3 planes are needed.
They all take off at the same time and fly 1/8th the way around the world. One gives 1/4th of a tank to each of the other planes and goes back to refuel.
The other two continue anothanother 1/8th of the way. The support plane gives 1/4th of a tank to Earhart and flies back to refuel.
When Earhart is running on fumes 6/8ths of the way around the world, she is met by a support plane that gives her 1/4th of a tank.
They fly to the 7/8ths mark and meet a second support plane which gives them both 1/4th of a tank.
As the planes from the first 4th and last 4th are reused, only 3 planes are needed.