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.