A theory of the equilibrium figure and gravitational field of the Galilean satellite Io: The second approximation |
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| Authors: | V N Zharkov |
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| Institution: | (1) Schmidt Joint Institute of Physics of the Earth, Russian Academy of Sciences, ul. Bol'shaya Gruzinskaya 10, Moscow, 123810, Russia |
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| Abstract: | We construct a theory of the equilibrium figure and gravitational field of the Galilean satellite Io to within terms of the second order in the small parameter α. We show that to describe all effects of the second approximation, the equation for the figure of the satellite must contain not only the components of the second spherical function, but also the components of the third and fourth spherical functions. The contribution of the third spherical function is determined by the Love number of the third order h3, whose model value is 1.6582. Measurements of the third-order gravitational moments could reveal the extent to which the hydrostatic equilibrium conditions are satisfied for Io. These conditions are J3=C32=0 and C31/C33=?6. We have calculated the corrections of the second order of smallness to the gravitational moments J2 and C22. We conclude that when modeling the internal structure of Io, it is better to use the observed value of k2 than the moment of inertia derived from k2. The corrections to the lengths of the semiaxes of the equilibrium figure of Io are all positive and equal to ～64.5, ～26, and ～14 m for the a, b, and c axes, respectively. Our theory allows the parameters of the figure and the fourth-order gravitational moments that differ from zero to be calculated. For the homogeneous model, their values are:\(s_4 = \frac{{885}}{{224}}\alpha ^2 ,s_{42} = - \frac{{75}}{{224}}\alpha ^2 ,s_{44} = \frac{{15}}{{896}}\alpha ^2 ,J_4 = - \frac{{885}}{{224}}\alpha ^2 ,C_{42} = \frac{{75}}{{224}}\alpha ^2 ,C_{44} = \frac{{15}}{{896}}\alpha ^2 \). |
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| Keywords: | Solar system Galilean satellites internal structure models equilibrium figures |
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