A small asteroid of mass 2.6E9 kg is discovered traveling at a speed of 18km/s on a direct heading for Starbase Alpha, which is in deep space well outside the solar system. Lacking weapons of sufficient power to destroy the asteroid, the frightened starbase inhabitants decide to deflect it by hitting it with a remote controlled spaceship. The spaceship has an empty mass of 25,000kg and a top speed of 85 km/s when its fuel is exhausted. The asteroid has to be deflected so that by the time it reaches the starbase, its center is 1800m away from its original path. What is the minimum time before the asteroids projected impact that the spaceship must reach the asteroid. Explain carefully.
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