: I'm sorry I didn't respond to your post above, I totally forgot about this thread until (@Unclear Engineer
) liked my posts. At any rate, ISS has an orbital inclination to Earth's equator of 51.6° and the Tiangong station has an inclination of about 41.48°. ISS orbital altitude is roughly 420 km, where Tiangong is roughly 384 km, which is lower.
The inclination really doesn't factor into the travel time to arrive at the target body. The most important factor during launch is that the orbital plane of the station is passing over the launch site about the time of launch. During ascent the launcher controller will make corrections to tune in the orbital plane so that when it arrives to orbit, it's in the same plane. It takes a lot of fuel to match the plane in space, which the spacecraft typically doesn't have.
Then if the ISS has an average altitude of 420 km and the Progress spacecraft ends up in an orbit altitude of 415 km, it will be going a bit faster than the ISS, if it's 425 km, it's going a bit slower. That's how they catch the ISS, just pick an orbit a bit lower to catch up, or a bit higher to let ISS catch up to it. If the ISS happens to be close by at the time, it won't take long, but if it's like on the other side of the orbit, it'll take a while. This is with no fuel usage. Then when it gets close enough, it does a small burn to raise or lower one side of its orbit to match that of ISS, then when they are real close, do a second burn to match the rest of the orbit. Then it can to small RCS burns to slowly capture the ISS.
I didn't look up the flights you were referring to, but, likely China chose to launch as the Tiangong orbit passed over the launch site, AND the Tiangong was actually located a few minutes from passing over at the same time: a few short burns. The Dragon may have launched when ISS orbit was passing over, but, the ISS was actually a fraction of an orbit ahead or behind the launch, hence a longer wait to catch up. The Space Shuttle typically was scheduled for 2 to 3 days flight to catch ISS, the first to go through the checklists and reconfigure for flight after launch, the rest of the day and next day to recuperate from space sickness (yes, most of them are space sick for a day or so after launch), then the last of day 2 or some of day 3 to rendezvous and dock. Unmanned craft need no recuperation time.
Much of orbital mechanics are counter-intuitive to us grounded folks, it just doesn't work like we think.