I agree. We use the moon's gravity to slingshot them around.
5 seconds sound clip from the Apollo 13 movie soundboard.
You can hear this line at 01:08:01 in the Blu-ray version of the movie.
Quote context
[...]
- From this moment on, we are improvising a new mission.
- Sorry about that. We'll get somebody to look at that.
- How do we get our people home? They are here. Do we turn them around, straight back, direct abort?
- Yes!
- No, sir! We get them on a free-return trajectory.
- It's the option with the fewest question marks for safety.
- I agree. We use the moon's gravity to slingshot them around.
- No, the LEM will not support three guys for that amount of time.
- I think we've got to do a direct abort. We do an about-face, bring the guys right home, right now.
- Get them back soon. Absolutely.
- We don't even know if the Odyssey's engine's working.
- If there's been serious damage to the spacecraft...
[...]