Anybody care to comment on the descriptions of Earth's orbital motion vs. distance from the Sun in this link

[Maol]

Can someone explain the Earth's orbit vs. the Solar System barycenter and the Sun's center of mass. It seems to me the motions are more complex than either the critics or the paper's authors assumptions. The authors proposition is Earth's distance from the Sun influences the planet's temperature, the critics defend the mainstream view by pointing out the Earth doesn't orbit the barycenter, it orbits the Sun's center of mass. Isn't it a little bit of both? If orbital mechanics consistently obeys the math, surely someone has a computer program written for calculation of this.

https://phys.org/news/2020-03-retracted ... e-sun.html

[jacmac]

Yes it is perhaps a little bit of both, I think.
The earth and the sun orbit around the earth/sun barycenter.
Each planet/sun combo orbits its barycenter.
The sun, of course, moves about as pulled by all the planets at once.
Maol:

It seems to me the motions are more complex than either the critics or the paper's authors assumptions

It seems that way to me also. That seems to always be true....in space everything is very complicated.
Jack