I will present analytical solutions for lightlike and timelike geodesics in Schwarzschild space-time and discuss two quite diverse areas of their applicability: In astrophysical studies of phenomena in strong gravity near a black hole they should be used for detail modeling of an orbiting blob of material, tidal disruption of a star or a comet, and line-profiles of an accretion disc. But also in the Earth's weak gravitational field, relativistic effects have to be taken into account in order to develop a highly accurate Global Navigation Satellite System, such as ESA's Galileo. Instead of just adding the relativistic corrections (as it is done at the moment), development of a fully relativistic navigation system, using geodesics solutions, would bring many advantages.