A look at how Martha and the Doctor might have seen the moon landing four times.
Disclaimer: Believe it or not, I don't own Doctor Who. If I did, I would probably be able to watch the new episodes as soon as they came out.
The first time they saw it, they weren't even trying.
In behavior that Martha was quickly realizing was typical, the TARDIS responded to the Doctor setting the coordinates for 2008 China ("If you're going to take me to the Olympics," Martha had insisted, "you're going to take me to them in a time where I have a chance of recognizing the athletes") by landing them in London, 1969. There, in behavior that Martha was quickly realizing was typical, the Doctor insisted on sticking around to explore. "You never know what you'll find, even in good old London!"
What they found was an alien who, in absence of its original food source, was absorbing the life energy of children. They finally managed to corner it in a suburban household, getting there just in time to save the life of the twelve-year-old boy who would have been its next victim.
They had been thanked profusely by the boy's family—the Doctor declared it was a nice change—and were about to leave when the grandmother, sitting in the den, called excitedly for them to come look at what was on the telly.
Neil Armstrong was walking on the moon.
It took a minute for that information to sink fully into Martha's brain. When it finally made it in, she had to stop herself from yelling. Instead, she settled for a hoarse whisper.
"This is the original moon landing broadcast!" she hissed at the Doctor, who was watching the screen with a look of—oddly enough—fatherly pride.
"Oh yes." He murmured back, smiling happily. "This is it—this is the start. And think—in just four or five more centuries, the human race will reach out farther and encounter alien species, and then there'll be no stopping you. You'll reach for the stars and you'll get them." By the end of his little speech, his smile had turned into a classic manic Doctor grin.
Martha shook her head in disbelief. "All that from one man bouncing around in the moon dust?"
The Doctor put an arm around her. "Humans." He said decisively, as though it explained everything.
Universal evidence was beginning to convince Martha that it really did.
The second time they saw it was a bit more deliberate.
The Doctor had obviously been in an historic mood. "Let's do America!" he decided eagerly, bouncing around the console one day. "They're very politically minded. Pick a president, any president, and we'll go pay him a visit."
Martha had considered her options for a moment before giving him a sneaky grin back. "Let's go see Nixon." She said smugly, "I've always wished I could ask him about Watergate. Think he'd level with us?"
The Doctor had responded with a laugh. "Oh, you are a bad one. Off we go!" and they went spinning through the vortex.
They landed in a service closet in the White House, and the Doctor produced two Secret Service outfits from the TARDIS wardrobe.
"Did they have female Secret Service agents in the seventies?" Martha asked skeptically as they stood just inside the TARDIS doors.
The Doctor gave her his 'of course you can walk around as a scantily-clad black woman in 1500s London' look. "They do now!" And with that, they were off.
After some liberal flashing of the Doctor's psychic paper, they were shown into the Oval Office where, to their surprise, the President appeared to be having a televised phone conversation.
The Doctor and Martha slowly moved around the area to the side of the desk that was out of the camera's range to see what appeared to be a teleprompter as Nixon continued speaking to whoever was on the phone.
"Because of what you have done," the President continued, oblivious to their movement, "the heavens have become a part of man's world…"
Martha glanced over at the Doctor just in time to see him form an "o" of realization with his mouth at the President's words. At her confused glance, he pulled out his psychic paper and discreetly handed it to her.
When she looked at it, a message formed in the Doctor's messy script. "He's talking to Neil Armstrong on the moon. Welcome back to 1969."
The box Martha had mistaken for a teleprompter was a television monitor, and displayed on it was Neil Armstrong wearing an astronaut's suit.
When the phone call was over, the Doctor gave her an apologetic look—it was too early for questions about Watergate.
Martha acted disappointed, but she really didn't mind.
The third time, the Doctor knew exactly where he was going.
When Martha appeared in the console room after a good night's sleep, he bounded up to her. "Want to see something cool?"
Martha stared at him in bemusement for a long second before nodding. "Sure, why not." It was too early for her to think to question his definition of "cool".
When they landed, he motioned her quiet and pulled her by the hand out the doors of the TARDIS and down several stark white hallways.
They came to a stop outside a door that had a nameplate that Martha might have read it she hadn't been taken by a sudden monstrous yawn.
The Doctor didn't seem to mind. "Ready?" he demanded eagerly, and when she gave him a sleepy nod he opened the door and pulled her inside.
Martha woke up.
They were in an amphitheatre-type room, with chairs and computers descending down to the main floor. The chairs were all filled with people, and the huge monitors on the far wall were filled with a larger-than-life Neil Armstrong climbing out of the moon lander.
"We're in Mission Control." She breathed in disbelief.
The Doctor nodded.
"We're in Mission Control in 1969."
The Doctor nodded again.
"Oh my God!"
It took the Doctor a great effort not to laugh.
The fourth time was beautiful.
Martha had been depressed all day. She was losing touch with her family, she had found a zit on her face for the first time in almost a month, and the last couple of trips she had taken with the Doctor had ended with people she had grown fond of dying. In short, she was completely miserable.
When the Doctor landed the TARDIS, she glared at him.
"I don't want to go anywhere today." She said crossly.
"We're not going to leave the ship." He reassured her, and opened the doors.
They were on the moon.
Specifically, they were parked behind and just to the left of the moon lander, which Neil Armstrong was climbing out of.
Martha crossed the console room to sit beside the Doctor in the doorway, and they watched long after the broadcast was over.
"Thank you," she said sincerely, afterwards, and didn't realize until long after they had left that his arm had been around her the entire time.
The moon landing, she decided, was her favorite extraterrestrial experience.
That fact didn't, unfortunately, save the Doctor from a slapping when, after stranding them both in 1969, he suggested that "at least we'll get to watch the moon landing again, right?".
But really, Martha wouldn't have him any other way.