INTERNATIONAL DATE LINE?

The International Date Line (IDL).
MOST READERS will have heard of the International Date Line (IDL), established as an irregular line, drawn by convention through the Pacific Ocean, substantially along the 180th meridian. IDL marks the place where the date changes.
Crossing the line from west to east, travellers gain a day and, conversely, lose a day traveling east to west.
The position of the IDL has been arbitrarily designated and is partly curved to accommodate eastern Siberia, then bulges westward again in order to avoid crossing land.
Let us now assume that a super-fast aircraft can take its passengers around the equator, circling the globe in six hours. Flying west to east it will cross the IDL four times in 24 hours and consequently lose four days. Starting, say, on March 18 it will land on March 14. Continuing the journey the passengers will go back into history, eventually reliving the birth of Jesus Christ. Traveling east to west they will travel into the future, giving them a decisive advantage in the lottery on one’s return.
Have I managed to build a time machine, or is there something wrong with this reasoning?
