Figure Created Using Geometry Expressions™
The Space Shuttle could (theoretically) be boosted to Geosynchronous Earth Orbit (GEO) using a Hohmann Transfer Orbit. It would require two burns. The first burn would increase the speed of the shuttle from 7.62 km/sec to 10.0 km/sec. After entering the transfer ellipse 5.3 hours would elapse until the second burn was necessary to circularize the orbit. Otherwise the shuttle would stay in an elliptical orbit. This second burn would produce a change in velocity of 1.45 km/sec, leaving the shuttle in GEO orbiting at 3 km/sec at a fixed point over the Earth's surface. The beauty of these two burns is that they are both tangent to the orbits, in opposite directions, and use the minimum amount of fuel.
For verification purposes I have included links to the two programs used for this analysis. It is important when driving spaceships to have consensus before turning on the motor.
