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| Titel |
Ceres' Rotation Solution under the Gravitational Torque of the Sun |
| VerfasserIn |
Martin Lara, Toshio Fukushima, Sebastián Ferrer |
| Konferenz |
EGU General Assembly 2011
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 13 (2011) |
| Datensatznummer |
250047219
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| Zusammenfassung |
| The protoplanet Ceres is one of the targets of the ongoing NASA’s DAWN
mission, which is expected to provide crucial information on the
history of the Solar System. An accurate determination of Ceres’ shape
is essential for the determination of its internal structure and,
therefore, for understanding its evolution. An accuracy better than
0.5 km is demanded while the accuracy derived from actual observations
limits to about 2 km. Even worse, some discrepancies are found when
comparing the available shape measurements from different authors.
Available observations on the shape of Ceres show it as a rotationally
symmetric, almost spherical, oblate spheroid. However, deviations from
axisymmetry could happen to Ceres at the level of observational
accuracy, and it is known that small deviations from axisymmetry may
show non-negligible effects on the rotational dynamics of rigid
bodies. Indeed, we check that a small departure from axisymmetry of
few hundreds of meters in the length of the intermediate axis would
have, by far, a larger effect on the rotation of Ceres than the small
perturbation of its torque-free rotation produced by the coupling with
its orbital dynamics about the Sun
When studying the rotational motion of Ceres, all these
inconsistencies in the values of the physical parameters should be
taken into account. Therefore, it seems desirable to have available a
rotation solution for Ceres that may assume a small triaxiality and
handles its physical parameters in a pure analytical way.
We study the perturbed rotation of a triaxial Ceres under the
gravitational torque of the Sun. The problem is formulated in Andoyer
variables, and the orbital motion of Ceres about the Sun is considered
to be purely Keplerian. The resulting Hamiltonian is of three degrees
of freedom and time dependent. The frequencies of the motion are
obtained after the reduction of the Hamiltonian to a function of only
momenta. This reduction is obtained by a chain of canonical
transformations computed by the Lie series approach. In this way, the
time and periodic terms are stepwise eliminated from the Hamiltonian
up to a certain order. The reduction is carried out in a pure
analytical way, although the ordering of the Hamiltonian is tailored
to the actual values of Ceres.
The rotation theory is provided in an algorithmic way. The actual
motion is recovered after propagating the secular terms and undoing
the canonical transformations that allow to recover the periodic
effects. Comparisons with numerical integrations show that the theory
is accurate up to the first order in the ratio of the free rotation
rate to the mean orbital motion. Thus, after six Ceres’ orbital
periods, the rotation state is recovered within one tenth of arc
seconds. Specifically, the analytical theory suffers from a secular
trend that remains below few mas times orbital period for any angle,
with periodic oscillations of the same order |
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