A Lorentz-invariant theory of gravitation is examined in which the field variable is a scalar in the sense of the four-dimensional tensor calculus. The Kepler-motion has the same form as in Nordström's theory and differs accordingly from the vector theory. The perihelion motion is of the same absolute value as in the vector theory, and hence much too small in comparison with the experimental value for the planet Mercury, and moreover of the wrong sign. The influence of radiation damping is discussed in a second paper which will be published shortly.