The furthest they could be is a point exactly center of the far side of the moon. If they travel along a great circle, they'd only have to travel a distance equal to one quarter to the moon's circumference to be able to see the Earth.
If they live not at the center of the far side - and if they choose the wrong direction (because how should they know?) - they can travel more than a quarter of the moon great circle.
Ah, good point. So really the at most is `0.5*circumference - epsilon` (starting just on the far side). In the worst case, if they manage to stay on a great circle.
From the article:
"Owing to various view angles from different parts of the Earth, the most ambitious jet-setting astronomer could have seen a maximum of 59 percent of the surface of our planetary companion. "
If we take into account that fact that Earth is not a point, then epsilon is not so tiny after all, it's around 0.045 times circunference.
This would make the final result 0.455 times circunference.
But they'd have to know which direction is the correct direction, and they wouldn't know which direction is correct until they knew where the Earth was.
