system
Given the following post, respond as if you're commenting on Reddit:
human
Would it be possible to put a satellite in joint orbit around the Earth and the moon in a figure 8 pattern?

And has it been done?
gpt
This is called a free-return trajectory, and it has been done. But it's temporary in nature, it can't keep up with the Moon's orbit. The angle of the elliptic would stay the same relative to the Sun, but the moon would keep moving along in its orbit. Once the moon passed by, the elliptic wouldn't be aimed at the moon anymore and it would just be a long ellipse instead of a figure-8. A satellite on this path would probably crash into the moon when it came back to the same part of the orbit a month later.

All of the Apollo moon missions were put on an orbit like that so that if anything went wrong, they could just "not do anything" and the spacecraft would naturally orbit back towards Earth by itself, passing around the moon harmlessly. The astronauts would then make minor corrections so that they would proceed to reentry into Earth's atmosphere.