Evolution of Mercury's obliquity

Yseboodt, Marie; Margot, Jean-Luc

doi:10.1016/j.icarus.2005.11.024

Cited by 72 publications

(79 citation statements)

References 21 publications

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“…In the S n case, after removing the amplitude of the high frequency fluctuations (about 0.6 as), the peak-to-peak amplitude of the resulting long period modulation of 1066.8 years is 3.4 as. Figure 7 is here Both sets of results, from S 2K and S n cases are globally consistent with those of Peale (2006) and implicitly with those of Yseboodt & Margot (2006). We note that the dynamically driven spin precession, which occurs when the planetary interactions are included, is geometrically more complex than the purely kinematic case.…”

Section: Figure 6 Is Heresupporting

confidence: 69%

On the oscillations in Mercury's obliquity

Bois

Rambaux

2007

Icarus

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Mercury's capture into the 3:2 spin-orbit resonance can be explained as a result of its chaotic orbital dynamics. One major objective of MESSENGER and BepiColombo spatial missions is to accurately measure Mercury's rotation and its obliquity in order to obtain constraints on internal structure of the planet. Analytical approaches at the first order level using the Cassini state assumptions give the obliquity constant or quasi-constant. Which is the obliquity's dynamical behavior deriving from a complete spin-orbit motion of Mercury simultaneously integrated with planetary interactions? We have used our SONYR model (acronym of Spin-Orbit N -bodY Relativistic model) integrating the spin-orbit N -body problem applied to the solar System (Sun and planets). For lack of current accurate observations or ephemerides of Mercury's rotation, and therefore for lack of valid initial conditions for a numerical integration, we have built an original method for finding the libration center of the spin-orbit system and, as a consequence, for avoiding arbitrary amplitudes in librations of the spin-orbit motion as well as in Mercury's obliquity. The method has been carried out in two cases: (1) the spin-orbit motion of Mercury in the 2-body problem case (Sun-Mercury) where an uniform precession of the Keplerian orbital plane is kinematically added at a fixed inclination (S 2K case), (2) the spin-orbit motion of Mercury in the N -body problem case (Sun and planets) (S n case).We find that the remaining amplitude of the oscillations in the S n case is one order of magnitude larger than in the S 2K case, namely 4 versus 0.4 arcseconds (peak-topeak). The mean obliquity is also larger, namely 1.98 versus 1.80 arcminutes, for a difference of 10.8 arcseconds. These theoretical results are in a good agreement with recent radar observations but it is not excluded that it should be possible to push farther the convergence process by drawing nearer still more precisely to the libration center. We note that the dynamically driven spin precession, which occurs when the planetary interactions are included, is more complex than the purely kinematic case. Nevertheless, in such a N -body problem, we find that the 3:2 spinorbit resonance is really combined to a synchronism where the spin and orbit poles on average precess at the same rate while the orbit inclination and the spin axis orientation on average decrease at the same rate. As a consequence and whether it would turn out that there exists an irreducible minimum of the oscillation amplitude, quasi-periodic oscillations found in Mercury's obliquity should be to geometrically understood as librations related to these synchronisms that both follow a Cassini state. Whatever the open question on the minimal amplitude in the obliquity's oscillations and in spite of the planetary interactions indirectly acting by the solar torque on Mercury's rotation, Mercury remains therefore in a stable equilibrium state that proceeds from a 2-body Cassini state.

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Section: Figure 6 Is Heresupporting

confidence: 69%

On the oscillations in Mercury's obliquity

Bois

Rambaux

2007

Icarus

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“…[33] We first use equation 12 of Yseboodt and Margot [2006], which is an explicit version of equation (2), to estimate Mercury's polar MoI C/MR 2 = 0.346 AE 0.014 ( Figure 7). We then use equation (3) to estimate the fraction corresponding to the outer librating shell C m /C = 0.431 AE 0.025 (Figure 8).…”

Section: Interior Structurementioning

confidence: 99%

Mercury's moment of inertia from spin and gravity data

et al. 2012

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[1] Earth-based radar observations of the spin state of Mercury at 35 epochs between 2002 and 2012 reveal that its spin axis is tilted by (2.04 AE 0.08) arc min with respect to the orbit normal. The direction of the tilt suggests that Mercury is in or near a Cassini state. Observed rotation rate variations clearly exhibit an 88-day libration pattern which is due to solar gravitational torques acting on the asymmetrically shaped planet. The amplitude of the forced libration, (38.5 AE 1.6) arc sec, corresponds to a longitudinal displacement of $450 m at the equator. Combining these measurements of the spin properties with second-degree gravitational harmonics (Smith et al., 2012) provides an estimate of the polar moment of inertia of Mercury C/MR 2 = 0.346 AE 0.014, where M and R are Mercury's mass and radius. The fraction of the moment that corresponds to the outer librating shell, which can be used to estimate the size of the core, is C m /C = 0.431 AE 0.025.

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“…In addition, the same dissipation brings Mercury to Cassini state 1, wherein Mercury's spin axis remains coplanar with the orbit normal and Laplace plane normal as the spin vector and orbit normal precess around the latter with a ∼ 300, 000 yr period (Colombo 1966;Peale 1969Peale , 1974. Because the Laplace plane is itself variable on long time scales, one can invoke an instantaneous Laplace plane that is valid at the present epoch (Yseboodt and Margot 2006). On the basis of theoretical calculations, Mercury is expected to remain close to the Cassini state (Peale 2006).…”

Section: Introductionmentioning

confidence: 99%

Consequences of a solid inner core on Mercury’s spin configuration

Peale

Margot

Hauck

et al. 2016

Icarus

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The pressure torque by a liquid core that drove Mercury to the nominal Cassini state of rotation is dominated by the torque from the solid inner core. The gravitational torque exerted on Mercury's mantle from an asymmetric solid inner core increases the equilibrium obliquity of the mantle spin axis. Since the observed obliquity of the mantle must be compatible with a solid inner core of any size, the moment of inertia inferred from the occupancy of the Cassini state must be reduced to compensate the torque from the inner core and bring Mercury's spin axis to the observed position. The unknown size and shape of the inner core means that the moment of inertia is more uncertain than previously inferred.

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Evolution of Mercury's obliquity

Cited by 72 publications

References 21 publications

On the oscillations in Mercury's obliquity

On the oscillations in Mercury's obliquity

Mercury's moment of inertia from spin and gravity data

Consequences of a solid inner core on Mercury’s spin configuration

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