Contributions to Earth's orbit

[james_berlin]

If one writes down the Newton's equations of motion for the Earth, the forces that act on the Earth are the gravitational forces exerted by all other massive bodies, such as the Sun, the Moon, the planets etc. The largest of these forces is that of the Sun: keeping into account only the Sun's force in the equations of motion, the two-body problem for the Sun-Earth system can be solved, and the orbit of the Earth around the Sun can be determined.

However, there are the contributions by other massive bodies that influence the Earth's orbit. What is the most relevant contribution to the Earth's orbit after that of the Sun? A rough estimate based on distances and masses shows that it should be the attraction of the Moon.

 

[BvU]

Hello James, welcome to PF !
I second your conclusion. And now we both are curious to hear what is (*) in third place, aren't we ? Anyone ?

(*) given that we move around in approximate circles, it may even be the third in line is time-dependent !

 

[Janus]

If one writes down the Newton's equations of motion for the Earth, the forces that act on the Earth are the gravitational forces exerted by all other massive bodies, such as the Sun, the Moon, the planets etc. The largest of these forces is that of the Sun: keeping into account only the Sun's force in the equations of motion, the two-body problem for the Sun-Earth system can be solved, and the orbit of the Earth around the Sun can be determined.

However, there are the contributions by other massive bodies that influence the Earth's orbit. What is the most relevant contribution to the Earth's orbit after that of the Sun? A rough estimate based on distances and masses shows that it should be the attraction of the Moon.

The effect of the Moon on the Earth is a periodic motion of some ~4682 km around the center of mass for the two(or barycenter). with a period equal to 1 synodic month. So basically, the Earth over the course of a month varies its distance from the Sun by ~9366 km. Since 4682 km is less than the radius of the Earth, some part of the Earth always remains the "average" distance from the Sun.
Now in astronomy, when one talks about the orbit of the Earth, the values listed ignore this "wobble" and what are actually given is the parameters for the orbit of the Earth-Moon barycenter.