How many planes are required to rotate around the Earth for half a week when the plane is full of oil?

At least five planes are required

 

The idea is as follows:

Five planes are set to a, B, c, d, e. First, A, B, and C fly at the same time. When they fly to 1/8 laps, C refuel A and B respectively, because it flew 1/8 laps, 1/4 of the oil was used. C adds 1/4 of oil to A and B respectively, so a and B are full boxes, and C can fly back to the original place. When B adds 1/8 oil to a during the flight 1/4, B can return to the original place, and a is full of oil. So when a flies to 3/4 laps, the oil just runs out, and then let d fly in the opposite direction, then D only has half of the oil, and then gives a half of the oil, then there is no oil in the last two flights. At this time, the plane e arrived, and E added 1/8 of the distance to A and D respectively. Then the three planes just completed the whole flight.