80 to 100 years in the future (late 21st, early 22nd century). As in ST:TOS, no concrete dates are given. (Future proofing).
The Solar System.
In general, the technology of the Rocket Ranch is more 2001 than Star Trek. Tech should be based on established physical principles, with engineering practices that are reasonably predictable today. Flights of fancy are less important than telling a story that actually could take place.
By the time of speaking, controlled fusion allows spaceflight under continuous acceleration (like The Expanse, but not as powerful).
Quantum computing is a reality, but plenty of computation still happens on silicon.
Optimistic, but realistic. The Rocket Ranchers live in our world, with divorce, famine, and genocide all part of it. There are no political conservatives on the Rocket Patrol, only engineering conservatives (Star Trek’s Scotty, or Clarke’s “Rescue Party”).
In the world of the Rocket Patrol, gendered English pronouns are no longer used, see Marge Piercy’s novel, “Woman on the Edge of Time”.