The principal moments of inertia calculated with the hydrostatic equilibrium figure of the Earth

As an indication of the Earth＇s mass distribution, the principal moments of inertia （PMOI, i.e., A, B, C） of the Earth are the basic parameters in studies of the global dynamics of the earth, like earth nutation, and the geophysics. From the aspect of observation, the PMOI can be calculated from the spherical coefficients of observed gravity field. In this paper, the PMOI are calculated directly according to its definition with the figures of the Earth＇s interior derived by a generalized theory of the hydrostatic equilibrium figure of the Earth. We obtain that the angle between the principal axis of the maximum moment of PMOI and the rotational axis is 0.184~, which means that the other two principal axes are very closely in the equatorial plane. Meanwhile, B-A is 1.60 x 10-5 MR2, and the global dynamical flattening （H） is calculated to be 3.29587 ~ 10-3, which is 0.67% different from the latest observation derived value Hobs（3.273795 × 10 ^-3） （Petit and Luzum, 2010）, and this is a significant improvement from the 1.1% difference between the value of H derived from traditional theories of the figure of the Earth and the value of Hobs. It shows that we can calculate the PMOI and H with an appropriate accuracy by a gener- alized theory of the hydrostatic equilibrium figure of the Earth.

Determination of grounding line on the Amery Ice Shelf using Sentinel-1 radar interferometry data

Delineation of the grounding line(GL) is necessary for calculating the mass balance of Antarctica, but GL measurements for most of the continent remain at a relatively coarse level. We used Sentinel-1 constellation data to map the GL of the Amery Ice Shelf(AIS) using double-differential synthetic aperture radar interferometry. The ice thickness anomaly deduced from hydrostatic equilibrium and existing Antarctic GL products is compared with our result. With this new and very accurate GL, we detected new ice rises in the north of the AIS. Our new measurement shows no major change of the AIS GL, particularly in the southernmost part.

Method to Calculate Resistance of High-Speed Displacement Ship Taking the Effect of Dynamic Sinkage and Trim and Fluid Viscosity into Account

A method is presented to calculate the resistance of a high-speed displacement ship taking the effect of sinkage and trim and viscosity of fluid into account.A free surface flow field is evaluated by solving Reynolds averaged Navier-Stokes(RANS) equations with volume of fluid(VoF) method.The sinkage and trim are computed by equating the vertical force and pitching moment to the hydrostatic restoring force and moment.The software Fluent,Maxsurf and MATLAB are used to implement this method.With dynamic mesh being used,the position of a ship is updated by the motion of "ship plus boundary layer" grid zone.The hull factors are introduced for fast calculating the running attitude of a ship.The method has been applied to the ship model INSEAN2340 for different Froude numbers and is found to be efficient for evaluating the flow field,resistance,sinkage and trim.

Shape and gravitational field of the ellipsoidal satellites

The shape and gravitational field of ellipsoidal satellites are studied by using the tidal theory. For ellipsoidal satellites, the following conclusions were obtained: Firstly, in the early stage of the satellite formation, strong tidal friction allowed the satellites move in a synchronous orbit and evolve into a triaxial ellipsoidal shape. Because the tidal potential from the associated primary and the centrifugal potential from the satellite spin are nearly fixed at the surface, the early satellites are the viscoelastic celestial body, and their surfaces are nearly in the hydrostatic equilibrium state. The deformation is fixed in the surface of the satellite. By using the related parameters of primary and satellite, the tidal height and the theoretical lengths of three primary radii of the ellipsoidal satellite are calculated. Secondly, the current ellipsoidal satellites nearly maintain their ellipsoidal shape from solidification, which happened a few billion years ago. According to the satellite shape, we estimated the orbital period and spinning angular velocity, and then determined the evolution of the orbit. Lastly, assuming an ellipsoidal satellite originated in the hydrostatic equilibrium state, the surface shape could be determined by tidal, rotation, and additional potentials. However, the shape of the satellite's geoid differs from its surface shape. The relationship between these shapes is discussed and a formula for the gravitational harmonic coefficients is presented.