Could anybody help me to find a mathematical equation ( model ) that explains  the waveform movement of the earth around the axis of the sun path line, according to the  attached figure؟.

As I said before, the earth does not circle around the sun, but  it's motion is in a waveform. I could illustrate this motion in the attached figure.

I hope that  anybody could help me to find a mathematical equation ( model ) that explains the waveform movement of the earth around the axis of the sun path line, according to the attached figure .

Thanks