As for the Ceta Alpha system.
Spock mentions in Space Seed that the system has been fulled charted and that "planet number 5 is habitable." stating that the environment is harsh, which means a survey ship was in the system monitoring each planet not all that long ago.
The Enterprise warps back to the Botany Bay, takes everything to CA5, settles them on the planet by bringing (somehow) the cargobays from the BB to the surface, which could have taken a while, got the colonists down there, Spock likely scanned the region while they were there, then left.
Reliant was at least the 3rd Federation starship inside that system in 30-50 years, with no less than one entire system wide survey and all of Spock's readings from the previous trip.
Suddenly it's all 'how do i science'.