Maurice talks about his seventh orbit as a Mercury astronaut. Since each flight was longer than the previous one, this means he had to have flown after Wally Schirra's October 3, 1962 flight on Sigma 7, but before Gordon Cooper's May 15, 1963 flight on Faith 7, making his flight the penultimate flight in the Mercury program.
Guest star Scott Paulin, who plays Lance Bristol, portrayed Project Mercury astronaut Deke Slayton in The Right Stuff (1983). Lance and Maurice discuss UFOs, with Maurice claiming to have seen one during his space flight. Although never stated explicitly, Maurice is assumed to also have been in Project Mercury, in which each flight had only one astronaut. Oddly enough, the only Mercury astronaut not to fly a Mercury mission (because of medical reasons) was Slayton, slated to fly the fourth mission but replaced by Scott Carpenter.
Although the specific NASA program in which Maurice flew in space is never explicitly stated, his conversation with homeless veteran Lance Bristol (Scott Paulin) concerning UFOs provides the series' strongest suggestion that Maurice was in Project Mercury. Each Mercury mission had only one astronaut aboard. Maurice describes his encounter with a UFO but never mentions flying with another astronaut who might have also seen the UFO or at least might have noticed if Maurice displayed any reaction to it.
Since Bernard talks about it being winter solstice (around 21sr December), the last 10 episodes have happened in a month since Thanksgiving.