NASA plans this summer to take the first step toward creating a new and more powerful rocket that will be used to lift space shuttles into orbit well into the next century. Contractors will be asked to submit proposals for a $1.2 billion program to design and build an advanced space shuttle booster rocket in a government-owned plant. The National Aeronautics and Space Administration now gets its shuttle rockets from a single source, Morton Thiokol Inc., which owns its manufacturing facilities in Utah. A government-owned plant will enable NASA to change contractors if it becomes dissatisfied.