Spacecraft Guidance Sensing at Relativistic Velocities

Abstract

In this chapter a solution to the problem of planning an interstellar voyage at relativistic velocities by automatic control was proposed. To this aim, position and velocity of a relativistic interstellar spacecraft can be found by means of automatic measurements onboard of the aberrated angular distances between three quasars, at least. Indeed, this set can represent a reliable inertial reference frame due to the circumstance that quasars can be considered fixed in the space due to their large distances from Earth. To this aim, the so-called apical latitude and longitude of some quasars can be obtained from their right ascension α and declination δ in astronomical catalogues, using some mathematical expressions to provide the aberrated coordinates of a relativistic spacecraft during an interstellar space mission. The algorithm used in this study showed that the accuracy of determining the aberrated apical coordinates of a spacecraft increases significantly using quasars with aberrated apical latitude values lower than 45°in the direction of motion, suggesting that one or more normal-sized telescopes aboard the spacecraft can use quasars within a cone with angular aperture of about 45°, providing aberrated apical latitudes of the spacecraft with errors ranging from 10 À7 to 10 À9 .