In all reality or to be very specific, there is no Center of the Solar System, ok, that is splitting hairs, the absolute 0 of space cannot be measured with any degree of accuracy to determine where a center or if a center exists.
As Earth revolves around the Sun, the Sun is revolving around the Milky Way, the only constant in the Universe is change.
Albert Einstein came up with that one, sorta.
Points to ponder:
1. The Earth rotates on an Axis that is in the Orbit of the Sun.
2. The Sun rotates on an axis around the Milky Way.
3. The Milky Way is moving by cause or change of the gravitational fields that is comprises and that may have an interaction upon the movement.
4. I can see Venus and Mars with an un-aided eye at night, they are moving, or orbiting around the Sun.
5. I can see Galaxies and other Space Objects that are moving n relation or proportion to Earth.
6. The fact that I can see other Stars and Objects appear to move is a direct relationship to the Earths position and rotation.
7. I read alot of books as a younger man, I still read books, a day I do not learn something is a day that I have wasted.
8. Have a great moment, and keep looking up, or down.