The minimum distance should be the planet's circumference.
Why is that? It seems as arbitrary as circumnavigating a rotational axis and returning home.
Good news, the Earth's circumference is around 40,000km, and the actual distances sailed by each of the competitors in the most recent Vendee Globe were all around 50-51,000km. So they all exceed your requirement.
The trail should also look pleasing to the eye. So I'll have to invent a new arbitrary rule.