### Will the earth be at approximately the same location

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Suppose an asteroid is found that appears to be heading directly toward Earth (using Earth's location at the time of discovery). It is 4.2 A.U. away (i.e., 4.2 times the Earth-Sun distance), and travelling through the Solar System with a speed of 20 km /sec. (a) How long would it take the asteroid to reach Earth (at Earth's location at the time of discovery), assuming the asteroid's speed is constant? (b) Will the Earth be at approximately the same location in its orbit around the Sun after the time interval computed in part (a)? Discuss what could happen.

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