J/A+A/667/A78 Small Saturnian moons Spherical Harmonics (Rambaux+, 2022)
Spherical harmonic decomposition and interpretation of the shapes of the small
Saturnian inner moons.
Rambaux N., Lainey V., Cooper N., Auzemery L., Zhang Q.F.
<Astron. Astrophys. 667, A78 (2022)>
=2022A&A...667A..78R 2022A&A...667A..78R (SIMBAD/NED BibCode)
ADC_Keywords: Solar system ; Planets
Keywords: planets and satellites: fundamental parameters -
planets and satellites: surfaces
Abstract:
The Cassini-Huygens space mission made a series of observations of
Saturn's small satellites during its grand finale stage. These
measurements were performed in order to study the shape, geology, and
surface composition of the small satellites as well as to study the
impact of the environment, in particular the rings, on these small
bodies. The purpose of this study is to focus on the shape analysis of
the small Saturnian satellites in order to describe their global
figure and large-scale topography, as well as to deduce fundamental
quantities, gravity field, and amplitude of the diurnal libration by
assuming that the bodies are homogeneous. We used two approaches in
this study. On the one hand, we directly exploited the Cassini images
of the small satellites by performing limb measurements and deducing a
confidence interval on the shape measurements. On the other hand, we
used previously published shape models which combine limb measurements
and control points. These shape models were then decomposed and
described in spherical harmonics. We found that the shape of the small
satellites can be described with a confidence interval between 50 and
150 metres. The low degree in spherical harmonics (degree 2) indicated
that Telesto, Pandora, Pan, Janus, and Helene have a degree 2 shape
close to the Omega sequence, which was defined recently, where the
potential is constant along a meridian perpendicular to the longest
axis. The degree 2 shape of Epimetheus, on the other hand, is close to
the Roche sequence. In contrast, Prometheus, Calypso, and Atlas are in
the Low-Brown region. The root mean square spectrum and spherical
harmonic maps then allowed us to describe the topography of the
satellites, and in particular to highlight equatorial ridges for some
satellites including Daphnis. Finally, our estimates of the libration
amplitude in the homogeneous case provide values in agreement with
previously published librational measurements for Epimetheus while
highlighting the proximity of the resonance for Epimetheus, Pandora,
and Prometheus. The high resolution images of the internal satellites
have allowed us to describe the geology and the geophysics of these
bodies. Future comparison of these amplitudes with new librational
measurements deduced, for example, by the astrometric method, will
allow us to obtain information on the internal structure of these
bodies. Similar studies could be carried out on the internal
satellites of Jupiter using images from the Europa Clipper (NASA) or
JUICE (ESA) missions.
Description:
The small saturnian inner moons have been observed by the
Cassini-Huygens spacecraft during Dec 2016 and April 2017. From these
observations a shape model were built by P. Thomas. They are
accessible at NASA Planetary Data System https://sbn.psi.edu/pds/
resource/saturnsatshapes.html. The various files untitled name.dat
presents a spherical harmonics decomposition for each satellite,
Atlas, Calypso, Daphnis, Epimetheus, Helene, Janus, Pan, Pandora,
Prometheus, and Telesto available from the shape models
nameinnermoon30k_plt.tab. The Spherical Harmonics decomposition uses
unnormalized Legendre polynomials. The uncertainties of each
parameters are formal uncertainties coming from the covariance matrix.
More realistic uncertainties are provided throughout the paper. The
degree 1 is imposed to be null.
File Summary:
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FileName Lrecl Records Explanations
--------------------------------------------------------------------------------
ReadMe 80 . This file
atlas.dat 99 118 Coefficients of the spherical functions of Atlas
calypso.dat 99 118 Coefficients of the spherical functions
of Calypso
daphnis.dat 99 118 Coefficients of the spherical functions
of Daphnis
epimethe.dat 99 118 Coefficients of the spherical functions
of Epimetheus
helene.dat 99 118 Coefficients of the spherical functions
of Helene
janus.dat 99 118 Coefficients of the spherical functions of Janus
pan.dat 99 118 Coefficients of the spherical functions of Pan
pandora.dat 99 118 Coefficients of the spherical functions
of Pandora
promethe.dat 99 118 Coefficients of the spherical functions
of Prometheus
telesto.dat 99 118 Coefficients of the spherical functions
of Telesto
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Byte-by-byte Description of file: *.dat
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Bytes Format Units Label Explanations
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1- 3 I3 --- deg Degree
5- 7 I3 --- order Order
9- 30 D22.15 km A Topographic coefficients of the spherical
functions (cosine term)
32- 53 D22.15 km B Topographic coefficients of the spherical
functions (sine term)
55- 76 D22.15 km e_A Formal uncertainty on A
78- 99 D22.15 km e_B Formal uncertainty on B
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Acknowledgements:
Nicolas Rambaux, Nicolas.Rambaux(at)imcce.fr
(End) Nicolas Rambaux [IMCCE, France], Patricia Vannier [CDS] 22-Jul-2022