Having flown in airplanes quite a few times (several times overseas too, a flight to Korea once took 14 hours bleh), and being scared of heights myself, I have to say that it wasn't easy for me.
While I'm not to the point of refusing to get on a plane, I do feel a lot of anxiety until we're at the flight altitude. I usually just bypass this by thinking about a lot of different things, or the feelings I'm currently going through. For instance, when I first left Korea to go home on leave after being there for 8 months, I kept thinking about how nice it would be to be back in the US. And I joked to myself and others about how I was going to kiss the ground once I got to LAX in Los Angeles. Sure enough, I almost did lol, and thinking about that stuff got me through the scariest part for me, the takeoff. But I have to admit, it was kind of nice seeing myself leave Korea (it was okay for me, but not knowing the language kind of sucked for going out and meeting hot girls lol

).
As you can see, just think about different stuff, and try not to think about the fact that you're flying. If nothing else, just arrive at the airplane tired, and then take a nap ASAP. Before long, you'll forget you're even flying, and it'll feel like a long bus ride or something (so long as you're not constantly looking out the window), and think instead of how cramped it is in the plane, and how you can't wait to get off and stretch hehe.
And since you're going to Japan, hope you don't see Godzilla down there, unless he's fighting another monster

. The Japanese military sucks when fighting Godzilla, unless they're helping him fight an alien monster hehe. Just think about anything else, and before long, you'll be back on the ground in your destination.
Jam it back in, in the dark.