The title is a reference to the line "I have no spur to prick the sides of my intent but only vaulting ambition, which o'erleaps itself and falls on the other" from Act I, Scene VII of William Shakespeare's play "Macbeth".
At the beginning of this episode, Burnham and Lorca are taking a shuttle from the ISS Shenzhou to the ISS Charon. Burnham sets the Autopilot, which states that the Charon is 27,000,000 kilometers away, and that it's setting course at Warp 1 (which is the speed of light, 300,000 km/sec). Dividing these values gives us 90 seconds for the total trip.
After warp is engaged, Burnham and Lorca have a conversation. It lasts just about a minute and a half, and the time in warp is nearly exactly 90 seconds.
After warp is engaged, Burnham and Lorca have a conversation. It lasts just about a minute and a half, and the time in warp is nearly exactly 90 seconds.
At 37 minutes and 53 seconds, this is the shortest live-action episode in "Star Trek" history.
The titanic ISS Charon, the home of the Imperial Palace and the residence of Emperor Georgiou, is a ship larger than anything else seen in the Imperial Starfleet. Hoshi Sato became the Terran Empress essentially because she was in command of the Constitution class Defiant, at the time both more powerful than any ship in the Terran Starfleet (capable of defeating an entire fleet of rebel ships) and home to a library that contained extensive information of future scientific and technological advancements as well as potentially subversive information about the alternate universe it came from. Emperor Georgiou is still in possession of the subversive information, and maintains it as a classified secret. It is possible that the most advanced technology the Imperial Starfleet has developed - jumpstarted by a century - has remained similarly tightly held to her flagship, to maintain a tactical edge over other ships. Even if that is not the case, the enormous size of the ISS Charon and its firepower may just be the consequence of considerable cost in resources it took to build it - confirmed as of this episode that the Terran Empire rules not just many Federation planets, but the Klingon home-world as well, countless worlds and thousands if not millions of slaves could have been involved with the ISS Charon's construction. The ISS Charon looks similar in size and relative shape to the Planet Killer from The Doomsday Machine (1967), which explains the "sun" in the center and the "tail" that appears to be at the back.
This is the first episode of the series in which neither Keyla Detmer (Emily Coutts) nor her mirror universe counterpart appear.