Solving Spacetime Diagram Homework: Ship Reversal from Cape Canaveral

[bowlbase]

Homework Statement

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
Canaveral.

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.

 

[BruceW]

yep. That sounds right to me. and sorry, I don't know of any websites like that. Maybe there is something useful in the math & science learning materials section of physicsforums.

edit: be careful with the units that you are using though. when you say x=2, there should be units with this.

 

[bowlbase]

Thank you, for all of our problems we're using arbitrary units.

Thanks again for the help.

 

[BruceW]

ah cool. No worries :)

 

[paranormal]

I would approach this problem by first considering the concept of spacetime diagrams and how they represent the motion of objects in space and time. In this case, the ship's worldline would be a straight line with a slope of 3/2, as you mentioned. However, when the ship reaches the satellite and engages its Magic Hyperdrive, its worldline would not simply reverse direction and continue in a straight line. Instead, it would experience a discontinuity in its worldline, as it would instantaneously change direction and velocity. This would result in a "kink" in the worldline, where the ship's velocity suddenly changes from 2/3c to 1/3c.

In terms of how this would appear on the spacetime diagram from Cape Canaveral's perspective, the vertical line representing Cape Canaveral would remain the same, but the ship's worldline would now have a slope of -3/1 as it heads back towards the Cape. The kink in the worldline would represent the moment of the instantaneous reversal.

In terms of resources for practicing these types of problems, I would recommend looking into textbooks or online resources on special relativity, as well as solving problems from past exams or assignments from courses on this topic. Additionally, there are several simulation tools available online that allow you to plot spacetime diagrams and experiment with different scenarios, which could be helpful for understanding the concept visually.