FREE TRANSLATIONAL OSCILLATIONS OF ICY BODIES WITH A SUBSURFACE OCEAN USING A VARIATIONAL APPROACH

Journal Article · Tue Mar 15 00:00:00 EDT 2011 · Astronomical Journal (New York, N.Y. Online)

DOI:https://doi.org/10.1088/0004-6256/141/3/77· OSTI ID:21583217

Escapa, A; Fukushima, T ^[1]

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1. National Astronomical Observatory, 2-21-1 Ohsawa, Mitaka, Tokyo 181-8588 (Japan)

We analyze the influence of the interior structure of an icy body with an internal ocean on the relative translational motions of its solid constituents. We consider an isolated body differentiated into three homogeneous layers with spherical symmetry: an external ice-I layer, a subsurface ammonia-water ocean, and a rocky inner core. This composition represents icy bodies such as Europa, Titania, Oberon, and Triton, as well as Pluto, Eris, Sedna, and 2004 DW. We construct the equations of motion by assuming that the solid constituents are rigid and that the ocean is an ideal fluid, the internal motion being characterized by the relative translations of the solids and the induced flow in the fluid. Then we determine the dynamics of the icy body using the methods of analytical mechanics, that is, we compute the kinetic energy and the gravitational potential energy, and obtain the Lagrangian function. The resulting solution of the Lagrange equations shows that the solid layers perform translational oscillations of different amplitudes with respect to the barycenter of the body. We derive the dependence of the frequency of the free oscillations of the system on the characteristics of each layer, expressing the period of the oscillations as a function of the densities and masses of the ocean and the rocky inner core, and the mass of the icy body. We apply these results to previously developed subsurface models and obtain numerical values for the period and the ratio between the amplitudes of the translational oscillations of the solid components. The features obtained are quite different from the cases of Earth and Mercury. Our analytical formulas satisfactorily explain the source of these differences. When models of the same icy body, compatible with the existence of an internal ocean, differ in the thickness of the ice-I layer, their associated periods experience a relative variation of at least 10%. In particular, the different models for Titania and Oberon exhibit a larger variation of about 37% and 30%. This indicates an absolute difference of the order of three and two hours, respectively. This suggests that the free period of the internal oscillations might provide a new procedure to constrain the internal structure of icy bodies with a subsurface ocean.

• OSTI ID: 21583217
• Journal Information: Astronomical Journal (New York, N.Y. Online), Vol. 141, Issue 3; Other Information: DOI: 10.1088/0004-6256/141/3/77; ISSN 1538-3881
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
AMMONIA
EQUATIONS OF MOTION
ICE
IDEAL FLOW
KINETIC ENERGY
LAGRANGE EQUATIONS
LAGRANGIAN FUNCTION
MATHEMATICAL SOLUTIONS
OSCILLATIONS
PLUTO PLANET
POTENTIAL ENERGY
SATELLITES
SYMMETRY
VARIATIONAL METHODS
WATER
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
ENERGY
EQUATIONS
FLUID FLOW
FUNCTIONS
HYDRIDES
HYDROGEN COMPOUNDS
INCOMPRESSIBLE FLOW
NITROGEN COMPOUNDS
NITROGEN HYDRIDES
OXYGEN COMPOUNDS
PARTIAL DIFFERENTIAL EQUATIONS
PLANETS
STEADY FLOW