I've created a model, on a flat coordinate plane, the movement of the sun and moon using their known positions throughout the year. Both the sun and moon are orbiting the north pole with their respective frequencies. What I was surprised to find was the moon orbiting an apparent second center. Even though it is revolving around the north center, it also appears to orbit around the orbiting sun. I was curious if this type of movement could be expressed in a formula. It seems this double orbit effect would only be possible if their respective speeds are as they are. If I were to change the orbital period of one or the other, this effect would not happen and I'm curious to see how a formula would show this but don't know if something like this has been described before with a formula.
Hoping one of the math wizards here will have a better clue than I :)
https://www.youtube.com/watch?v=jTB6w6CHhIk
TIA!