So, many of the time dilation thought experiments have periods of accelerating away from the origin, stopping, turning around, and returning, which precipitates an observable time differential between the traveler and those remaining behind.
- Is there a requirement that the path be straight line?
- Is is possible to accelerate to almost the speed of light (or a large fraction thereof) along a curved path (say a circle or ellipse) rather than "out and back"?
I'm happy to put aside the realities of the movement of the universe (the planet won't be in the same place to return to later on) for this thought experiment insofar as it simplifies the question.
My intuition says it must be straight, but I cannot articulate why, my physics is rusty.