As Jupiter (or any planet) orbits the sun, the sun responds by orbiting in a much smaller “orbit” around their mutual center of mass.
a) At what distance from the center of the sun is the Sun-Jupiter center of mass?
b) What is the sun’s circular velocity around that center of mass?
c) If an alien civilization were observing our solar system (conveniently edge-on so they see the maximum velocity), how small a velocity would they need to be able to detect to infer the presence of Earth by observing the sun’s radial velocity?