ASTEROID SPIN VECTOR DETERMINATIONS
collected from the literature by
Per Magnusson
Astronomiska observatoriet
Box 515
S-751 20 Uppsala
Sweden
Per.Magnusson@astro.uu.se
Version of
1995 December 29
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 by anonymous ftp from
Internet address ftp.astro.uu.se (in directory
pub/Asteroids/SpinVectors).
An ascii-version has been submitted to the Small Bodies Node of NASA's
Planetary Data System.
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 =
C =
D =
E =
F =
I =
M =
O =
P =
R =
S =
V =
Z =
former
Amplitudes of lightcurves
Close observations from spacecraft during fly-by or rendezvous
Individual data-points of photometric lightcurves
Epochs (e.g. times of lightcurve extrema)
Fourier coefficients of photometric lightcurves
Infrared pre- and post-opposition differences
Magnitudes (usually at maximum light)
Occultation observations
Infrared polarimetry
Radar observations
Surface resolved (e.g. speckle data, adaptive optics)
Visual position angles
Zero and non-zero amplitude apparitions imply pole-on view in
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
geometries 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 nonuniform
time-distribution of the observations, which tend to give many welldefined
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
nongeometric 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.