Modeling the obliquity of Mercury

Noyelles, Benoît; D’Hoedt, Sandrine

doi:10.1016/j.pss.2011.07.024

Cited by 3 publications

(10 citation statements)

References 26 publications

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“…This expansion induces the apparition of fast sinusoidal perturbations, that disappear after averaging. Such a calculation is already present in (Noyelles & D'Hoedt 2012), but the gravity field of Mercury is there considered only up to the second order, and the expansion in eccentricity / inclination limited to the degree 3.…”

Section: The Dynamical Modelmentioning

confidence: 99%

“…From these formulae we extract trigonometric expressions (Eq.24 to 27 in (Noyelles & D'Hoedt 2012)):…”

Section: Influence On One Examplementioning

confidence: 99%

“…In order to bypass the uncertainty on the Laplace Plane, Noyelles & D'Hoedt (2012) proposed a Laplace Plane-free study of the obliquity, using averaged equations of the rotational motion, averaged variations of the eccentricity, inclination and the associated angles, and a quasi-periodic representation of these quantities. This yields a quasi-periodic representation of the equilibrium obliquity that is very close to the Cassini State over the domain of validity of the JPL DE 406 ephemerides (Standish 1998), i.e.…”

Section: Introductionmentioning

confidence: 99%

“…We first present how we average the equations ruling the rotational dynamics of Mercury (Sect.2). This averaging is more accurate than the one given in (Noyelles & D'Hoedt 2012), i.e. it is done in higher order in eccentricity.…”

Section: Introductionmentioning

confidence: 99%

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The influence of orbital dynamics, shape and tides on the obliquity of Mercury

Noyelles

Lhotka

2013

Advances in Space Research

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Earth-based radar observations of the rotational dynamics of Mercury combined with the determination of its gravity field by MESSENGER (Smith et al. 2012) give clues on the internal structure of Mercury, in particular its polar moment of inertia C, deduced from the obliquity (2.04 ± 0.08) arcmin.The dynamics of the obliquity of Mercury is a very-long term motion (a few hundreds of kyrs), based on the regressional motion of Mercury's orbital ascending node. This paper, following the study of Noyelles & D'Hoedt (2012), aims at first giving initial conditions at any time and for any values of the internal structure parameters for numerical simulations, and at using them to estimate the influence of usually neglected parameters on the obliquity, like J 3 , the Love number k 2 and the secular variations of the orbital elements. We use, for that, averaged representations of the orbital and rotational motions of Mercury, suitable for long-term studies.We find that J 3 should alter the obliquity by 250 milli-arcsec, the tides by 30 milli-arcsec, and the secular variations of the orbital elements by 10 milliarcsec over 20 years. The resulting value of C could be at the most changed from 0.346mR 2 to 0.345mR 2 .

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Section: The Dynamical Modelmentioning

confidence: 99%

“…From these formulae we extract trigonometric expressions (Eq.24 to 27 in (Noyelles & D'Hoedt 2012)):…”

Section: Influence On One Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The influence of orbital dynamics, shape and tides on the obliquity of Mercury

Noyelles

Lhotka

2013

Advances in Space Research

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“…The Laplace plane orientation ofYseboodt and Margot (2006) (grey disk) overlaps with the values derived in this work. Note that the longitude of the Laplace pole is given incorrect in(D'Hoedt et al, 2009) and was corrected in(Noyelles and D'Hoedt, 2012). The figure shows the corrected position (blue disk).…”

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confidence: 99%

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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New insights on Titan's interior from its obliquity

Noyelles,

Nimmo

2014

Preprint

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We constructed a 6-degrees of freedom rotational model of Titan as a 3-layer body consisting of a rigid core, a fluid global ocean, and a floating ice shell.The ice shell exhibits partially-compensated lateral thickness variations in order to simultaneously match the observed degree-two gravity and shape coefficients.The rotational dynamics are affected by the gravitational torque of Saturn, the gravitational coupling between the inner core and the shell, and the pressure coupling at the fluid-solid boundaries. Between 10 and 13% of our model Titans have an obliquity (due to a resonance with the 29.5-year periodic annual forcing) that is consistent with the observed value.The shells of the successful models have a mean thickness of 130 to 140 km, and an ocean of ≈250 km thickness. Our simulations of the obliquity evolution show that the Cassini obliquity measurement is an instantaneous one, and does not represent a mean value. Future measurements of the time derivative of the obliquity would help to refine the interior models. We expect in particular a variation of roughly 7 arcmin over the duration of the Cassini mission.

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Modeling the obliquity of Mercury

Cited by 3 publications

References 26 publications

The influence of orbital dynamics, shape and tides on the obliquity of Mercury

The influence of orbital dynamics, shape and tides on the obliquity of Mercury

Mercury’s resonant rotation from secular orbital elements

New insights on Titan's interior from its obliquity

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