A rocket is traveling at (1/3)c relative to Earth when a lightbulb in the center

Question

A rocket is traveling at (1/3)c relative to Earth when a lightbulb in the center of a cubical room is suddenly turned on. An astronaut at rest in the rocket and a person at rest on Earth both observe the light hit opposite walls of the room. Call these Events A and B. Which statement (statements) is (are) accurate concerning the observation?

The correct answers are B and C, so E, but I am having a hard time understanding this.

I've seen the explanation, "The bulb and the astronaut are in the same frame of reference, so to him, both events are happening at the same time. But for the observer on Earth, B happens first because the rocket is traveling in the direction from B to A."

Can someone really break this down for me please? I'm not understanding how the bulb and astronaut are in the same frame of reference or why the observer on earth sees these events at two different times.

Thank you in advance!

A) To the observer on Earth, both events happen at the same time. B) To the astronaut in the rocket, both events happen at the same time. C) To the observer on Earth, Event B happens before Event A. D) To the astronaut in the rocket, Event A happens after Event B. E) More than one of the above statements are accurate. 3 3

Explanation / Answer

The bulb and the astronaut are in the same frame of reference because the cubicle is in the rocket only.

The observer on Earth see the events in a different fashion:
The observer standing on the Earth, on the other hand, sees the rear of the rocket moving (catching up) toward the point at which the bulb flash was given off and the front of the rocket moving away from it. As the speed of light is finite and the same in all directions for all observers, the light headed for the back of the rocket will have less distance to cover than the light headed for the front. Thus, the flashes of light from bulb will strike the ends of the traincar at different times.

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