The theory of general relativity includes both acceleration and gravity. Constant acceleration is completely equivalent to a uniform gravitational field. A beam of light bends under acceleration, so it should bend under gravity. This was shown to be correct during a solar eclipse. Clocks run slower in gravitational field.
Energy is lost by means of increasing the wavelength, known as gravitational redshift .
Einstein suggested a test. Starlight grazing near the surface of the Sun should bend. This phenomenon can only be observed during a solar eclipse. The deflection was measured and it agreed perfectly with the predicted value. The orbit of Mercury is close to the Sun, which has a strong gravitational field.