- Second ecliptic longitude from [2]
114-116 I3 deg beta3 [-84,74]?=- Second ecliptic latitude from [2]
118-120 I3 deg eps3 [20,555]?=- Second obliquity from [2]
122-129 F8.5 yr Trev [1.52/11.96] Revolution period
131-135 A5 --- T0 [K129U] Epoch (K129U)
137-143 F7.5 AU Oa [1.3/5.3] Semi-major orbital axis
145-153 F9.7 --- e [0.003/0.325] Orbital eccentricty
155-162 F8.5 deg i [0/35] Inclination
164-172 F9.5 deg omega [0/360] Argument of pericenter {omega}
174-182 F9.5 deg Omega [0/360] Longitude of ascending node {Omega}
184-192 F9.5 deg M [07/360] Mean anomaly (M)
194-202 F9.7 deg/d n [0.08/0.65] Mean motion (in deg per day) (n)
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Note (1): m, taken from PDS (Planetary Data System Asteroid/Dust Archive
[1]) or WCD (Wolfram Curated Data [4]), is the mass of the object
given in the mass unit of Ceres.
Note (2): The integer no. gives the number of spin-vector solutions, which
are published for one object in PDS (the number of triplets of the
form ({lambda},{beta},{epsilon}) that could be calculated using the
different ({lambda},{beta}) that are published in PDS ([1]) on the
basis of the orbital parameters given in columns Trev-n).
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Byte-by-byte Description of file: table2.dat
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Bytes Format Units Label Explanations
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1- 5 I5 --- Seq [1/25143] Designation number
7- 16 A10 --- Name IAU designation name
18 A1 --- Rem [+*] switched elliposidal dimensions (3)
20- 24 F5.3 --- e [0.003/0.324] Eccentricity
26- 30 F5.3 --- Hd [0/0.43] Dynamical ellipticity
32- 37 F6.3 h Trot [2.87/35.5] Rotation period
39- 44 F6.4 yr Trev [1.52/7.66] Revolution period
46- 48 I3 deg eps [0/180] Obliquity {epsilon}
50- 56 F7.3 arcsec/yr K [0/881.2] Scaling factor
58- 64 F7.2 arcsec/yr psi Precession rate d{psi}/dt
66- 70 F5.2 arcsec dpsi1 [0/42] Longitudinal nutation
coefficient 1 {Delta}{psi}
72- 76 F5.2 arcsec dpsi2 [0/94] Longitudinal nutation
coefficient 2 {Delta}{psi}
78- 82 F5.2 arcsec deps [0/31] Latitudinal nutation
coefficient {Delta}{epsilon}
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Note (3): Note that the final values (a,b,c) in a few cases are switched to
follow the usual convention a>=b>=c. We indicate this by a "*" or "+".
See section 4 for further explanations.
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Acknowledgements:
Christoph Lhotka, ,
University of Vienna
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(End) Christoph Lhotka [univie], Emmanuelle Perret [CDS] 17-Jul-2013