At time t = 0, a spaceship leaves Cape
Canaveral (x = 0) at speed 2/3c, heading
directly upwards (+x direction) toward a
satellite in orbit. The satellite is located a
distance 2 AU (see footnote2 if you forget
what that is) above the earth’s surface.
When the ship reaches the satellite, it
engages its Magic Hyperdrive to instantly
reverse course, and head back toward Cape
Canaveral at speed 1/3c.
Plot the worldlines of the ship and of Cape
Canaveral itself, both as seen from Cape
The Attempt at a Solution
My question is primarily for the "instant reversal" of the ship. I believe that the world line for Cape Canaveral will be exactly vertical and the ship will have a straight line with a slope of 3/2 terminating at x=2. At x=2 it goes in reverse but I'm not sure how this would look in the Cape's frame. Will the line of the ship then go left with a slope of -3/1 until it intersects with the Cape's vertical line? Or is there some other path?
Also, if anyone knows of a website or downloadable pdf that has example problems of these types of problems I'd love to see it/them.
Thanks for the help.