Small objects do not have much influence, but are themselves influenced by large objects. There are several highly developed and detailed models of the solar system. The smaller a body is, the more predictable its trajectory because uncertainty in its mass has little effect on massive bodies.
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.
Cheesy carnival ride to help explain earth-moon