It does share Fortunately, we have a magnetosphere and distance to protect ourselves from that: round our parts the Sun's power output is diluted by a factor of 1.5 * 10^9 due to distance alone, diluted further the farther we get from the Sun. Which means within the Earth's magnetosphere it's not at all a useful source for propulsion. To be sure that is better than the alternative, without such protection solar storms could fry the electronics of the craft before it even got going.
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