What does it means to say two events are simultaneously observed?

[Fewmet]

This is not homework problem, but I am using a problem from Elementary Modern Physics by Weidner and Sells as context for my question. It reads
"A star is moving away from the Earth at 0.60c as measured in inertial system S, at rest with respect to the earth. At time t=0, when the star is 1.0 x 10⁹ light years (ly) away, the two following events occur simultaneously as observed in S: (1) a bomb explodes nearby on earth; (2) a bomb explodes on the moving star.

"Give the space and time coordinates for events 1 and 2 in S', at rest with respect to the star..."

I know the mechanics of solving the problem correctly, but I wonder about the language. Does this mean that light from both explosions enters the eyes of the observer in S at the same instant? Or does it mean that the observer sees light of the explosion on Earth and then 1 billion years later sees light from the bomb on the star and calculates that the two explosion were simultaneous?

 

[Timo]

It means that in the coordinate system S both events have the same time coordinate; the second of the two options you propose. Your first option would additionally depend on the location of the observer, which is not given.

 

[Fewmet]

It means that in the coordinate system S both events have the same time coordinate; the second of the two options you propose. Your first option would additionally depend on the location of the observer, which is not given.

Thanks, Timo.

I'm not trying to be picky, but your last sentence makes me think I might be missing something. Don't both depend on the location of the observer in S?

 

[Timo]

Unless I am mistaken somewhere the 2nd case should depend only on the observer's velocity (which is dictated by S), but not on his position. There's a lot of possible ways to explain that, but I guess with the emphasis on "depends on velocity, not on position" you should be able to make up your own explanation, which is probably preferable over me picking one that I consider appropriate.