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| We apply the theory of incompressible fluid to simulate the deformation of massive celestial bodies and work out the equation of static equilibrium state. The generalized equipotential conditions on the surface give rise to the surface equations, which reflect both the local properties
and the global distributive characters. Subsequently, practical examination of the surface equation concludes that this model succeeds in interpreting the degree of magnitude of certain quantities, yet needs improvements for fine analysis. The addition of spinning properties transforms a standard sphere into a rotational ellipsoid, whose mass centroid shifts away from the gravitational center, and leads to nonvanishing moment of gravity by external particles. In the end, we use Lagrangian and Hamiltonian mechanics to analyze the two-body gravitational systems with spin parameters, and come up with the analytical Lagrangian and the integrals of motion, and put forward some suggestions for the modification of this formulation. |
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| Keywords:Spin;Incompressible Fluid;Static Equilibrium;Equipotential Surface;Two-Body Gravitational System |
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