Satellites dealt with by the Shuttle are never in a Geostationary (Clarke) orbit (GEO) which is far further than it can reach. The shuttle is operating in LEO (Low Earth Orbit) where the time around the world is around 90 minutes give or take.
Getting into the right orbit (something around 500km) is easy, but that orbit only passes the same spot on the earth's surface every few days. So, the Shuttle has to launch such that it is meeting the orbit at the same point as it's target (give or take a few hundred miles), if it doesn't it will forever be following something the other side of the world doing almost exactly the same speed.
To use an aviation analogy, imagine you want to fly formation circuits with another aeroplane of the same type that is flying overhead the circuit patternn. If you take off a little before it passes directly overhead, it will slowly overtake you as you climb then you should be able to formate somewhere downwind. But if you take-off at the same time, you will be chasing it but never quite getting there - you can catch up a bit by tighter circuits but not too tight because of the aircraft's manoeuvre limits (or in the shuttle's case the atmosphere), or allow it to slowly catch you up by flying wider circuits - but in the Shuttle's case it hasn't got the fuel to go to a vastly higher orbit.
So, just as you would have had to take-off at a pretty precise point to formate on this chap, so does the shuttle. The difference for the Shuttle is that the "circuit" as opposed to the orbit - the time for something to pass over the same spot again, is days or weeks long.
G