Newton's theorem of revolving orbits does not go to infinity. However, this conclusion holds only when two bodies are present (the two-body problem); the motion of three bodies or more acting under their mutual gravitation (the "n"-body problem) remained unsolved for centuries after Newton, although solutions to a few special cases were discovered. Newton proposed that the orbits of planets about the Sun are largely elliptical because the Sun's gravitation is dominant; to first approximation, the presence of the other planets can be ignored. By analogy, the elliptical orbit of the Moon about the Earth was dominated by the Earth's gravity; to first approximation, the
Gravity anomaly Gravity anomaly A gravity anomaly is the difference between the observed acceleration of free fall, or gravity, on a planet's surface, and the corresponding value predicted from a model of the planet's gravity field. Typically the model is based on simplifying assumptions, such as that, under its self-gravitation and rotational motion, the planet assumes the figure of an ellipsoid of revolution. Gravity on the surface of this ellipsoid is then given by a simple formula which only contains the latitude, and subtraction from observed gravity in the same location will yield the gravity anomaly. Anomaly values are typically much smaller