Equivalence Orbits Related to Moon-Synodic Motion

The Moon forms a double planetary system with the Earth, which is unique in its relation in the solar system. The Moon is always outside the sphere of attraction of the Earth but still inside the sphere of activity. Its motion is therefore bound to the Earth, but it is dominated by the influence of the Sun. The motion of the Moon can be described mathematically as a motion around the Earth, while physically the motion is primarily around the Sun. This is shown by the fact that the motion of the Moon is always directed concave to the Sun. A reliable theory of the motion of the Moon must therefore always include the Sun. This was first accomplished by Ptolemy. Modern theories are an extension of the theory of Ptolemy, caused by improved observations and the advancement of celestial mechanics.