Gravity and Shape of the Earth
摘要
This chapter presents the fundamentals of the gravity and shape of the Earth. The spherical harmonic series of the Earth’s external gravitational potential, along with the gravitational attraction and its gradient, is derived. The determination of the Earth’s external gravity field using data of ground gravity is briefly formulated with approximations. The concepts introduced include the geoid, the normal gravity field, the reference Earth ellipsoid, height systems, the geoidal height, the deflection of the vertical, the disturbing gravity field, gravity reductions, and isostatic assumptions. A global model of the gravitational potential is presented as a reference. The internal shape and gravity of the Earth is formulated assuming the Earth to be in hydrostatic equilibrium state, i.e., the Earth behaves like a fluid body rotating as a whole without any relative motion inside. Finally, the gravitational potential of a layer of mass on the Earth’s surface considered as either spherical or aspherical is formulated.