I think the author of this article should go back to grade school and retake some basic science classes.
http://www.geek.com/articles/geek-cetera/scientists-find-super-earth-2012025/
Nothing... but since you ask... look at your animation... same if the sun rotate around the center of mass, in some way, the planet seam to rotate around the sun and not the reverse... in fact, planet and star don't rotate at the same speed... change the speed of the planet and it will explain the season...
Not really... the sun rotate around the marked point on the center of mass curve... by example, for 1945, the center of the sun rotate around the point marked "1945"... you need to see the curve "center of mass" like a extra dimension called "time"... well, if someday i have enough free time, i will maybe make a 3D animation of it...
Mainly append when both of the massive planet ( jupiter and saturn ) align in their perihelion orbit ( more near the sun in a elliptical orbit )