If a reader looks at the sources he/she will find an animated video of the sun, earth and moon better than any diagram. "From what I understand, it suggests that at full moon, an observer on earth sees it travel at 2,288 mph and one on the sun would see it travel at 69,288 mph. This figure is calculated by adding the relative speeds of the earth and moon. This is ok." All observations are from Earth in the proof, because there are no observers near the sun, however, an observer near the sun would have the same frame of reference as an announcer in a racetrack infield tower. He would see objects travel at their relative velocity to the tower, as well as to each other. We can calculate the relative speed of the moon to the sun using that equation at full moon. The calculated velocity is constant and does not change based on the location of the moon in its orbit (at least I have never heard that claim from any source) Relative motion theory is totally dependent upon frame of reference, there is no way to reconcile relative motion theory with the moon phases due to the constantly varying changes of direction (frame of reference) the moon must make orbiting around a planet that is also in an orbit. (Unsigned by JasonZ)
I'm confused with your explanation. Perhaps you could bullet point it as I generally find a large block of text hard to follow.
The speed of the moon is more or less constant in the earths frame of reference (the orbit is slightly elliptical but we can assume it is circular for the purposes of this discussion). As velocity is a vector the moon's velocity does change, but I'm guessing your using velocity to mean speed?
I'm going to have another look at your argument. I'll reply again shortly. [[User:PeterIceHockey|PeterIceHockey]] ([[User talk:PeterIceHockey|talk]]) 14:20 , 16 December 2016 (EST)