Modelling and Characterizing the Earth's Gravity Field: From Basic Principles to Current Purposes
The Earth is a specific body in the Universe. Nowadays, thanks to the high accuracy of the measurements obtained by different techniques of geodesy, its shape, as well as its gravity field, can be described and characterized in a very precise way, with thousands of parameters: the Earth is a spherical body only in a very first approximation! In this paper, we start from Newton's universal law of gravitation; we remind the reader of some basic principles of the field theory, in order to get the development of a gravity field in spherical harmonics. Then we show the usual method of orbital dynamics used to get the coefficients of such a development. In practice, the development in spherical harmonics can also be used to describe the gravity field of each celestial body which does not differ too much from a sphere. But, it is all the more well adapted to the Earth as the temporal variations of many coefficients, which can be very high, can be linked to global geophysical and geody namical phenomena, enlighting the activity of an "alive planet" These phenomena, linked more or less to mass transfers between the different components of the Earth solid earth, oceans, atmosphere in particular are briefly discussed. We conclude with the current purposes about the modelling of the Earth gravity field, and with the required links which have to be kept and developed between geophysics, space geodesy, and celestial mechanics.