Gravitational coupling in a triaxial ellipsoidal Earth

Szeto, A. M. K.; Xu, Shixin

doi:10.1029/97jb02787

Cited by 34 publications

(39 citation statements)

References 11 publications

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“…Therefore, the resulting corrections to the gravitational field may be obtained by substituting the ellipsoidal expansion coefficients C lm , equations (53a)-(53b), into the expressions for ∂ψ/∂τ, equations (71)-(72). The resulting estimates are consistent with the estimates obtained by Szeto and Xu in [10] for the gravitational potential inside an ellipsoidal cavity.…”

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A way to compute the gravitational potential for near-spherical geometries

Grinfeld

Wisdom²

2006

Quart. Appl. Math.

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Abstract. We use a boundary perturbation technique based on the calculus of moving surfaces to compute the gravitational potential for near-spherical geometries with piecewise constant densities. The perturbation analysis is carried out to third order in the small parameter. The presented technique can be adapted to a broad range of potential problems including geometries with variable densities and surface density distributions that arise in electrostatics. The technique is applicable to arbitrary small perturbations of a spherically symmetric configuration and, in principle, to arbitrary initial domains. However, the Laplace equation for an arbitrary domain can usually be solved only numerically. We therefore concentrate on spherical domains which yield a number of geophysical applications.As an illustration, we apply our analysis to the case of a near spherical triaxial ellipsoid and show that third order estimates for ellipticities such as that of the Earth are accurate to ten digits. We include an appendix that contains a concise, but complete, exposition of the tensor calculus of moving interfaces.1. Introduction. This paper demonstrates how to use the calculus of moving surfaces to compute the gravitational potential for near spherical geometries based on a perturbation theory approach. Our expressions apply equally well (with a minus sign!) to the electrostatic potential when no surface charges are present.The perturbation of the potential is induced by a small deformation of the boundary of the domain. Our analysis applies to an arbitrary sufficiently smooth small deformation. We consider the case of constant density which can be extended to piecewise constant by the superposition principle. We do not consider the case of varying density, since the most challenging and interesting part of the analysis deals with the density discontinuities at the boundary of the domain. The presented technique can also be applied to boundary density distributions that arise in the analysis of the electrostatic potential of a conductor.

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confidence: 80%

“…The gravitational correction inside a slightly ellipsoidal shell was also calculated to second order in [10].…”

Section: Ellipsoidal Perturbationmentioning

confidence: 99%

A way to compute the gravitational potential for near-spherical geometries

Grinfeld

Wisdom²

2006

Quart. Appl. Math.

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“…From Szeto & Xu (1997), we express the torque on the interior due to the shell and the top ocean and the torque on the shell caused by the misalignment with the bottom ocean and the interior as…”

Section: A New Cassini State Solutionmentioning

confidence: 99%

Titan’s obliquity as evidence of a subsurface ocean?

Baland

Hoolst

Yseboodt

et al. 2011

A&A

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On the basis of gravity and radar observations with the Cassini spacecraft, the moment of inertia of Titan and the orientation of Titan's rotation axis have been estimated in recent studies. According to the observed orientation, Titan is close to the Cassini state. However, the observed obliquity is inconsistent with the estimate of the moment of inertia for an entirely solid Titan occupying the Cassini state. We propose a new Cassini state model for Titan in which we assume the presence of a liquid water ocean beneath an ice shell and consider the gravitational and pressure torques arising between the different layers of the satellite. With the new model, we find a closer agreement between the moment of inertia and the rotation state than for the solid case, strengthening the possibility that Titan has a subsurface ocean.

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“…Other formulations for gravitational and pressure torques between inner core, outer core, and mantle have been given by Szeto and Xu (1997); Baland and van Hoolst (2010) ;Baland et al (2011).…”

Section: Torque On the Fluid Corementioning

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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Gravitational coupling in a triaxial ellipsoidal Earth

Cited by 34 publications

References 11 publications

A way to compute the gravitational potential for near-spherical geometries

A way to compute the gravitational potential for near-spherical geometries

Titan’s obliquity as evidence of a subsurface ocean?

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

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