Canonically, Natira is actually considered to be McCoy's wife from this point on. Talk about a long-distance relationship.

We know Spock is a genius, but he just happens to be able to read some random 10,000-year-old dead civilisation's writing?

Transcript

1
{sick bay}
Chief Medical Officer's log, Stardate 5476.3. I have contracted a rare space PLAGUE.
McCoy: Plotdevicemia. I have a year to live.
2
{bridge}
Chekov: An asteroid fired missiles at us!
Spock: It is hollow. A ship.
McCoy: Hey, this episode's supposed to be about me!
3
{transporter room}
Kirk: We're going to beam over and immediately get captured. You better stay here, Bones.
McCoy: I'm coming with you!
4
{on the asteroid}
Natira: I am Natira, high priestess of the world of Yonada.
Kirk: World?
Spock: They do not know this is a ship. Fascinating.
5
{Oracle room}
Natira: Our Oracle will now punish you.
SFX: ZAP!
6
{quarters}
Old Man: I climbed the forbidden mountains. I know this is not a planet, for the world is hollow, and I have touched the sky.
Kirk: Nice title drop.
7
Natira: {to McCoy} I choose you as my mate.
McCoy: No argument from me!
8
{Oracle room}
Caption: Meanwhile:
Spock: Fabrini writing. When their sun went nova 10,000 years ago, they sent this colony ship.
Kirk: And concealed the purpose from the crew, by disguising a computer as a god. Yes, it all makes sense.
9
{quarters}
Kirk: Bones, you can't contact a primitive culture ruled by an ancient computer concealed in some mysterious obelisk and marry the high priestess!
McCoy: <koff> The Paradise Syndrome <koff>
10
Spock: The Prime Directive says you cannot tell the Yonadans they are on a space ship.
Kirk: Then we know what we have to do!
11
Natira: Huh. That actually explains a lot of stuff. I will lead my people to a new world!
Natira: McCoy, you must leave me to seek a cure for your incurable disease.
12
{Enterprise sick bay}
Spock: The Fabrini memory banks contained a cure for Dr McCoy.
McCoy: I have a wife and I'm going to live!
Kirk: Yes, but we'll never mention her again.