Spartan was the long range missile used for area defense. It was designed to destroy incoming targets before they re-entered the atmosphere. Because the interception occured much earlier in the trajectory of the target re-entry vehicle, protection could be provided for a large geographical area, thus the term "area defense".
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Sprint was the ultra high acceleration missile used for terminal defense. This was a "last ditch" effort to destroy incoming re-entry vehicles that had survived the area defense provided by Spartan. Terminal defense occurred within the atmosphere only a short time before the RV's reached their targets, necessitating Sprint's ultra high acceleration.
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