4 Model of the Moon-Earth

We assume the Earth and the Moon are solid spheres of respective known masses as well as moments of inertia. The Moon orbit is circular and the bodies' own axis and of all rotation is perpendicular to the orbital plane. The relevant angular velocities are to be found.

The aim is to find the variable radius/-s of the Moon's orbit for which the nearest "fixed" point of the Moon remains as it faces the Earth. Should the Moon's orbit be thus synchronised with it's own rotation for any value of the orbital radius it would mean it is true and it was so right from the beginning and will be in the future.

These rotational speeds are our variables and the orbit radius is the independent variable. The mechanical considerations are centrifugal force, gravitational force and the conservation of angular momentum.

The model can apply as well to any pair of rotating bodies under the force of gravity. All of this of course is in the classical mechanics setting.