It takes about 10 minutes to reach the ISS orbital speed and velocity, but you don’t go directly to the station. You’ll do some checks once you’re in orbit to ensure that the craft is still operating normally after all the vibrations from launch, then you will slowly adjust your orbit to synchronise with the ISS.
The reason you do this is because the ISS Is very big and expensive and fragile, you want to approach it slowly so if your craft has a complete systems failure the ISS can move out of the way and avoid a collision. You also don’t want to fire your thrusters directly at the station so you approach slowly from a slight angle. Movement in orbits doesn’t work the same way as on earth, so there’s a while long checklist of careful movements that need to be followed.
So most of the time is spent in orbit doing checks and slowly aligning orbits. You could theoretically launch directly to the ISS and that would take about an hour, but this would be very dangerous to the station if anything went wrong. A fast ascent takes about 4 hours and a regular rendezvous can take about a day in total.
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