Westernmost point of Alaska is in the Aleutian islands, 51~53 degrees latitude. If you maintain a heading of due east you won’t hit any other US state.
However, that path would require you consistently curve left a bit to stay on that line. the only line of latitude that’s a great circle is the equator. If you start somewhere else, facing due east, and don’t turn as you travel, you’ll cross the equator when you’re 1/4 the way around the planet, and be at the same latitude in the opposite hemisphere when you’re halfway around the planet(at that point you’d be facing East again)
Get a ball and a couple rubber bands that can fit on it, put one on so it divides the ball in half, this is the equator, now start the second rubber band higher up, and parallel, like you were at Alaska and going East, now continue that path such that it divides the ball in half again.
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