By Ripoll J.
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Additional resources for A characteristic property of spherical caps
When Mercury does not react as a single rigid body to external gravitational forcing, which is the case if Mercury has a liquid core, angular momentum equations for the separate solid and liquid layers are needed. If Mercury has one solid layer (mantle+crust, hereafter denoted by ‘mantle’) and one spherically symmetric liquid layer (the core), libration equation (16) remains valid with C replaced by C m since only the mantle responds to the forcing. Pressure coupling between the core and the mantle due to an equatorially flattened core–mantle boundary does not change the libration of the mantle (Van Hoolst 2007), and other core–mantle couplings such as electromagnetic coupling, viscous coupling, and gravitational coupling between the mantle and a solid inner core have a negligible effect on the libration (Peale et al.
2004). This amplitude is larger than the model values calculated above with B − A = 4 × 10−5 MR 2 (see (17)), even for the largest liquid cores (see Fig. 5 × 10−5 ). By taking into account that the equatorial moment of inertia difference B − A has a 50% uncertainty (Anderson et al. 1987), it can be concluded with very high probability that Mercury has a liquid core (Margot et al. 2004). 5) × 10−5 for the moment nevertheless prevents improving the moment of inertia estimate. By averaging equation (16) over an orbital period, the periodic forcing terms in the righthand member vanish, and the equation reduces to the pendulum equation 3B −A 123 2 d 2γ e sin 2γ = 0, + e 7− dM 2 4 C m 8 (18) 34 T.
Sci. Lett. 193, 509–514 (2001) J. Longhi, E. R. Holloway, H. Wänke, in Mars, ed. H. M. W. S. Matthews (The University of Arizona Press, Tucson, 1992), pp. 184–208 J. J. F. A. V. Holin, Earth-based measurements of planetary rotational states. American Geophysical Union, Fall Meeting 2004, abstract G33A-02, 2004 J. J. F. A. V. Holin, Observational proof that Mercury occupies a Cassini state. L. J. F. A. V. Holin, Science 316, 710–714 (2007). 1140514 A. Milani, A. Rossi, D. Vokrouhlicky, D. Villani, C.
A characteristic property of spherical caps by Ripoll J.