A new satellite-based test of special and general relativity is proposed. For the Michelson-Morley test we expect an improvement of at least three orders of magnitude, and for the Kennedy-Thorndike test an improvement of more than one order of magnitude. Furthermore, an improvement by two orders of magnitude of the test of the universality of the gravitational redshift by comparison of an atomic clock with an optical clock is projected. The tests are based on ultrastable optical cavities, lasers, an atomic clock and a frequency comb generator.