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How many orbits does it realistically take for the shuttle to intercept the ISS?
It could do it in a pretty short time, depending on how close to the ISS it is launched. The final approach just takes four orbits, the orbit insertion takes two orbits, so you could minimal need six orbits for it.
But in reality, you have also other constraints that influence the flight plan:
- You need to do a OBSS survey of the heat shield.
- Your crew needs at least 36 hours for adapting to micro-gravity, otherwise you would have potentially space-sick astronauts during manual docking.
- The ground stations need to calculate the maneuvers that are not done by the on-board computer by radar data. Having more orbits for measurements means better accuracy.