With both their clocks synced at 00:00 (12 AM), spaceships A and B leave earth in oposite directions, each at 17308257.5 m/sec (.57735027c), So the Lorentz factor of their relative velocity 259627884.49 m/sec (.866025404c) is 2. They travel in opposite directions at this velocity for 2 hours by their own clocks. At which point each (somehow) stops and reverses course at this same velocity. Looking through a powerful telescope and allowing for c, A should see that it's 1 AM on B's clock, and B that it's 1 AM on A's. So for A's next hour, from her frame of ref, she's traveling in the same direction as B. And for B's next hour, she's traveling in the same direction as A. I.e., for the next hour each sees the other traveling away from earth while they are traveling towards it. So their relative velocity is now zero and each should see the other's clock to go from 1 AM to 2 AM while theirs goes from 2 AM to 3 AM. Then, in A's next hour, when they are traveling towards each other at a relative velocity of .866025404c (for Lorentz factor of 2), her clock will run to 4 AM, at which time she will be back at earth. And vice versa. However, wouldn't each, during their final hour see (through that super powerful telescope) the other's clock run from 2 AM to 2:30 AM? I'm having trouble getting them both back at the same time, despite their completely symmetrical trips.