Neutron stars and black holes have the strongest gravity, and hence--according to Einstein9s general theory of relativity--curve space-time the tightest, of all known objects in the universe. Observations by NASA9s Rossi X-ray Timing Explorer (RXTE) are now providing the first direct measurements of the orbital motion of matter in these strongly curved space-times. These observations provide insights into the fundamental properties not only of space-time but also of matter itself.