When a planet is spinning around its own axis, it has an effect on the trajectory of its satellites. I believe it is called frame dragging.
Spin increases the kinetic energy of an object, contributing to its mass-energy, but some other effect must come into play as well.
How does one differentiate between spin and orbit velocity?
What is the effect of the spin? Lets say that Earth suddenly started spinning faster, what would happen to the moons trajectory?