Ah, Khan. We last saw him stranded on Ceti Alpha V back in the original series episode Space Seed. In the film, Khan explains that the next planet out—Ceti Alpha VI—exploded not long after Kirk stranded him and his crew on the fifth planet, thereby shifting its orbit, such that V now appeared to be the sixth planet. This also rendered the planet less habitable, causing the marooned victims to struggle to survive, until found.

Now it's true that Kirk dispensed some good old fashioned frontier justice on Khan and his gang, marooning them on Ceti Alpha V without really going through proper Starfleet protocols, so he might not have wanted to submit a formal report on what he did, but you'd think that he would at least make some sort of note that the Ceti Alpha system was... I dunno, dangerous or to be avoided or something. But no, Reliant stumbles upon the same system looking for a lifeless planet to test the Genesis device on.

That quibble aside, this is one of, if not the most esteemed movie in the Star Trek oeuvre, and deservedly so. It has everything. The old crew back to the sort of banter that made them so endearing. A proper villain, with some panache. Decent uniforms after the beige nightmare of The Motion Picture. And Kirstie Alley.

And one of the neatest coincidences of movie making history. The writers wanted to highlight the revenge theme, and to do so they drew some obvious parallels to Moby-Dick, and had Khan quote some choice lines from Captain Ahab. And this was all completely independent of the fact that back in the 1960s episode Kirk had stranded Khan on the fifth planet of the Ceti Alpha system, Ceti Alpha being an obvious twist on Alpha Ceti, a significant real world star in the constellation of Cetus - the whale.

Transcript

1
{Enterprise bridge}
Captain's log, Stardate 8130.3. Training mission to Gamma Hydra.
Uhura: Distress call from vessel Kobayashi Maru. In... the Neutral Zone.
Saavik: {in captain's chair} Plot intercept course.
Sulu: Klingons!!
2
Caption: Everyone dies!
SFX: Kaboom!
Caption: Pointedly including Spock!
3
Caption: It was all a simulation!
Saavik: Not fair, Admiral. There was no way to win.
Kirk: A no-win situation is something every commander faces, Mr Saavik. Except me!
4
{Kirk's apartment}
McCoy: Happy birthday, Jim. Have these antique reading glasses to remind you how old you are.
Kirk: Did you ever get over that plague thing?
5
Caption: Meanwhile, on Ceti Alpha VI:
Chekov: "Find a lifeless planet, Chekov. Make sure it's really lifeless, Chekov..."
Captain Terrell: That doesn't look lifeless to me.
6
Khan: I never forget a face Mister... Chekov.
Chekov: Do I know you?
Khan: We met in a bathroom once, I believe.
Chekov: Khan...
7
Khan: This Ceti eel will gnaaaw at your brain. You will tell me how to find Kirk.
Chekov: Aaargh!!
8
Caption: Enterprise on a training mission, for real, with Admiral Kirk inspecting:
Carol: {on viewer} Jim! Why are you taking Genesis?
Kirk: Carol, what? Who's taking Genesis?
Carol: On whose—
Uhura: {over communicator} Uhura here, Admiral. Transmission jammed at the source.
9
Kirk: Genesis is the power to destroy a planet and create new life.
McCoy: Oh good. That can't possibly go wrong now, can it?
Kirk: Regula I, allons-y!
10
{near Regula}
Saavik: It's Reliant, sir. Their comms are down. Regulations say we should raise shields.
Kirk: Naaah...
11
SFX: ZOOORCH!!! {Enterprise is hit amidships}
12
Khan: {on viewscreen} Kirk, my old friend. You left me marooned to die. I shall return the favour.
Kirk: Khan! Well I suppose that's better than Harry Mudd.