Everyone knows the story.
Damaged by an explosion on the way to the moon in 1970, the three astronauts and the folks at NASA pulled out every stop to get them home in their crippled spacecraft. Using the engines on the Lunar Module that should have taken Lovell and Haise to the surface, they were able to add enough boost to the velocity to get them home to Earth before their air ran out.
But what if it hadn’t worked? They would have missed Earth and then orbited endlessly in the cold vacuum of space, right?
In an analysis of the trajectory, it turns out they would have missed Earth by only 2500 miles, and then been flung out past the Moon’s orbit. But the next time around, they’d have passed close enough o the moon for it’s mass to affect their orbit and then the spacecraft would have returned to Earth on an intercept course and burned up in the atmosphere.