Technically yes most flights between the US and Asia fly over the Pacific. It would be too far round for any current plane to fly eastward from the US to Asia without stopping.
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Rather than flying directly across the Pacific Ocean, most commercial flights take curved routes because they are actually shorter than shooting straight across a distance. This may sound counterintuitive, but since the Earth is spherical, a straight line is not necessarily the shortest distance between two points.
Most flights are intended to spend as little time as possible over water, since storms are more common over the ocean than on land. An aircraft would not be safe to fly over the Pacific Ocean due to the stormy weather and frequent lightning strikes that occur there.
The primary reason airplanes don't fly over the Pacific Ocean is because curved routes are shorter than straight routes. Flat maps are somewhat confusing because the Earth itself isn't flat. Rather, it's spherical. As a result, straight routes don't offer the shortest distance between two locations.
What is the longest flight in the world by distance? The longest flight in the world by distance is New York (JFK) to Singapore (SIN) on Singapore Airlines clocking in at 9,537 miles. What plane can fly the farthest in the world?
Thanks to the low visibility and undeveloped infrastructure, flying over Antarctica is extremely difficult. Specifically, because of the strong magnetic fields that surround the polar regions, navigating there, no matter how well-equipped the airplane is in terms of instrumentation, can be particularly challenging.
The simple answer is yes, pilots do, and are allowed to sleep during flight but there are strict rules controlling this practice. Pilots would only normally sleep on long haul flights, although sleep on short haul flights is permitted to avoid the effects of fatigue.