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CMEs can have velocities from 20-3200 km/sec, with an average of 489 km/sec. The escape velocity from the surface of the Sun is 618 km/sec, so the higher speed CMEs will escape the Solar system. As to how much this will effect the Sun's motion:The average mass of a CME is 1.6e12 kg. If we assume a top end velocity for the CME, the velocity change generated owuld be in the order of 2.6 picometers per second* At this rate, it would take the Sun ~12378 years to move 1 meter from its original position. During which time, other CMEs will have occurred, all pointing in different directions, On average, they will cancel each other out. So the net movement of the Sun due to CMEs over any time period will be exceedingly small, and over long scales averages out to being none. * This number is a tad high, as it just used the CME ejection velocity directly, and doesn't account for the effective velocity loss caused by climbing out of the Sun's gravity well.
does the loss of mass caused by nuclear fusion have any effect on that trajectory?
Does the position of the Sun change?