【大地测量学基础】200603 The Gravity Field of the Earth.ppt

Foundation of Geodesy 3. The Gravity Field of the Earth The external gravity field is the reference system for the overwhelming part of the measured quantities in geodesy. If the distribution of gravity values on the surface of the earth is known, then in combination with other geodetic measurements, the shape of this surface may be determined (Law of Clairaut). The most important reference surface for height measurements, the geoid, as an idealized ocean surface is a level surface of the gravity field. The analysis of the external gravity field yields information on the structure and characteristics of the interior of the earth. 3 .1 Components of the Gravity Field A body rotating with the earth experiences the gravitational forces of the earth and of other heavenly bodies, as well as the centrifugal force due to the earths rotation. The resultant force is the force of gravity. unit of gravity : gal=cms-2 (Galelio Galelei) mgal=10-5ms-2 ugal= 10-8ms-2 Galileo was born in Pisa, Italy on February 15, 1564 3.1.1 Gravitation, Gravitational Potential The value of the potential at the point P in the gravitational field indicates the work that must be done by the gravitation in order to move the unit mass from infinity (V =0) to P. 3.1.2 Gravitational Potential of a Spherically Symmetric Earth To a first approximation, the earth can be viewed as a sphere with a centrally symmetric density structure. For an attracted point lying in the exterior, it is equal to the potential of the entire mass M of the earth concentrated at the center of mass. For a point in the interior, we have: 3.1.3 Properties of the Gravitational Potential We investigate the properties of the potential function V and its first and second derivatives. They are single-valued, finite, and continuous functions in the entire exterior space. They all vanish at infinity. Applying the Laplacian operator to V, we obtain L