A 190-day comparison of the optical frequencies defined by an optical cavity and a molecular electronic transition is analyzed for the velocity independence of the speed of light (Kennedy-Thorndike test) and the universality of the gravitational redshift. The modulation of the laboratory velocity and the gravitational potential were provided by Earth's orbital motion around the Sun. We find a velocity-dependence coefficient of (1.9+/-2.1)×10-5, 3 times lower compared to the best previous test. Alternatively, the data confirm the gravitational redshift for an electronic transition at the 4% level. Prospects for significant improvements of the tests are discussed.