Originally posted by HUGH JASS
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The asteroid would have an attraction by virtue of a force to your spacecraft (as all masses are attracted to all other masses in Newtonian gravitation).
Force is used to accelerate objects by either changing their velocity or direction, in this case the force the asteroid has for your spacecraft would change it's direction over time, plotting a new course that would miss the earth.
Obviously the gravitational force isn't massive but you don't need to alter the direction much at all to create a large change when the massive distances of space are involved.
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