Recently I became aware the barycenter of Jupiter’s orbit about the sun and the Sun’s subsequent wobble is centered slightly above the surface of the sun. How does this affect the other planets when say Jupiter is on the far side which would bring the sun one solar diameter and change closer to say Mercury. Does Mercury (and the rest) slightly speed up in their orbits? Does the sun react to the sum of the parts and orbit the center of the entire solar systems non-solar mass? In that case, what stresses are put on the involved parties as gravitational effects are incurred? I understand this is one tool in the toolbox when looking for exoplanets. The barycenter factoid is one I was unaware of from my Gemini & Apollo era science books. And I hadn’t stumbled acrost it since until this week.
Jupiter has about 1/1000 the mass of the sun, and it isn’t going to rip the other planets apart, but it definitely does perturb their orbital elements (eccentricity, longitude, and so on).
It is also true that the sun orbits the solar-system barycenter. Here is a tool to visualize the effect of different planets on the sun’s orbit.