  In this work some aspects of the detection of certain general relativistic
effects in the weak gravitational field of the Earth via laser-ranged data to
some existing or proposed geodetic satellites are examined. The focus is on the
Lense-Thirring drag of the orbit of a test body, the gravitomagnetic clock
effect and the gravitoelectric perigee shift. The impact of some sources of
systematic errors is investigated. An experiment whose goal is the measurement
of the PPN parameters beta and gamma in the terrestrial field with LAGEOS
satellites at a level of 10^(-3)is presented. A modified version of the
proposed LARES mission is examined.
