Doctor Who/Recap/S5/E07 The Wheel in Space

Jamie: Just you watch your lip or I'll put you across my knee and larrap you.

Zoe: Oh, this is going to be fun. I shall learn a lot from you.

Logic, my dear Zoe, merely enables one to be wrong with authority.

—The Doctor delivers a Take That to rival show Star Trek: The Original Series...

The Doctor and Jamie arrive on a spaceship and are attacked by a servo robot. Contacting a nearby space station, simply known as "the Wheel", they are rescued, but needless to say, more peril awaits.

The spaceship also releases some Cybermats which travel to the station and begin to prepare for an attack by the Cybermen. Meanwhile the Doctor and Jamie meet the crew, including a young teenage mathematical genius called Zoe Heriot. Most of the rest of the crew are being hypnotically controlled by the Cybermats, and the Doctor sends Jamie and Zoe to fetch a piece of phlebotinum from the TARDIS which will allow him to beef up the station's laser enough to destroy the approaching cyber-fleet.

Zoe stows away on the TARDIS, but is discovered by the Doctor who asks if she really wants to come with them, and shows a clip of a previous adventure to demonstrate the dangers. She still seems keen, so they agree to let her come along.

Episodes 3 and 6 can be viewed here.^{[dead link]}

Tropes

Action Figure Speech
Auto Kitchen: The spaceship that the Doctor and Jamie spend Episode 1 on has one.
But This Is Ridiculous: Jamie, on discovering that people in the future eat cube-shaped Food Pills: "I've heard of a square meal, but this is ridiculous!"
Emotionless Girl: Zoe, in her first couple of episodes.
Freak-Out: Jarvis Bennett is the latest in a series of base officers to go nuts during this season.
Heroic Sacrifice: Gemma Corwyn
Line-of-Sight Name: Jamie coins the long-running "John Smith" alias for the Doctor from a piece of medical equipment.
Sci-Fi Writers Have No Sense of Scale: The Cybermen's plan requires meteor showers—which they cause by blowing up distant stars.
Space Clothes: Zoe's catsuits are fondly remembered by fandom.
Tainted Veins
Tin Can Robot: The servo robot in episode 1.
Zeerust: Never mind Rose, Zoe was actually the first 21st century companion. A different, much groovier 21st century, featuring Space Clothes, Raygun Gothic, and Food Pills. Zoe probably played with jetpacks when she was a kid, it's just not mentioned...