I didn't downvote you. Anyway, one degree of a broom handle would be miniscule but one degree longitude of the earth is about 70 miles so there should be quite an arc shouldn't there?
70 miles seems about the limit of length of a contrail I could see.
The earth curves about 1 degree in 70 miles.
A contrail of a plane at constant altitude above the ground would likewise curve about 1 degree in 70 miles.
You see the contrail from the edge, like the broomstick from the edge.
If you want to see very small curves (and 1 degree is small) people usually need to look down the length of the item.
Here's a video which seems to go over most of the issues with airplanes. It gives some details about the emergency landing in Alaska. It took off from Taiwan (more south than Tokyo). However, there is no indication that the flight path was the line on a FE map - it appears to be a great circle.
The video claims that when the emergency happened (woman gave birth) Alaska was the closest landing and much closer than Los Angeles. I don't know if that's exactly correct, but the emergency certainly had nothing to do with airplane functionality and Alaska may have been the best place to land for other reasons (airport with sufficient runway*, airline hub, medical facilities).
*An aircraft can land at a lot of places in an emergency. I remember a few years back when a large passenger aircraft landed at a small regional airport near me. It needed to land and didn't have a choice. But getting it out of that airport was a problem. Had to take off unloaded with just the pilots, and still needed an FAA exemption (runway too short). This sort of takeoff is risky because at a small airport they don't have the runway length for a large aircraft to abort if an engine goes out or other problems. They don't land an airplane at an airport without enough takeoff runway (for that aircraft), if they can avoid it.
I'm also aware of airline management insisting on flying to a hub despite an emergency warranting landing at a closer airport. Because $$$.