Question

You are flying your personal rocket craft at $0.90c$from Star $A$toward Star $B.$ The distance between the stars, in the stars’ reference frame, is $1.0ly.$ Both stars happen to explode simultaneously in your reference frame at the instant you are exactly halfway between them. Do you see the flashes simultaneously? If not, which do you see first, and what is the time difference between the two?

Short answer

$1.)$I am at rest in my frame.

$2.)$The explosions are about the same distance apart.

$3.)$The speed of light is $c,$all light will arrive at the same time.

Step-by-step solution

Given Information

We have given that,

You are flying your personal rocket craft at $0.90c$from Star $A$toward Star $B.$

The distance between the stars, in the stars’ reference frame, is $1.0ly.$

Simply

$0.90c$from Star $A$toward Star $B,$and the distance between the stars is $1.0ly.$

Star $A$is moving away from me and Star $B$is moving toward me in my frame.

Both stars erupt at the same time when I am exactly halfway between them.

The flashes from the two stars travel toward me with speed $c.$Since,

$1.)$I am at rest in my frame.

$2.)$The explosions are about the same distance apart.

$3.)$The speed of light is $c,$all light will arrive at the same time.