Theory of an experiment in an orbiting space laboratory to determine the gravitational constant.

An experiment is discussed for determining the gravitational constant with the aid of an isolated system consisting of an artificial satellite moving around an artificial planet. The experiment is to be conducted in a spherical laboratory traveling in an orbit around the earth. Difficulties due to the gravity-gradient term are considered, and the three-tunnel method proposed by Wilk (1969) is examined. The rotation of the sphere is discussed together with aspects of the reference systems used, the equations of motion of the spacecraft and of the test objects, the field from the earth's gravity gradient at the test object, higher harmonic terms in the gravity gradient force, gravitational effects of the spacecraft itself, and a computer simulation.