Assuming a 747 could fly around Jupiter at its top Earth speed (I know this assumption is unrealistic), how long would it take to fly around Jupiter once?
It will depend on the speed of the jet, however:
Jupiter has an equatorial circumference of 449,200 km, a current-generation 747 has a top speed of 988 km/h so it will take about 455 hours or nearly 19 days (18.9) (this doesn't allow for re-fueling).
Someone else answered a somewhat related question (can you fly through Jupiters atmosphere?).
From the website:
Jupiter: Our Cessna can’t fly on Jupiter; the gravity is just too strong. The power needed to maintain level flight is three times greater than that on Earth. Starting from a friendly sea-level pressure, we’d accelerate through the tumbling winds into a 275 m/s (600 mph) downward glide deeper and deeper through the layers of ammonia ice and water ice until we and the aircraft were crushed.
Not sure if it would work with a stronger airplane. So, the answer is probably "you can't do that".