[Elsie]

Almost 100% of all earth-moon diagrams show the earth traveling a smooth ellipse around the sun, with the moon making smooth circles around the earth.

But this is NOT how it is in actuality.

The baricenter of the earth-moon system is below the surface of the earth, and THAT point is what is going around the sun smoothly.

This picture is NOT accurate, but a lot closer to reality than 99.999 of the ones we see all the time.

[Lonesome in Massachussets]

If you work out time of the equinox in Meeus's Astronomical Algorithms there is a term for the effect of the moon, which shifts the time about two and a half minutes year to year. The orbital velocity of the earth is about 30 km/second, the displacement of the earth center from the barycenter of the earth-moon is about 4700 km. 4700/30 ~ 157 seconds. This is easily the largest perturbing term in calculation of the orbit of the earth, but well modeled and understood. In Meeus's formula for calculating the phase of the moon there are over 250 parameters, including terms for planets including Jupiter, Saturn, Venus, and Mercury. Meeus is for amateurs (like me). Sophisticated models are far more complete.