The Enterprise and the Klingon Battle Cruiser

A Klingon Battle Cruiser is equiped with a disruptor cannon mounted on its rear end which can only fire perpendicularly to its direction of motion. A standard Klingon tactic is to fly by its enemy and fire this cannon as the front end of the Battle Cruiser passes the enemy ship's rear end. In the following discussion, assume that the Battle Cruiser flies by so closely that you can neglect the time it takes for the disruptor beam to travel from the cannon to the target.

The Starship Enterprise, which is the same length as the Battle Cruiser when both are at rest, is about to be attacked. Dr. McCoy is worried that, due to Lorentz contraction, the Klingon Battle Cruiser will be shorter than the Enterprise and therefore cannot miss. Captain Kirk, on the other hand, claims that the Enterprise will be shorter than the Battle Cruiser when seen from the Klingons' frame so that there is nothing to worry about.

Kirk : It's them that's doing the shooting so it's their frame of reference that matters.
McCoy : Damn it Jim! We're the ones getting shot at. It's our frame of reference that matters!

You, Mr. Spock, must calmly draw a space-time diagram and explain to them which of them is right.

McCoy : Spock! Are you out of your Vulcan mind? We're about to die! And you find nothing better to do than to draw pictures?
Spock : Doctor, I assure you that I am doing the best I can under the circumstance.

Answer the following questions:

1. At which space-time point labeled A through H, does the front end of the Battle Cruiser pass by the rear end of the Enterprise?
2. As the front end of the Battle Cruiser passes by the rear end of the Enterprise, at which space-time point is the rear end of the Battle Cruiser in the Enterprise's frame?
3. As the front end of the Battle Cruiser passes by the rear end of the Enterprise, at which space-time point is the front end of the Enterprise in the Battle Cruiser's frame?
4. At which space-time point does the disruptor cannon fire?
5. When the disruptor cannon fires, at which space-time point is the front end of the Battle Cruiser in the Enterprise frame?
6. Explain to Captain Kirk and Dr. McCoy which of them is correct. Refer to the space-time diagram in your explanation.