The ISS is around 400km above us. A rocket needs a speed of at least 8km per second to get to space. If we cut out the acceleration part it could in theory reach the ISS in around 50 seconds. Even if we factor in the acceleration part etc. it should still be very quick up there. Yet the fastest possible time to get to the ISS is 4 hours. That would be an average speed of 100Km/h which is way slower than the speed of the rocket after a few seconds. Why the long journey?
In: Planetary Science
Well, it took an SM-3 [a few minutes](https://web.archive.org/web/20120214031001/http://www.mda.mil/system/aegis_one_time_mission.html) to hit a satellite about 220 miles up, so your math seems about right.
Like people say, it’s docking. The real reason is that it’s most fuel efficient to [adjust an orbit halfway around from where you want the effect](https://en.wikipedia.org/wiki/Orbital_mechanics#Orbital_maneuver). Launch – ISS docking takes [a few different orbits](https://www.researchgate.net/publication/260971173/figure/fig1/AS:883542645022721@1587664390571/Profile-of-vehicle-transfer-from-insertion-orbit-to-the-ISS-orbit.png): launch into one, lift up to the right altitude, match position to docking approach, match orbit to ISS. Or something like that, not a rocket scientist. They may be waiting to do each one of those adjustments to the exact right time on the orbit, so up to 45 minute delays or so with each step.
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