ASTEROID SPIN VECTOR DETERMINATIONS
-----------------
collected from the literature by
Per Magnusson
Version of
1995 December 29
UPDATE
created by
Agnieszka Kryszczynska
Astronomical Observatory
A. Mickiewicz University
Sloneczna 36
60-286 Poznan
Poland
Version of
2014 Feb 14
This is a comprehensive tabulation of asteroid spin vector determinations.
Supplementary information on shape models and albedo variegation is also
included, but only when part of a spin vector determination. If you find
omissions and errors or have suggestions for future improvements please
contact me on the above address.
Availability
------------
The table and related documentation is available from
http://www.astro.amu.edu.pl/Science/Asteroids
Comments on the nomenclature used
---------------------------------
The terms "North Pole" and "South Pole" are ambiguous and they are avoided in
this table. Instead I use the direction of the spin angular velocity vector,
as defined by the "right-hand-rule". Note that a full specification of the
spin vector makes it superfluous to use the ambiguous terms "prograde rotation"
and "retrograde rotation". These are ambiguous since the sense of rotation
can be based on the ecliptic plane, the asteroid's orbital plane, or something
else (the truth usually depends in a complicated way on the distribution of
observing geometries).
Synthesis of independent results
--------------------------------
For some asteroids a large number of independent solutions have been published.
This may be confusing for readers who are not interested in the spin vector
determination process as such. For the benefit of readers who just want
reliable results for their own applications I include a "synthesis" of our
knowledge for some asteroids. I estimate that these synthesis results have
a high reliability and an accuracy in the spin vector direction of order 10
degrees or less. They were obtained by taking averages of the most recent
independent results, with weights based on the method used and the amount and
type of the input data. This procedure is necessarily somewhat subjective,
and can't replace a careful evaluation of the original results.
Explanation of table columns
-----------------------------
BASIC DATA
The data from which the spin vectors and rejections of spurious solutions
are based are designated by the letters:
A = Amplitudes of lightcurves
C = Close observations from spacecraft during fly-by or rendezvous
D = Individual data-points of photometric lightcurves
E = Epochs (e.g. times of lightcurve extrema)
F = Fourier coefficients of photometric lightcurves
I = Infrared pre- and post-opposition differences
K = KOALA algorithm (optical lc + stellar occ. + disc resolved images)
L = Lightcurve inversion based on lightcurves
L*= Lightcurve inversion based on lightcurves and sparse data
L**=Lightcurve inversion based on sparse data only
M = Magnitudes (usually at maximum light)
O = Occultation observations
P = Infrared polarimetry
R = Radar observations
X = Radar speckles
S = Surface resolved (e.g. speckle data, adaptive optics)
T = Thermophysical modelling
V = Visual position angles
Z = Zero and non-zero amplitude apparitions imply pole-on view in former case
SPIN VECTOR SOLUTIONS
The direction of the spin vectors (defined by the "right-hand-rule") are
given in degrees in the ecliptic system for equinox B1950.0. The
corresponding ecliptic coordinates for equinox J2000.0 can be obtained by
adding 0.7 degrees to all tabulated longitudes, but this adjustment is
far below the level of accuracy for most spin vector determinations.
The table contains column space for four spin vector directions per line.
These reflect the symmetry properties of most spin vector determinations.
Methods based on aspect dependences (e.g. amplitude and magnitude methods)
tend to give two spin axis solutions for main-belt asteroid with moderate
orbital inclination (due to the near symmetry of the observational geo-
metries in the ecliptic plane). Corresponding to each spin axis solution
we have two opposite spin vector directions, which are given explicitly in
the table. Thus, whenever the method used does not contain information on
the sense of rotation I interpret "poles" as spin axis solutions and
calculate the implicit spin vector directions. The result is generally
four different solutions. I try to put the two prograde ones in the two
left columns the two retrograde ones in the columns to the right. If
subsequent determinations agree reasonably then corresponding solutions
appear in the same column, making comparison easy. The 4-fold symmetry is
not applicable to certain objects. The distinction between the four groups
may break down for objects in high inclination orbits (e.g. 2 Pallas),
for objects with spin axes close to the ecliptic plane, and for objects
whose lightcurves are difficult to interpret (e.g. 532 Herculina). For
Earth-approaching objects it often reduces to a 2-fold clustering.
A result which demonstrates (explicitly or implicitly) that one of the four
solutions can be rejected is shown as a horizontal bar in the appropriate
column. A letter in the middle of the bar, e.g. "----E----", indicates the
type of data primarily responsible for the rejection (see table above).
Rejection bars have not been used for asteroids where the solutions don't
cluster in a clear way.
SIDEREAL PERIOD
Only periods accurate enough to bridge inter-apparitional gaps and produce
absolute rotational phases for the whole data set are included. Less
accurate synodic period determinations exist for many more objects. As
evident from the table, the agreement between sidereal period determinations
tend to be either very good or very bad. This is due to the non-uniform
time-distribution of the observations, which tend to give many well-defined
local chi-square minima.
ELLIPSOIDAL MODEL
Many pole determination methods are based on a tri-axial ellipsoid model
with semi-axes a>=b>=c rotating about the c-axis. Corrections for non-
geometric scattering and albedo variegation have often not been made. A
warning must therefore be made against direct identification of the model
axis-ratios with the asteroid shape. When a non-ellipsoidal model is used
it is described in a footnote (TeX/PostScript version only). Note that the
table is not a comprehensive list of asteroid shapes, but includes models
obtained as by-products of spin vector determinations only.
ALBEDO VARIEGATION
Albedo models are also often by-products of spin-vector determinations,
and therefore noted in the table. However, the table is not a complete
collection of such models. The footnotes give some additional information
(TeX/PostScript version only).
REFERENCE CODE
The reference codes are formed by 2-3 letters of the first author name,
followed by '+' if there are more authors, and the last two digits of the
publication year. Full expansions of the codes are given in the reference
list.