Satellite Geodesy

Introduction
New satellite missions are carried out for a better understanding of the dynamic processes that occur in our planet. Generally we can say that terrestrial gravity field is a function which reflects the internal and superficial mass distribution and its inhomogeneities. The measure of this gravity field is also essential for geoid determination, which is the reference physical surface for many geodynamic processes.

Several disciplines are benefited with the information from satellite missions. For example:

Geodesy: a high- accuracy geoid determination will give us a unified global high-reference system. High- accuracy measurements of global gravity field will also improve the orbit determination of satellites.

Oceanography: knowing the geoid with high precision makes it possible to determine determine the sea surface topography (SST), which allows to describe ocean currents and circulation. The time variations of the currents and circulation are an important indicator of climatic changes.

Geophysics: the knowledge of the Earth´s gravity field together with magnetic and seismic data are useful to improve our Earth´s internal structure models and to understand the geodynamic processes that occur in its interior.

Definitions
The gravitational potential V is a function which depends on the mass distribution in the Earth. A Global Geopotential Model (GGM) is a set of coefficients that allows to write the gravitational potential V as a spherical harmonic expansion. These coefficients are obtained from terrestrial and satellite data.

The geoid is one of the equipotential surfaces of the potential V and it is defined as “that level surface which best fits the mean sea level”. This ideally means that a fluid on this surface will not flow. Due to the dynamic processes that occur continuously the geoid changes through time, therefore we should correct this definition and add “in a certain period”. The geoid is a very important surface because it is the datum (i.e. reference level) from which we measure heights and it determines the vertical in each point on the Earth´s surface. These concepts are useful, for instance, in engineering.

Satellite missions: CHAMP, GRACE and GOCE
CHAMP (Challing Minisatellite Payload) This satellite was launched on July 15, 2000. The mean targets of this mission were : mapping the global gravity field, specifically to determine the long wavelengths and their temporal changes; determining accurately the Earth´s magnetic field and its temporal variations; and finally profiling the ionosphere and troposphere to obtain information about temperature and other physical parameters.

This mission was finished on September 19, 2010, after ten years orbiting around the Earth.

GRACE (Gravity Recovery and Climate Experiment) This mission was launched on March 17, 2002 and has two identical satellites 220 km apart. Its mean goals are(3)	 : mapping global gravity field with high resolution and mainly determining temporal variations of gravity field.

GOCE (Gravity field and steady-state Ocean Circulation Explorer) This satellite is the lowest and is orbiting at a height of about 250km. It was launched on March 17, 2009 and has very specific aims : to determine gravity anomalies with an accuracy of 1mgal; to determine the geoid with an accuracy of 1-2 cm and to achieve these objectives at a spatial resolution of about 100km.

The last two missions are working at this moment.