Relativistic space-time positioning: principles and strategies

Starting from the description of space-time as a curved four-dimensional manifold, null Gaussian coordinates systems as appropriate for relativistic positioning will be discussed. Different approaches and strategies will be reviewed, implementing the null coordinates with both continuous and pulsating electromagnetic signals. In particular, methods based on purely local measurements of proper time intervals between pulses will be expounded and the various possible sources of uncertainty will be analyzed. As sources of pulses both artificial and natural emitters will be considered. The latter will concentrate on either radio- or X ray-emitting pulsars, discussing advantages and drawbacks. As for artificial emitters, various solutions will be presented, from satellites orbiting the Earth to broadcasting devices carried both by spacecrafts and celestial bodies of the solar system. In general the accuracy of the positioning is expected to be limited, besides the instabilities and drift of the sources, by the precision of the local clock, but in any case in long journeys systematic cumulated errors will tend to become dominant. The problem can be kept under control properly using a high level of redundancy in the procedure for the calculation of the coordinates of the receiver and by mixing a number of different and complementary strategies. Finally various possibilities for doing fundamental physics experiments by means of space-time topography techniques will shortly be presented and discussed