ShreyasR, I'm going to draw some spacetime diagrams to illustrate a scenario similar to the one you proposed. In your scenario, you had A remaining stationary while B traveled away and back at 2.8x10^8 m/s which is about 0.933c. You stated that B would come back to find that A had aged by 10 years and B would age about 1 year. In fact, at that speed, B would age 3.59 years. So I want to change B's speed to 0.96c because that will make the drawing easier to make and understand since the Relativistic Doppler factor is exactly 7.
Here is the first diagram for the Inertial Reference Frame (IRF) in which A remains at rest:
Please note that B ages by exactly 1.4 years at the point of his turnaround and then ages another 1.4 years for a total age gain of 2.8 years compared to A's 10 years.
Now you also suggested a different IRF in which a 3rd person C remains at rest while A and B start off traveling away from him at the same speed in opposite directions. That speed would be 0.75c and here is a diagram showing that:
Now you will quickly see what was brought to your attention in earlier posts that C does not remain equidistant from A and B.
Finally, I want to show you how A can use radar to measure B's trajectory. I added in three radar signals in green, red and orange to the first diagram:
Remember, A cannot see B as we see him on the diagram. A needs to wait for the image of B at each different location to propagate to him. So when A sends out a radar signal, he has to wait the entire time before the return signal comes back to him.
His first radar signal shown in green is sent at 0.1 years into the mission and he receives the return signal at his time of 4.9 years. Note how the signal propagates along diagonal lines of exactly 45 degrees. The calculation that A does is simple. He first figures out how much time progressed between sending and receiving the radar signals. That's just the difference between the emit and return times or 4.8 years. He divides this time in half to get 2.4 years which tells him that A was 2.4 light-years away, but when?. For that, he takes the average of the two times, which is the midpoint of the interval, to get 2.5 years. This tells him that when his clock was at 2.5 years, B was 2.4 light-years away from him. You can confirm this on the diagram.
The red radar signal was sent at 0.2 years and received at 9.8 years so he concludes that B was located 9.6/2 or 4.8 light-years away at his time of 5 years.
The orange radar signal was sent at 5.1 years and received at 9.9 years so he concludes that B was located 4.8/2 or 2.4 light-years away at his time of 7.5 years.
Obviously, I hand-picked these three particular measurements because they were easy to make and illustrate on the diagram. Twin A would likely be sending out a new radar signal at a repetitive interval such as every 0.1 years but this would merely fill in more points along B's path.
You can also use the second spacetime diagram to calculate the same radar measurements. I would suggest that you copy the diagrams and paste them into Paint documents so you can add your own radar signal paths along 45-degree trajectories.
After you get proficient at determining the location of B as a function of A's time in either IRF diagram, you can use the same process to calculate A's location as a function of B's time. This will be a little more challenging but it will be worth it for you to do it. You asked us in post #9 to tabulate this kind of information but now that I have shown you how to do it, I'm asking you to do it yourself. If you need help or have any questions, just ask.
