Determination of an instantaneous Laplace plane for Mercury’s rotation

D’Hoedt, Sandrine; Noyelles, Benoît; Dufey, Julien; Lemaître, Anne

doi:10.1016/j.asr.2009.05.008

Cited by 7 publications

(7 citation statements)

References 17 publications

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“…Stark et al (2015b) performed an independent analysis and confirmed the values of Yseboodt and Margot (2006), including the orientation of the instantaneous Laplace plane, the inclination ι, and the precession ratė Ω. D'Hoedt et al (2009) used a Hamiltonian approach and found an instantaneous Laplace plane orientation that differs from our preferred value by 1.4 • .…”

Section: Orbital Precessionsupporting

confidence: 52%

Mercury’s Internal Structure

Margot¹,

Hauck²,

Mazarico³

et al. 2018

Mercury

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We describe the current state of knowledge about Mercury's interior structure. We review the available observational constraints, including mass, size, density, gravity field, spin state, composition, and tidal response. These data enable the construction of models that represent the distribution of mass inside Mercury. In particular, we infer radial profiles of the pressure, density, and gravity in the core, mantle, and crust. We also examine Mercury's rotational dynamics and the influence of an inner core on the spin state and the determination of the moment of inertia. Finally, we discuss the wide-ranging implications of Mercury's internal structure on its thermal evolution, surface geology, capture in a unique spin-orbit resonance, and magnetic field generation.

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Section: Orbital Precessionsupporting

confidence: 52%

Mercury’s Internal Structure

Margot¹,

Hauck²,

Mazarico³

et al. 2018

Mercury

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“…Further, the plane to which the inclination of Mercury remains constant, i.e., the Laplace plane, also undergoes slow variations (Noyelles and D'Hoedt, 2012). Several attempts have been made to calculate the orientation of the Laplace plane normal (Yseboodt and Margot, 2006;Peale, 2006;D'Hoedt et al, 2009), each of them leading to different results in the Laplace pole position and the precession period (see Fig. 2).…”

Section: Laplace Planementioning

confidence: 99%

“…Note that without additional assumptions the instantaneous precession vector w is only constrained to a line. In order to overcome the ambiguity in the instantaneous Laplace plane either a fit to the ephemeris (Yseboodt and Margot, 2006) or some additional assumptions (Peale, 2006;D'Hoedt et al, 2009) are used.…”

Section: Laplace Planementioning

confidence: 99%

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Mercury’s resonant rotation from secular orbital elements

Stark

Oberst

Hußmann

2015

Celest Mech Dyn Astr

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We used recently produced Solar System ephemerides, which incorporate 2 years of ranging observations to the MESSENGER spacecraft, to extract the secular orbital elements for Mercury and associated uncertainties. As Mercury is in a stable 3:2 spin-orbit resonance, these values constitute an important reference for the planet's measured rotational parameters, which in turn strongly bear on physical interpretation of Mercury's interior structure. In particular, we derive a mean orbital period of (87.96934962 ± 0.00000037) days and (assuming a perfect resonance) a spin rate of (6.138506839 ± 0.000000028) • /day. The difference between this rotation rate and the currently adopted rotation rate (Archinal et al. in ), corresponds to a longitudinal displacement of approx. 67 m per year at the equator. Moreover, we present a basic approach for the calculation of the orientation of the instantaneous Laplace and Cassini planes of Mercury. The analysis allows us to assess the uncertainties in physical parameters of the planet, when derived from observations of Mercury's rotation.

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“…This ‘precessional axis’ is also commonly called the Laplace pole Z L , and it can be determined by averaging the perturbations over a suitable time‐span (e.g. see Peale ; Yseeboodt & Margot ; D'Hoedt et al ). The precession period obtained from the theory is around ∼250 000 years, and the angle η between the orbit normal Z 1 and the spin axis V s is called the obliquity .…”

Section: Secular Theory: Laplace Plane and Cassini Statementioning

confidence: 99%

Determination of the rotation of Mercury from satellite gravimetry

Cicalò

Milani

2012

Monthly Notices of the Royal Astronomical Society

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Space missions can have as a goal the determination of the interior structure of a planet: this is the case for the ESA BepiColombo mission to Mercury. Very precise range and range‐rate tracking from the Earth and onboard accelerometry will provide a huge amount of data, from which it will be possible to study the gravity field of Mercury and other parameters of interest. Gravity can be used to constrain the interior structure, but cannot uniquely determine the interior mass distribution. A much stronger constraint on the interior can be given by also determining the rotation state of the planet. If the planet is asymmetric enough, the gravity field as measured by an orbiting probe tracked from the Earth contains signatures from the rotation. Are these enough to solve for the rotation state, to the required accuracy, from tracking data alone, without measurements of the surface? In order to reach some result analytically, a simplified analytical model is developed, and the symmetry breaking, occurring when the shape of the planet deviates from spherical symmetry, is characterized by explicit formulae. Moreover, a full cycle numerical simulation of the Radio Science Experiment is performed, including the generation of simulated tracking and accelerometer data and the determination, by least‐squares fit, of the Mercury‐centric initial conditions of the probe, of Mercury's gravity field and its rotation state, together with other parameters affecting the dynamics. The conclusion is that there is no reason of principle prohibiting the determination of the rotation from gravimetry, and the sensitivity of the measurements and the coverage are good enough to perform the experiment at the required level of accuracy. This will be important also in ensuring independent terms of comparison for the rotation experiment performed with a high‐resolution camera. The mission is currently under development and much care has to be taken in guaranteeing the scientific goals even if there is some change in scenario.

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Determination of an instantaneous Laplace plane for Mercury’s rotation

Cited by 7 publications

References 17 publications

Mercury’s Internal Structure

Mercury’s Internal Structure

Mercury’s resonant rotation from secular orbital elements

Determination of the rotation of Mercury from satellite gravimetry

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